B Bhanu ââåautomatic Target Recognition State of the Art Surveyã¢ââ

• Loading metrics

Open Access

Peer-reviewed

Inquiry Article

Automatic Target Recognition Based on Cross-Plot

• Derek Abbott

Automated Target Recognition Based on Cantankerous-Plot

• Kelvin Kian Loong Wong,
• Derek Abbott

x

• Published: September 29, 2011
• https://doi.org/x.1371/journal.pone.0025621

Figures

Abstract

Automated target recognition that relies on rapid feature extraction of real-time target from photo-realistic imaging will enable efficient identification of target patterns. To attain this objective, Cantankerous-plots of binary patterns are explored as potential signatures for the observed target by high-speed capture of the crucial spatial features using minimal computational resources. Target recognition was implemented based on the proposed design recognition concept and tested rigorously for its precision and think operation. We conclude that Cross-plotting is able to produce a digital fingerprint of a target that correlates efficiently and effectively to signatures of patterns having its identity in a target repository.

Citation: Wong KKL, Abbott D (2011) Automated Target Recognition Based on Cross-Plot. PLoS Ane half dozen(nine): e25621. https://doi.org/x.1371/journal.pone.0025621

Editor: Teresa Serrano-Gotarredona, National Microminiaturization Center, Spain

Received: April nine, 2011; Accepted: September 8, 2011; Published: September 29, 2011

Copyright: © 2011 Wong, Abbott. This is an open-access article distributed nether the terms of the Artistic Commons Attribution License, which permits unrestricted employ, distribution, and reproduction in any medium, provided the original writer and source are credited.

Funding: The authors accept no support or funding to report.

Competing interests: The authors take declared that no competing interests exist.

Introduction

1.one Automated Target Recognition

Automatic target recognition (ATR) is a technology that can isolate a target from a noisy background and perform classification of the object [one]. A reliable computerized blueprint recognition system is crucial for image assay especially when images are registered at rates higher than human-assisted visual review processes. For such applications, the time-disquisitional identification of targets that are caused by an imaging modality is vital.

The involvement and research in ATR technology has resulted in the development of diverse systems for identification of targets over the past few decades. Utilization of the sophisticated synthetic aperture radar (SAR) to collect information on target vehicles may exist deployed [two]. An airborne SAR takes radar soundings from the basis forth a precisely measured flight path and then separates the various target locations by sophisticated signal processing. This allows the formation of extremely detailed fine-resolution maps of radar-reflectivity of a target scene. The SAR prototype data is analyzed for feature modeling. Each target paradigm has its own unique signature for utilise in ATR algorithms.

Concepts in designing and implementing ATR algorithms include signal and image processing, target detection, isolation and sectionalisation, movement analysis and tracking, statistical or model-based recognition, and signature modeling. An ideal shape pattern recognition system has an inbuilt identification algorithm that can fully recognize targets without human intervention and with low simulated warning rates [1]. This performance is required to be relatively robust to sensor dissonance and target orientation. The issues in existing methods are the heavy computational overhead in identifying targets rapidly, while taking into account all the filtering and pattern normalization procedures.

In ATR systems, the central operational procedures are target detection, discrimination and recognition, and performance assessment. In this paper, the emphasis is on the second and third procedures. The aim is to reduce computational expense for this purpose, and the objective is to develop an operational system that addresses this issue when predicting target identity. Here, the Cross-plot [three], [4], [five] is proposed to address the same problems in pattern recognition and to identify the target of interest. This study highlights the conceptual development of the technique and performs proof-of-concept experiments.

1.2 Feature Extraction and Classification

Nosotros can identify two binary objects according to the deviation between their features. In pattern recognition, features are extracted from a target prototype containing distinctive information.

Choosing discriminating and independent features is the fundamental to any successful blueprint recognition system. It is unremarkably difficult to guess a registered object of interest by acquiring raw data related to it as the recorded data is usually noisy. Therefore, the raw data must be transformed into a reduced set of features to be used by the classifier. A process of mapping the original measurements into more effective features is generally known as characteristic pick or extraction (Figure 1). The low dimensional features incorporate sufficient relevant data to avoid the trouble of classifier over fitting.

Figure 1. Operational stages of a pattern recognition system.

The period chart of recognition processes tin be illustrated using four simple stages: registration of data, extraction of the target's features, classification, and decision making. The feature extracted from the registered data is fed into a classifier, which tin can exist based on Cross-plot, artificial neural network or Bayesian network, for target object classification. The accuracy of identification is dependent on the quality of features beingness extracted. Finally a decision is made based on the classified results that will lead to the identification of the interested target.

https://doi.org/10.1371/periodical.pone.0025621.g001

For a given prepare of signal features that have been extracted, an advisable classifier needs to be trained by utilizing part of the data and the known corresponding labels for fitting data into feature space. Specifically, the grooming data is used to populate the hypothesized clusters of the training data, and the congenital clusters can represent the classes in the feature space. Typically, the data is divided into two parts: 1 for training and the other for testing in order to verify the nomenclature adequacy. Generally, it is causeless that the grooming and testing data accept similar properties and distribution, which is a pre-condition of feasibility in nomenclature.

ane.3 Shape-Based Image Retrieval

Image-based target recognition has been developing rapidly in by decades. Shape-based image retrieval [vi], [seven], [8] is one of the virtually popular methods and inspires the proposed Cross-plot technique. The shape-based prototype technique lies inside the shape assay and characteristic extraction paradigm. In shape assay, complex spatial features of binary images are represented using their linear approximations, and easing the computational burden for carrying out matches between spatial objects. Shape pattern representation techniques can be divided into two categories, namely, the boundary-based and region-based methods [ix]. Both methodologies tin be further sub-categorized as the transform and spatial (geometric) domains, depending on whether direct measurements of the shape are used or a transformation is applied [10]. Characteristic extraction is the process of gaining geometrical information from a shape that has the location, scale and rotational effects filtered out from information technology. The resulting feature vector will exist a design representation of an exact geometry of the spatial object. Shape-based retrieval takes into consideration issues such every bit robustness and stability of the various shape representation techniques. Successful retrieval systems accept expert matching abilities for shape objects that are subjected to distortion, scaling, translation, noise, and region loss when using the aforementioned feature set. Therefore, the selection of a characteristic extraction technique is disquisitional for achieving loftier recognition functioning [11].

1.3.1 Region-based Methods.

Region-based techniques extract information regarding the internals of the shape besides the boundary details. Some of the more than established methods utilizes the Zernike [12], pseudo-Zernike moments and wavelet moment invariants [thirteen]. Transform-based methods encompass the Hough transform and spatial-based methods have into account geometrical measurements of the shape's central characteristics. Shape-based image retrieval is performed using a characteristic vector comprising of the solidity (South), eccentricity (C), and extent (X) of shapes, which form the SCX feature set up [14]. The choice of these shape measures is not a conditional necessity. There are many other features such as shape firmness, aspect ratio, holes, rectangularity, max-min radii, elongation, symmetry, circularity, and Euler number that can be used [10]. The Query By Epitome Content (QBIC) system by International Business Machine (IBM) uses statistical features to represent the object shape [15]. Its characteristic set includes area, circularity, eccentricity, major axis orientation, and algebraic moment invariants. The Hough transform [16] has been extensively used for shape detection and recognition. Specific requirements of geometric invariance, storage and computational complexity, also equally support of appropriate similarity measures are considered.

1.3.two Purlieus-based Methods.

In boundary-based image retrieval, methods using chain codes [17], [18], [xix], polygonal approximations [xx], Delaunay triangulation [21], Fourier descriptors [9], [22], [23], [24], purlieus moment invariants [15], [21], [25], and two-dimensional (2D) strings [26] can exist deployed. Boundary-based epitome retrieval uses but the contour of the object shape and ignores the region in the interior. The System for Trademark Archival and Retrieval (STAR) [27], [28] uses features based on invariant moments and Fourier descriptors extracted from manually isolated objects. A spatial-based object retrieval technique that is a sub-category of the boundary-based methods such every bit the Touch on-Indicate-Vertex-Angle-Sequence (TPVAS), Bounding Circles (MBC) and Angle-Sequences (AS). A retrieval compages based on MBC utilizes three different structures on features that are extracted from the objects' MBC. The Hausdorff distance between planar sets of points is known to exist an effective measure for determining the degree of resemblance between binary shape patterns [29], [thirty]. For chain codes, the boundary of a binary paradigm is traversed and a cord representing the curvature is constructed. A shape tin can be converted into chain information representing the boundary. Transformation-based approaches can exist further broken down into 2 sub-categories: functional and structural [31]. Functional transformations such equally Fourier descriptors to structural transformations, such every bit chain codes and curvature scale infinite feature vectors, comprise some of the transform-based methods. A comparison of the operation for Fourier descriptors, concatenation codes, Delaunay triangulation, and TPVAS that are used in shape representation and retrieval of scaled, rotated and translated shape pattern variants is studied [10]. Pattern recognition based on shape context relies on the normalized spatial distribution of landmark coordinates from shape contours [xi], [30], [32], [33]. For this method, the shape of an object is essentially captured past a finite subset of its points. Distribution of shape part is based on a reference point relative to it, thus offering a global discriminative characterization [34]. However, some issues exist such that the reference points taken on a discontinuous profile of an incomplete shape with meaning loss of regions may result in poor same characterization. Other techniques such as the inner-altitude, which is divers as length of the shortest path betwixt landmark points within the shape silhouette, can exist incorporated into shape context and is specialized to identify contrast in patterns that may be similar in spatial distribution but dissimilar in part structures [35], [36]. Moreover, shapes parts may be asunder and renders the inner-distance method unreliable. As a result, identification of region-loss shapes will non be optimal as their correlation indices will be highly different.

i.iv Cross-plot Based Target Recognition

One of the of import breakthroughs in the early on work of computer vision research is the recognition of a two-dimensional pattern as a perspective view of the 3-dimensional scene of objects [32]. From the technical viewpoint, capturing the silhouette of the object every bit a shape pattern and generating its Cross-plots unique to that pattern tin be accomplished. At the present stage, the notable concept is the introduction of strategically positioned reference nodes, thereby generating Cantankerous-plots of each of the individual node and the feature points representing the target design. This modification contributes significantly to the success of the technique in recognizing binary silhouettes of visually captured air targets. Cross-plot signature generation satisfies the characteristics of automatic target recognition. Performance verification was carried out by assessing the robustness of target recognition to lacking imaging based on a catalogue of patterns with incremental degrees of deviations (Appendix S1). Performance calibration is based on a repository of target images (Appendix S2) and arrangement validation is achieved by real-time air target recognition from a documented video database.

It is impractical to excerpt every single characteristic of a target design with high precision while ignoring the dissonance in the background. As such, only the vital features of a design should be selected for the signature design in order to accomplish an constructive pattern differentiation. The proposed technique is able to excerpt the significant shape content of the pattern for signature formation with minimum pre-processing of the image and no prior normalization of the target size. Details of the proposed technique based on this Cross-plot concept are shown in the post-obit sections.

Methods

2.one Definition of Cantankerous-plot

We briefly introduce the cadre mathematics related to the proposed Cantankerous-plot signature generation technique. The Hausdorff fractal dimension [37] is the fundamental Cross-plotting. Denote D equally the fractal in a state space for a given pattern of points. The infinite is divided into grid cells of dimension r. Here, N(r) denotes the number of cells that are penetrated by a specific set of points. The box-counting fractal dimension D of a fractal, by counting the number of cells that contain one or more of its points, is given by (ane)

The Cross-plot [4] is a graphical representation of the Hausdorff fractal dimension, and is defined every bit a plot of the logarithm of the number of pixel object pair counts that do not exceed a specified proximity altitude versus the logarithm of this variable proximity distance. More formally, the Cantankerous-plot between two binary pattern data sets A (with Due north_A pixel points) and B (with N_B pixel points) is (2) where N _A,B(r) is the count of pixel object pairs inside a altitude r. The specified proximity distance tin can exist normalized by dividing the distance r with the maximum object pair altitude.

ii.2 Features by Cross-plotting

Cross-plots are generally used to place interesting patterns in complex information sets. The notion of the Cross-plot is defined in terms of relative distance betwixt ii types of point sets. The objective is to excerpt the location information about the pattern by judiciously placing reference nodes around the data prepare and computing the Cross-plots with respect to these node points one at a time. The Cross-plot curves tin exist presented in the same signature graph. This section demonstrates that Cross-plot of different binary target characteristic sets results in singled-out signature graphs and has the potential to be used for blueprint recognition.

To simplify the assay, an arbitrary number of eight reference node points are positioned around the binary blueprint image in a circular manner. The radius of this circular organisation is taken equally the altitude from the middle of the boundary, encapsulating the binary target to any one corner of it. Cross-plots tin can be created with an arbitrary number of coordinates depending on the resolution. In all the examples, an arbitrary resolution of thirty-one coordinates is fixed for each curve in the family of Cross-plots. Notation that dist denotes the altitude betwixt two data points; and count-of-pairs is the number of betoken-to-point pairs that are equal or smaller than dist. A description of Cross-plot generation tin can be found from steps 1 to 3 in Section 3.1 and the detailed pseudo-code tin exist referenced from Appendix S3.

Each curve of the prepare of Cross-plots demonstrates registration of feature indicate counts through the circular blueprint in the region just earlier the plateau of a Cross-plot bend. The plateau region is the location where no new information points are accumulated after the expanding radius reaches the end of the data blueprint. The growth in the aggregating of points decelerates sometime after the middle of the design – the count rate of feature points representing the pattern encapsulated by the purlieus extended from a node of interest decreases.

Every unique pattern will yield a unique set of curves for Cantankerous-plots of the pattern with nodes positioned around information technology. Therefore, a set of curves for a particular binary image representing a target tin can exist used as the signature or thumbprint of that object. Figure ii gives some examples of the Cross-plots corresponding to three capricious binary targets.

Figure 2. Effect of pattern target variants on Cross-plots based signatures.

Images (a, c, due east) are three different binary patterns with 8 reference nodes positioned effectually their feature point data sets; and (b, d, f) are their respective Cross-plot signatures respectively. Binary images of a silhouette target that are generated from acquired images with variations in target roll, pitch and yaw (from a two-dimensional visual perspective) are presented in (g, i, m). The images (h, j, l) bear witness the Cross-plots of binary patterns.

https://doi.org/10.1371/periodical.pone.0025621.g002

For a corresponding Cantankerous-plot signature, at that place are an arbitrary number of viii graphs based on number of reference nodes (N = 8) that are all superimposed onto a single set of axes. Each node point is able to capture the details of the pattern from a different spatial perspective. The placements of nodes effectually the blueprint result in the curves represented past a family of plots. Note that the chain of reference nodes is superimposed onto a bounding square box, which may non signal the minimum encapsulation of the target silhouette.

The technique of characterizing patterns in a data set by using Cantankerous-plots has been previously studied [5]. In an try to detect cluster locations for a given geometrical pattern through Cross-plot analysis, sure interesting observations accept been fabricated. Cantankerous-plots of different patterns (with every reference node point) volition yield curves with varying curvature depending on the distribution of the data ready under specific configurations. For instance, the number of plateaus is related to the number of clusters in the information set. Based on such observation, the uniqueness of the Cross-plot that is obtained for every specific pattern and node is dependent on the characteristics of the data set.

The unique features of a particular shape can be extracted by computing a fix of Cantankerous-plots based on a set of reference nodes with the shape design and representing them simultaneously using the same graph. Every unique pattern will result in a set of Cross-plots that draw the pattern characteristics. Despite that, it may be possible for corresponding sets of Cross-plots to exist identical even based on different shapes, and resulting in a incorrect identification. This problem can be solved by designing a new organization of node points spatially.

2.3 Identification Metric

Detection and identification of a target is based on the outcome of comparison or similarity between signatures. The signatures of some images of the observed target and the reference target have a stiff correlation due to the loftier similarity in their family of Cross-plots. Awarding of the algorithm will output the shape contrast index. A high correlation means a successful match and the identity of the reference target is reported.

The similarity metric is commonly defined via a altitude measure that volition be used for a nearest neighbor friction match in the feature space. Various dissimilarity measures such as the Minkowski or L_λ metric [38], the Cosine metric [39], and the Hellinger metric [40] can exist used in matching two sets of data points. The Minkowski L_λ metric for the case of λ = 1 has been chosen for comparison of signatures as information technology is able to simply differentiate the dissimilarity of ii signatures effectively. The Shape Contrast Index (SCI) is merely the sum of all the Fifty_λ = 1 distances. It is inversely proportional to the similarity of the two patterns for shape comparison. With this similarity quantification, the proposed characteristic extraction technique is able to convert two-dimensional features into one-dimensional scalars for comparing.

2.4 Invariant Properties of Cross-plot

The Cantankerous-plots are generated from the binary pattern epitome. Therefore, the various distortions on the binary pattern prototype will affect the generated respective Cross-plots. Ideally, the binary pattern image is pre-processed from the original 2-dimensional image to reduce various distortions. Nevertheless, this is not always applied. This department discusses the effects of pattern deviations, which are sampled from the catalogue of images in Database B (Appendix S2), on the corresponding Cross-plots of target patterns.

two.4.1 Baloney.

This section describes how the shape distortion affects the Cantankerous-plots. Figure 3 shows three targets with the same structure only mapped onto different projections and their corresponding Cantankerous-plots. Assume the shape in Figure 3 (a) is the reference shape, target in iii (c) is spatially compressed to 75% of its original size in the horizontal orientation and target in 3 (e) is sheared vertically at an angle of 20°. As can be seen, the divergence between the binary patterns Figure 3 (a), (c) and (e) are detectable, however, the alter in their Cross-plots is small. The SCI of Cantankerous-plots for Figure 3 (b) with (d) and for Effigy 3 (b) with (f) are 10.3 and 15.6 respectively (Refer to Section 2.3 for the definition of identification metric used in hither). This shows the relatively low sensitivity of Cantankerous-plots to a certain level of shape baloney.

Figure 3. Issue of binary pattern with shape distortion and Cross-plots based signatures.

The graphs demonstrate that the variation of Cantankerous-plots can be attributed to the slight distortion in target patterns. The differences presented by the shape dissimilarity indices of these variants are relatively insignificant.

https://doi.org/10.1371/journal.pone.0025621.g003

2.4.2 Target Mirroring.

Generating Cross-plots using an encapsulation of nodes that are arranged uniformly around the pattern boundary results in graphical representation that are identical irrespective of the aforementioned target blueprint taken from different isometric views of the same visual plane. The sequence of nodes taken to generate Cross-plot curves is different for different views. Figure 4 demonstrates four symmetrical views (vertical and horizontal) of the same target and their corresponding Cross-plots.

Effigy iv. Effect of target orientation on Cross-plot based signatures.

Pattern images representing aircraft target silhouettes based on iv different views and their corresponding Cross-plots. The orientation of the target generates Cantankerous-plots with like curvatures but having different positions exist in the same signature gear up.

https://doi.org/10.1371/journal.pone.0025621.g004

Each reference node betoken that is Cantankerous-plotted with the pattern produces a curve (each existence represented by using a different symbol). Difference in arrangement of the blueprint with respect to a set of node points volition result in the aforementioned corresponding curve to be represented past different symbols. If the node at the nose of the shipping is taken as the start node point for Cross-plotting with the entire target design, the signatures produced from each of these node points will be like for all four target orientations. The SCI of Cantankerous-plots for side views 1 to 4 is derived to be 3.00. Every bit the number of node points in the circular encapsulation increases, the variation of angle of orientation of the pattern in affecting the signature decreases.

two.four.3 Target Pitching.

Dissimilar orientations of the three-dimensional object produce different orthographic views when they are superimposed onto a 2-dimensional visual plane during monitoring (Refer to Figure 5). Figure 5 (a, c) shows the corresponding signatures for images of the fighter jet pitched at 0° and Figure v (b, d) illustrates that for target silhouette pitched at 45°. For the case of side view of the target in Figure 5 (a, b), nosotros determine the boundary of nodes encapsulating the target blueprint using the Minimum Boundary Circumvolve (MBC) method [14]. The displacement in angular orientation of the object with respect to a specific axis results in the same graph that is represented by unlike ordering of symbol representing the nodes. Rotating the arrangement of the nodes using the aforementioned bending as the pitch of the shipping reduces deviation in its signature. The SCI of Cross-plots for Figure 5 (a) with (b) and for Figure 5 (c) with (d) are 7.1 and 6.ix respectively (Refer to Section 2.3 for the definition of identification metric used in here).

Effigy v. Effect of silhouette targets pitched at 0° and 45° on Cantankerous-plots based signatures.

The orientation of the target generates a dissimilar pattern based on its silhouette onto a two-dimensional plane. The signatures based on the Cross-plots that pertain to every target are shown to have modest variations.

https://doi.org/ten.1371/journal.pone.0025621.g005

two.4.4 Scaling.

The Cantankerous-plots retain their curvature integrity despite scaling of the resolution of the target pattern (Refer to Figure vi). The scaling for a typical image in multiples of two is performed in one case (Effigy half dozen (a, c)) and the corresponding Cross-plots are computed in Figure vi (b, d). The scaling of pattern resolution will crusade a very slight shift in the logarithmic altitude axis of the Cross-plots, without any change in their curvatures.

Figure 6. Consequence of scaling of shape pattern on Cross-plots based signatures.

The subfigures are as follows: (a) Binary paradigm at resolution of 128 by 128; (b) Cross-plots of binary image at resolution of 128 by 128; (c) Cantankerous-plots of binary paradigm at resolution of 128 by 128 with encapsulations spanned past distances that are normalized; (d) Binary image at resolution of 256 past 256 without normalized spanning distance; (e) Cantankerous-plots of binary image at resolution of 256 past 256 without normalized spanning altitude; (f) Cross-plots of binary image at resolution of 256 by 256 with encapsulations spanned past distances that are normalized.

https://doi.org/10.1371/periodical.pone.0025621.g006

The Cross-plot extracts information from the pattern such as the number of feature points in the data fix encapsulated by a radial purlieus, from a stationary reference node signal, in the two-dimensional Euclidean space. The number of points relative to the image size is similar for both resolutions, if twice the radial extension from the node is taken for the two times resolution image. Based on this observation, obtaining the signature of a pattern epitome at n times resolution tin can be accomplished by a shift of magnitude of log(n) for the logarithmic axes of the Cross-plots for the given i fourth dimension resolution binary pattern, instead of applying computationally expensive spatial quantization to the prototype before signature generation as shown in Figure 6 (c) and six (d). Normalization of the number of counts of the pixels and the radial scanning distances for whatever specified image resolution, every bit demonstrated in the Cantankerous-plot formula, is equivalent to a shift of the axes by log(n). Figures half-dozen (e) and half dozen (f) illustrate that Cross-plots for the aforementioned pattern of unlike dimensions will be similar after normalization. This is in dissimilarity to the Figures six (b) and (e), which stand for non-normalized count-of-pairs and radius spanned for the pixel counts.

2.4.5 Noise.

The main sources of degradation are sensor racket, and the scattering and attenuation of electromagnetic radiations by atmospheric particles in an intervening propagation medium, resulting in fuzzy target boundaries [41], [42]. This blazon of noise can touch the binary image blueprint profoundly. However, the dissonance on the binary image blueprint can be mitigated using the Cross-plot technique because the fine details tin be smoothed and then reduced in resolution.

For simplicity in our experiments, we generalize noise using a randomly generated normal distribution. The level of dissonance is denoted by the point-to-noise ratio (SNR), where the SNR is defined equally the contrast of object divided by the standard deviation of usually distributed random noise. The unit of this measurement is the decibel (dB). Figure 7 shows the Cross-plots of images with three dissimilar signal-to-racket ratio (SNR) levels. Figure 7 (a) is a binary image design without any racket; Effigy 7 (c) is a binary image pattern with SNR of 23 dB and the SNR in Effigy 7 (east) is 20 dB; Figure vii (b),(d),(f) are the corresponding Cross-plots of Figure 7 (a),(c),(eastward) respectively. As the SNR decreases, the possibility of correct target recognition decreases accordingly. Therefore, the level or threshold of SNR to which this technique is robust relates the accuracy of correct target recognition to be accomplished.

Effigy 7. Upshot of noise on Cross-plot based signatures.

(a) Binary pattern of target without racket; (c) Binary blueprint of target with SNR of 23dB; (e) Binary pattern of target with SNR at twenty dB; (b, d, f) are the Cross-plots of patterns from (a, c, e) respectively.

https://doi.org/10.1371/journal.pone.0025621.g007

2.iv.6 Part Discontinuities.

The beingness of astringent noise in an paradigm may result in the disconnection of the pattern into segments but with the overall shape being retained. The outcome of pattern truncation and segregation is investigated based on such a defect (Refer to Figure viii). Due to the overall statistical contribution of pixel counts from the complete regions of the design, the destruction of counts from the missing regions will not modify the general characteristic of the Cantankerous-plots. The aggregation of pixel counts for each scanning distance is affected slightly and retains much of the inherent pattern data. This can exist seen from the SCI of Cross-plots for 8 (b) with (d) that has a value of 3.20 (Refer to Section ii.3 for the definition of identification metric used in here).

Figure 8. Effect of pattern defects on Cross-plot based signatures.

Comparison of signatures (b,d) generated from clear (a) and noisy (c) images. The subfigures are as follows: (a) Binary pattern of target without region loss; (b) Cross-plots generated from pattern without region loss; (c) Segregated binary design of target due to region loss; (d) Cross-plots generated from segregated pattern due to region loss.

https://doi.org/10.1371/journal.pone.0025621.g008

2.5 Standardized Alignment of Targets

This section explores the concepts behind Singular Value Decomposition (SVD) [43], [44], [45] and demonstrates how SVD can be applied onto a pattern information set to enable mapping to a standard orientation. The consequence map can serve as a base pattern for all target variants of unlike orientation. The previous observations show that the Cross-plot signatures may take similar curvatures that are generated by nodes at dissimilar positions. To solve this problem, the concept of primary component analysis is applied. Figure 9 illustrates that the near prominent principal component tin serve as the directional alignment of the target and presents the reconstructed pattern along this component. The reconstructed targets for all the variants are identical and serve as the standard base pattern for which their signatures volition be generated for identification or database storage in the retrieval system.

Figure ix. Alignment of patterns along their about prominent principal components.

The above ascertainment demonstrates that all variants of targets at different orientations can be mapped onto a base pattern, which fulfills standardization of target alignment. This volition enable a standard fix of reference node points around the binary targets.

https://doi.org/10.1371/journal.pone.0025621.g009

2.6 Verification based on Blueprint Variants

To quantify the degree of variation in shape and size, images of binary patterns in Appendix S1 illustrates various degrees of structural and dimensional distortions. Figure ten presents some of these deviations from the original pattern and their corresponding SCIs. Under each category of pattern deviation, the SCI of corresponding modified binary image is computed and compared. The start image along horizontal centrality in each subfigure is the original pattern image (or reference epitome). The values on the vertical axis are the SCIs of their corresponding images. The system quantifies the degree of blueprint variation when correlated with a standard model, i.e. acme view capture of a target that is the start pattern on the left of the images. The degree of contrast varies incrementally as the variant patterns distortions amplify in incremental stages. This allows the model to detect the degree of dissimilarity for the input pattern variant as it varies with the level of distortion or orientation.

Effigy 10. Measurement of shape contrast based on its pattern variations.

The sub-figures that represent Shape Contrast Index (SCI) variations of pattern variants with respect to a reference pattern are equally follows: (a) Correlation of distorted variants; (b) Correlation of pixel-lost variants; (c) Correlation of scaled variants; (d) Correlation of blurred variants; (e) Correlation of rotated variants (rotation in a two-dimensional plane virtually an centrality); (f) Correlation of disoriented variants (target displacement about gyre centrality in three-dimensions and captured as a binary image from a two-dimensional perspective).

https://doi.org/10.1371/journal.pone.0025621.g010

The effect of horizontal distortion is investigated (Effigy 10 (a)). The images post-obit reference image are horizontally compressed with a step 5%. In Figure ten (b), the effect of pixel loss is investigated. The pixel loss is performed by handful random white pixels on the pattern image. In this simulation, it is to add noise to the image pixel. For the successive images following the reference image, the noise is increased by 0.four dB for each image. In Figure 10 (c), scaling is performed by decreasing the size of both vertical and spatial dimensions by an interval of 10% for each step. In Figure 10 (d), the result of blurring is achieved in the spatial domain by pixel averaging in a neighborhood which is known as sharpening in term of epitome processing [46]. The degree of sharpness changes with the radius of the neighborhood to be averaged. Images shown in Figure 10 (d) are 256 by 256 pixels. The sharpness of the successive images post-obit the reference image is adjusted based on the change of sharpening radius with an increment by ii% of the paradigm width. In Effigy 10 (e), each image after reference image is clockwise rotated on the same airplane at athwart increment of 36°. In 10 (f), the target is rotated along its roll centrality with an angular displacement of 20° on a single plane. Note that this fix of images based on 3-dimensional rotations is from Dassault Aviation [47].

The SCI indicator of the query patterns is affected by increasing scales of distortions for shape object changes based on a set of ten frames. The effectiveness of the shape-based representation model tin can be gauged by its recognition of variant patterns based on a different geometric feature for each target ready. The whole procedure shows that nether a controlled experimental setup, the increase in the SCI value corresponds to an increment in the variation of the reference target pattern. The smoothness of the correlation bend demonstrates the sensitivity of the model when responding to incremental modification for variant geometrical patterns.

Results

3.1 System Methodology

A computational prototype of the automatic target recognition (ATR) methodology based on the proposed Cantankerous-plot technique is developed. This section provides the details of the system that is implemented to match a target signature to an identical one in the database. For an appropriately tested user-defined number of node points and resolution of the Cross-plot signature, target identification based on a repository of 60 targets in real time is reliable and doable inside fourth dimension in the social club of milliseconds.

To generate the signature of the target, the raw prototype must be pre-processed to remove noise and to segment all the objects in the image for identification. The outline of the target, in terms of structural details in the image, has to exist extracted accurately. The following procedures provide the guidelines for image preprocessing. For preprocessing of images of targets with distinct demonstrated features, the image is converted into a binary grade through amplitude quantization. For 2nd feature space, such as an image, the process of representing the amplitude of the 2d bespeak at a given coordinate as an integer value with L different grey levels is usually referred to every bit amplitude quantization or simply quantization. The effectiveness in capturing the silhouette of the aircraft for images depicting a target with an evenly shaded interior and a background that differs in dissimilarity to a specified degree varies.

To excerpt the targets from low contrast images where the gradient magnitude of the target and background is in the intermediate range, utilization of border information is indispensable [42]. Segmentation of different objects in the paradigm can be achieved past performing paradigm partitioning such equally continued component labeling [48], [49], [l]. For less distinct images of targets whose intensity contrast with the background is low due to light reflection, segmentation techniques such as Markov random fields [51] and watershed division [48] may be applicative for segregation of different objects in the image based on intensity and proximity.

Based on the understanding of the theory and observations of the Cross-plots discussed in the previous sections, the pseudo code of our method is formulated. A more detailed pseudo-code tin be referenced in Appendix S3 to further breakup the following steps.

1. Remove outliers and noise surrounding the central target. Construct a boundary encapsulating the binary target. Determine the dimensions of the circular boundary to exist encapsulated around the target. The radius of the circumvolve is taken as the altitude from the center of the rectangle to any one corner of its purlieus.
2. Position an arbitrary number of node points uniformly and circumferentially effectually the circular boundary encapsulating the binary target.
3. Obtain the set up of Cantankerous-plots for α = i to North, where D is the binary pattern points and α is the current node of interest from a set of N reference node points. The signature of the pattern is represented in a matrix that represents coordinates of Cross-plot curves that are concatenated cavalcade-wise.
4. The signatures of items in the database are compared with the target signature to give an indicator for caste of shape dissimilarity. To compare 2 signatures, piecewise elemental differences in the two matrices are summed to decide a Shape Dissimilarity Index (SCI) value.
5. The database detail pertaining to the signature with the lowest SCI is returned as the identified target. Shapes with subsequent increment in SCI can be output for reference and analysis. If the SCI of all the items exceeds a user-specified threshold, reporting of an unidentified target will be returned.

3.2 System Prototyping

In this section, the pattern principles of the automatic target recognition organization are described in detail and the functionalities of the system such as the actual image indexing, i.e. the computation of blueprint signatures and the quantification metric for the perceptual similarity betwixt two snap shots of the target are implemented and analyzed. These are typically off-line operations. For this system, the process of signature differentiation with respect to the chosen signature and metric is of lower complexity every bit compared to the image indexing. The overall complexity is dependent on the specificity of the signature and conservation of the spatial arrangement of the pattern. This method generates low-level signatures efficiently, capturing merely the global content of the pattern irrespective of pattern distortion or target disorientation that affects information technology locally. The implementation and testing of the design indexing and recognition demonstrates the efficiency and effectiveness of our target recognition system.

3.two.1 Schematic System Layout.

This section briefly describes some of the working functionalities of the ATR organisation and how units tin can be integrated to class a classification system. It harnesses the Cross-plot in pattern recognition to enable an efficient and effective way of identifying airborne targets. The signature reflects the geometrical distribution of the image without executing sophisticated image processing or extracting excessive information from the shape pattern content. As a issue, the computational load in generating a target's signature is low and to reach real-time target identification is technically possible.

The identification of a target tin can be achieved past the find-and-match procedure (Figure xi). The speed of matching depends on the size of the signature, and its low complexity. The implemented design identification and retrieval can be adjusted for speed at the expense of accuracy and vice versa. This flexibility allows for customization of the organization based on the type of pattern types and size of its prototype library. Based on the design of the system outlined in this section, a prototype of the machine that performs target recognition is built and analyzed for its performance. Note that sampled images are from the target repository in Appendix S2.

Figure xi. Retrieval and classification procedures for target identification.

This framework lays the architecture for the development of automatic target recognition system. Cardinal advantages of this model are that the signature generation does non require heavy computational resources, and the accuracy and speed of matching can exist adjusted by the user.

https://doi.org/10.1371/journal.pone.0025621.g011

three.2.ii System Implementation.

A prototype of the automatic target recognition system was built with the desired level of interactive user control and tested on a platform with unlike design registrations. The Shape Dissimilarity Index (SCI) of the reference shape blueprint with respect to the actual pattern is calculated and the patterns are well-matched based on their SCIs. The signatures of the target patterns are displayed graphically for reference. We reduced the size of the library database and use only selected input patterns of different air targets. Our main objective is to illustrate how different shape targets with high perceptual similarity may exist identified. The caste of accuracy can besides exist displayed forth with the matched target. The objective of the different experiments in the post-obit sections and which relies on a small organization database of samples is for demonstration purposes. A more reliable organization can be developed by increasing the (i) database of target variants, and (ii) resolution of signatures, which can be customized to accomplish the all-time pattern recognition efficiency.

Users import the digital patterns and perform characteristic extraction in the indexing process to generate unique signatures. There are options for entry updates into the multimedia database for matching and identification of patterns. The pattern images in the database are ranked according to their similarity with the query pattern and with their respective Shape Dissimilarity Index (SCI) label. The automatic target recognition paradigm is implemented and tested for reliability. In this experiment, a synthetically generated target from the side view is loaded and identified using a target library of ane hundred and eighty reference patterns as shown in Effigy 12 (a). In the case of a video capture of the same target, the shape object has been segmented for analysis and very similar result is obtained as observed in Figure 12 (b). No prior processing techniques to clean the image or ameliorate the outline of the target shape are carried out.

Figure 12. Programmable human being-calculator interface template for automatic target recognition system.

Data for (a) Synthetic shape pattern equally the identified target and (b) Photorealistic paradigm that depicts actual target are recorded. The interface system shows that it is able to effectively identify targets with fuzzy outlines and discontinuous interiors.

https://doi.org/ten.1371/periodical.pone.0025621.g012

From the ranking and correlation values, the similarity of the target and the target library data set A (in Appendix S1) can be quantified and a module has been implemented to predict the probability of its right identification. Series of designed experiments that are based on real and synthetically generated patterns are performed with the target recognition trials, and have demonstrated robustness, accurateness, and the system suitability in the context of target recognition.

3.2 Arrangement Testing and Performance

In this department, the proposed technique was tested on a real data set and analyzed for effective operation and efficiency. Sampled images from a multimedia file [52] was used to create Data Fix C and the thumbprints of an air target (Dassault Rafale) are provided for testing and demonstration.

The organization is able to detect targets, and predict the accurateness as well as confidence of identification based on statistical assay of SCI of every frame capture. The calculated SCI for a frame is inversely proportional to the confidence of matching. Figure 13 shows the SCI generated for every frame in a graphical format. Although our proposed technique tin can handle fuzzy, noisy, distorted or incomplete patterns at varying degrees, the poor image resolution of target and lack of appropriate preprocessing tin affect the system accuracy to a certain degree.

Figure xiii. Correlation analysis of an airborne target based on caused video clip.

The data registration and feature extraction of a Dassault Rafale from a video database can be performed in existent-time to consolidate sufficient content information of its shape. The time taken to verify its identity is in the society of milliseconds. The Shape Contrast Alphabetize (SCI) versus time graph demonstrates the variations in these indices as each paradigm is captured per time frame increment. The probability and confidence of identification are output for decision makers.

https://doi.org/10.1371/journal.pone.0025621.g013

A well-established pattern recognition technique by artificial neural network (ANN) was used to validate the operation of Cantankerous-plot based ATR. The extracted features are dependent upon the structure of the segmented target and based on a prepare of standardized invariant moments, which encompass the property of the rotation invariant. These properties were passed to a multi-layer fully-continued perceptron neural network with ane hidden layer [53]. The weights of this network were trained using a back propagation algorithm, which is based on the generalized Delta dominion [54].

For the ANN classifier, training set is based on the target library (Data Prepare A and B) in Appendix S1 and S2 respectively. For the Cross-plot technique, the same sets of pre-classified data are stored in its repository database. Experiments are conducted from a loftier-resolution video of the Dassault Rafale air target and the extracted images were received from this video (Data Set C). Here, D_ane is divers as the pre-classified information gear up for ANN and Cross-plot ATR, D_ii equally the test data set up, P_TP as the percent of objects correctly identified as positive targets (Truthful-Positive), P_FP as the pct of objects incorrectly identified as positive targets (False-Positive), and P_FN as the percentage of objects incorrectly identified as negative targets (Faux-Negative). The Precision is defined every bit the ratio of P_TP to (P_TP  +P_FP ), and Recall is the ratio of P_TP to (P_TP  +P_FN ). The Cross-plot has a college precision and recall performance compared to the ANN method. This lends support to justification of the better performance past the Cantankerous-plot pattern recognition technique.

Information technology may be worthwhile noting that fake-warning and detection rate reduces every bit the number of nodes, N that is used in Cantankerous-plot, or the number of subconscious neurons, n in the subconscious level of an ANN classifier increases. So to achieve a fair comparison of accurateness in pattern identification, suitable adjustments are made such that N = 8 and north = 5 such that the speed of processing is equal for both frameworks. The results based on their identification performance (Tabular array 1) show that the ATR system based on Cantankerous-plot technique has a lower false alert rate and accomplished a greater accuracy of detection as compared to the ANN based system.

Word

The proposed approach requires the generation of object signature from the data set and all the information about this particular can be derived from the Cross-plot. The forcefulness of this technique is the element of computational efficiency. The computation of the Cross-plot between the pattern and the node is of complication O(N + NlogN), where Northward is the number of data points. Considering the comparing of the signature can be achieved without exhausting huge computational resources, this technique enables the possibility of the identification of targets in real fourth dimension.

In shape retrieval systems, partial content information from a pattern is ever extracted and condensed into a signature. The limitation of this approach becomes credible when the structural details of the target are vague. This is considering of the increase in perceptual similarity of the shapes pertaining to the binary target image as the air target is captured at greater distances. The loss of shape content information is determined by the resolution of the signature. The signature map is efficient in extracting the shape feature of binary image data with minimum computational and retention resource, and information technology is used as a thumbprint of the target in the database. Despite the many advantages, total data of the structural specifications of the target that is presented in its binary pattern cannot be independent. Nevertheless, storage space in the memory constrained database can be made available for more instances of training data to be added considering of their depression-memory signatures. The size of the signature is proportional to the duration for comparison, and can be made minimal at the expense of limited characteristic extraction and accuracy of identification. This signature can be scaled to an appropriate size depending on the memory infinite in the target reference database and an optimized accuracy of identification.

Comparison with pattern recognition systems based on different tools such every bit neural networks tin be made. For the neural network-based recognition organisation [55], more neurons may be required to maintain the aforementioned accuracy of detection if the number of known targets with dissimilar shape contents increases. It is also difficult for the value of correlation to exist indicated. Complexity of computation exceeds O(N), N is number of pixels that form the binary design. In add-on, this model is not rotation, scaling, and translation invariant. When using the SCX (Solidity Eccentricity Extent) model, there is poor accuracy in identification of airplane silhouettes specially when there is region loss within patterns. Moreover, the poor accurateness in distinguishing airplanes that accept close perceptual similarity makes the organization inflexible. Every bit there are no correlation metrics, the degree of matching is hard to bespeak. The accuracy of identification cannot be varied with the speed of retrieval. The model is not dissonance, orientation, pixel-loss, and blurring invariant and patterns need to exist preprocessed before classification.

For the shape context method, histogram of relative distances based on a log r versus θ grid serves a discriminative descriptor [56]. Analogously, consolidative count-of-points based on a Cartesian grid serves every bit the discriminative descriptor for the Cross-plot technique. Both approaches relies on global shape information into a local descriptor based on developing a ready of vectors that express the configuration of the shape relative to a reference point. Therefore, the two methods piece of work optimally only when comparing shapes derived from gray-scale images rather than from line representations. In improver, when implementing the shape context approach, reference points taken on a discontinuous profile of the shape as a outcome of region loss may non stand for the true shape contour accurately. Sectional loss of shape parts violates the assumption that the sampled points are able to guess the underlying continuous shape, and causes ambivalence in matching. Since the Cantankerous-plot matching is contained of contour coordinates, an accurate discriminator tin can be achieved for shape objects that are subjected to distortion, racket, and region loss when using the aforementioned feature set. Therefore, the Cross-plot remains relatively robust for discontinuous shape recognition, whereas the shape context method will have failed for the above mentioned discrepancies.

The technique of using Cross-plots for blueprint recognition surpasses many existing techniques due to its robust functioning. The measurements of (i) area and perimeter, (ii) length of maximum dimension, (three) moments relative to the centroid, (iv) number and surface area of holes, (5) surface area and dimensions of convex hull, (six) number of sharp corners, (vii) number of intersections with a check circle, and (viii) angles between intersections, are some of the shape analysis techniques used in pattern recognition [9]. Most of these feature measurements will have failed for disconnected patterns such as that shown in Figure vii (c) if the features extraction is not able to identify the overall shape characteristics despite such disquisitional feature defects.

This paper presents the proof for using the Cantankerous-plot as a potential tool for pattern recognition and motivates a number of open questions for further investigation. In particular, determination of the optimal resolution of the signature vis-à-vis the number of nodes and the resolution for each Cross-plot curvature that is sufficient to develop an authentic shape retrieval system running on low computational resources requires further investigations. The threshold of prediction failure based on incrementing the degree of design baloney for a specific configuration of signature is a claiming to the reliability of this proposed approach. Exploration of the upshot of different datasets along with varying database sizes is across the scope of this proof-of-concept study, and is an interesting open question for future implementations. Other future works may include investigation of multiple distortion mechanisms such as a combination of shape transformation, noise and pixel loss on the accuracy of the target recognition system.

Supporting Information

Author Contributions

Conceived and designed the experiments: KKLW. Performed the experiments: KKLW. Analyzed the information: KKLW. Contributed reagents/materials/analysis tools: KKLW. Wrote the paper: KKLW. Checked the manuscript: DA.

References

1. 1. Messer One thousand, de Ridder D, Kittler J (1999) Adaptive texture representation methods for automatic target recognition. pp. 443–452. British Machine Vision Conference BMVC99.
2. 2. Burroughs C (2001) Sandia uses sophisticated synthetic aperture radar to collect data nigh military vehicles. Sandia Lab News, Sandia National Laboratories 53: 6–7.
   • View Article
   • Google Scholar
3. 3. Oncel AO, Wilson Thursday (2002) Infinite-time correlations of seismotectonics parameters: examples for Japan and from Turkey preceding the Izmit earthquake. Bulletin of the Seismological Society of America 92: 339–349.
   • View Article
   • Google Scholar
4. 4. Pan JY, Faloutsos C (2002) GeoPlot: spatial information mining on video libraries. pp. 405–412. 11th International Conference on Information and Knowledge Direction (CIKM'02). Mclean, Virginia.
5. 5. Wong KKL, Chawla S (2003) An efficient approach to detect cluster locations using Cross-plots. second Workshop in conjunction with 9th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. Washington DC, Usa.
6. half-dozen. Theodoridis Southward, Koutroumbas Thousand (1999) Design Recognition. Elsevier Academic Printing.
7. 7. Kliot Yard, Rivlin East (1998) Invariant-based shape retrieval in pictorial databases. Estimator Vision and Image Understanding 72: 182–197.
   • View Article
   • Google Scholar
8. 8. Fukunaga Thou (1990) Introduction to Statistical Pattern Recognition. San Diego, CA, USA: Academic Press Professional, Inc.
9. 9. Mehtre BM, Kankanhalli MS, Lee WF (1997) Shape measures for content based image retrieval: a comparison. Information Processing & Management 33: 319–337.
   • View Commodity
   • Google Scholar
10. 10. Safar Chiliad, Shahabi C (2002) Shape Analysis and Retrieval of Multimedia Objects (Multimedia Systems and Applications). Springer.
11. eleven. Trier OD, Jain AK, Taxt T (1996) Feature extraction methods for character recognition - a survey. Pattern Recognition 29: 641–662.
    • View Commodity
    • Google Scholar
12. 12. Li Due south, Lee M-C, Pun C-Chiliad (2009) Complex Zernike Moments Features for Shape-Based Prototype Retrieval. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 39: 227–237.
    • View Article
    • Google Scholar
13. xiii. Shen D, Ip HHS (1999) Discriminative wavelet shape descriptors for recognition of 2-D patterns. Pattern Recognition 32: 151–165.
    • View Article
    • Google Scholar
14. xiv. Badawy OE, Kamel M (2002) Shape-based image retrieval applied to trademark images. International Journal of Image and Graphics 2: 375–393.
    • View Commodity
    • Google Scholar
15. 15. Niblack CW, Barber R, Equitz W, Flickner Dr., Glasman EH, et al. (1993) QBIC Project: querying images by content using colour, texture and shape. pp. 173–187. SPIE Storage and Retrieval for Image and Video Databases. San Jose, Calif.
16. 16. Zaharia T, Prêteux F (2003) Shape-based retrieval of 3D mesh models. pp. 39–45. 5th ACM SIGMM International Workshop on Multimedia Information Retrieval. Berkeley, California, USA.
17. 17. Park JA, Chang MH, Choi TS, Ahmad MB (2003) Histogram based concatenation codes for shape description. IEICE Trans Commun (Inst Electron Inf Commun Eng) E86-B: 3662–3665.
    • View Article
    • Google Scholar
18. xviii. Lu G (1997) An arroyo to epitome retrieval based on shape. Journal of Computer science 23: 119–127.
    • View Article
    • Google Scholar
19. 19. Baruch O, Leow MH (1988) Segmentation of ii-dimensional boundaries using the chain lawmaking. Pattern Recognition 21: 581–589.
    • View Commodity
    • Google Scholar
20. 20. Schettini R (1994) Multicolored object recognition and location. Pattern Recognition Messages xv: 1089–1097.
    • View Article
    • Google Scholar
21. 21. Tao Y, Grosky W (1999) Delaunay triangulation for image object indexing: A novel method for shape representation. pp. 631–942. SPIE Symposium on Storage and Retrieval for Paradigm and Video Databases VII.
22. 22. Persoon E, Fu KS (1997) Shape discrimination using Fourier descriptors. IEEE Trans on Systems, Human being Cybernetics 7: 170–179.
    • View Article
    • Google Scholar
23. 23. Zahn CT, Roskies RZ (1972) Fourier descriptors for plane airtight curves. IEEE Trans On Comput 21: 269–281.
    • View Commodity
    • Google Scholar
24. 24. Zhang D, Lu G (2002) Shape-based image retrieval using generic Fourier descriptor. Signal Processing: Image Communication 17: 825–848.
    • View Article
    • Google Scholar
25. 25. Dudani SA, Breeding KJ, McGhee RB (1977) Aircraft identification by moment invariants. IEEE Trans on Comput C-26: 39–45.
    • View Article
    • Google Scholar
26. 26. Petrakis E (2002) Design and evaluation of spatial similarity approaches for image retrieval. Epitome and Vision Computing 20: 59–76.
    • View Article
    • Google Scholar
27. 27. Lam CP, Wu JK, Mehtre B (1996) STAR—A System for Trademark Archival and Retrieval. Globe Patent Data xviii: 249–249.
    • View Article
    • Google Scholar
28. 28. Wu JK, Mehtre BM, Gao YJ, Lam CP, Narasimhalu Advert (1994) STAR-A multimedia database arrangement for trademark registration, applications of databases. Lecture Notes in Reckoner Science 819: 109–112.
    • View Article
    • Google Scholar
29. 29. Wang Y, Baciu G (2002) Robust object matching using a modified version of the Hausdorff measure. International Journal of Prototype and Graphics ii: 361–374.
    • View Article
    • Google Scholar
30. 30. Trahanias PE (1992) Binary shape recognition using the morphological skeleton transform. Pattern Recognition 25: 1277–1288.
    • View Article
    • Google Scholar
31. 31. Sajjanhar A, Lu G (1997) A grid based shape indexing and retrieval method. Australian Calculator Journal on Multimedia Storage and Archiving Systems 29: 131–140.
    • View Article
    • Google Scholar
32. 32. Stimets RW, Tang H (1996) Procedures for rapid pattern recognition of iii-dimensional objects using parallel processing on a hexagonal pixel grid. pp. 2–viii. SPIE Image and Video Processing Iv.
33. 33. Tepper K, Gómez F, Musé P, Almansa A, Mejail Yard (2009) Morphological Shape Context: Semi-locality and Robust Matching in Shape Recognition. pp. 129–136. Progress in Pattern Recognition, Image Analysis, Estimator Vision, and Applications.
34. 34. Belongie S, Malik J, Puzicha J (2002) Shape Matching and Object Recognition Using Shape Contexts. IEEE Transactions on Design Analysis and Machine Intelligence 24: 509–522.
    • View Article
    • Google Scholar
35. 35. Ling H, Jacobs DW (2005) Using the Inner-Distance for Nomenclature of Articulated Shapes. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) two: 719–726.
    • View Commodity
    • Google Scholar
36. 36. Ling H, Jacobs DW (2007) Shape classification using the inner-distance. IEEE Transactions on Pattern Analysis and Machine Intelligence 29: 286–299.
    • View Article
    • Google Scholar
37. 37. Falconer K (1990) Fractal Geometry - Mathematical Foundations and Applications. Wiley.
38. 38. Arya S, Mount D, Netanyahu N, Silverman R, Wu A (1998) An optimal algorithm for approximate nearest neighbor searching. Journal of the ACM 45: 891–923.
    • View Article
    • Google Scholar
39. 39. pp. 25–32. Lee L. Measures of distributional similarity; 1999.
40. 40. Brigo D, Hanzon B, LeGland F (1998) A differential geometric approach to nonlinear filtering: the projection filter. IEEE Trans on Auto Cont 68: 181–188.
    • View Commodity
    • Google Scholar
41. 41. Oakley JP, Satherley BL, Harrison CG (1996) Enhancement of image sequences from a forward-looking airborne camera. pp. 266–276. SPIE Image and Video Processing IV.
42. 42. Sang Due north, Peng J (1996) Model-based multi-resolution sectionalization of FLIR images. pp. 259–269. SPIE Prototype and Video Processing IV.
43. 43. Zhuang Y, Sun XH (2001) A high-club fast direct solver for singular Poisson equations. Journal of Computational Physics 171: 79–94.
    • View Article
    • Google Scholar
44. 44. Schmidt Yard, Rajagopal Southward, Ren Z, Moffat M (2003) Awarding of singular value decomposition to the analysis of time-resolved macromolecular X-ray data. Biophysical Journal 84: 2112–2129.
    • View Article
    • Google Scholar
45. 45. Greenacre M (2003) Singular value decomposition of matched matrices. Periodical of Applied Statistics 30: 1101–1113.
    • View Commodity
    • Google Scholar
46. 46. Gonzalez RC, Forest RE (2002) Digital Paradigm Processing. New Bailiwick of jersey: Prentice-Hall Inc.
47. 47. Silbert LE, Ertas D, Grest GS, Halsey TC, Levine D, et al. (2001) Granular flow down an inclined airplane: Bagnold scaling and rheology. Physical Review Eastward 64: 051302.
    • View Article
    • Google Scholar
48. 48. Bieniek A, Moga A (1998) A connected component approach to the watershed segmentation. Dordrecht Kluwer Bookish Publishers.
49. 49. Horn BKP, editor. (1998) Robot Vision. 4th ed. The MIT Press.
50. 50. Samet H (1981) Connected component labeling using quadtrees. Journal of the ACM 28: 487–501.
    • View Article
    • Google Scholar
51. 51. Kervrann C, Heitz F (1995) A Markov random field model-based approach to unsupervised texture segmentation using local and global spatial statistics. IEEE Trans Image Proc 4: 856–862.
    • View Article
    • Google Scholar
52. 52. Landry JW, Grest GS (2004) Granular packings with moving side walls. Physical Review E 69: 031303.
    • View Article
    • Google Scholar
53. 53. Zhang H, Guan J, Sunday GC (1992) Bogus neural network-based image pattern recognition. pp. 437–441. ACM Southeast Regional Conference. Raleigh, North Carolina, USA.
54. 54. Leonard J, Kramer MA (1990) Improvement of the backpropagation algorithm for preparation neural networks. Computers & Chemical Engineering science 14: 337–341.
    • View Article
    • Google Scholar
55. 55. Khan JF, Alam MS, Bhuiyan SMA (2009) Automatic target detection in forrad-looking infrared imagery via probabilistic neural networks. Applied Optics 48: 464–476.
    • View Commodity
    • Google Scholar
56. 56. Mori G, Belongie S, Malik J (2005) Efficient shape matching using shape contexts. IEEE Trans on Pattern Anal and Machine Intelligence 27: 1832–1837.
    • View Article
    • Google Scholar

bennettovelly1984.blogspot.com

Source: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0025621

Share this post