PROKOP, R. J., AND REEVES, A. P. 1992. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graph. Models Image Process. 54, 5, 438--460.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of shapes of fixed configurations and are not suitable 8 for modeling variability in the observed shapes such as a gesturing person. Finally, a third description approach is based on modeling the geometric distribution of the shape properties such as histograms of angles [11] algebraic moments [16]. These descriptions are view dependent and do not perform well as the localization of the features is lost in the statistical representation used (commonly a histogram) We present a statistical shape description model that preserves the localization of the geometric features considered. This ....

R. J. Prokop and A. P. Reeves. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graphics Models and Image Processsing, 54(5):438--460, 1992.

....with moments and or moment invariants as object features. Index Terms 3D Cartesian moments, superellipse, superellipsoid, transformations of 3D moments, registration I. INTRODUCTION OMENT BASED techniques have a well established tradition in object recognition and pose estimation [1]. Initial two dimensional moment invariants techniques were extended to three dimensions [2] 4] and three dimensional moments were used for object recognition [5] Although algorithms and methods for segmentation and recovery of superellipsoids exist (see survey in [6] momentbased methods ....

....# m pqr #m pqr : 38) The result can be generalized to an arbitrary number of parts by a simple induction. V. RANGE IMAGE REGISTRATION The basic idea of range image registration based on moments is to construct a coordinate frame which is rigidly attached to the object in each image [1], 3] 5] After constructing the two frames, we know their relationship to the global coordinate system and thus we also know the rigid transformation between the two frames, which is also the rigid transformation of the object. We will name the constructed frames the canonical frames. The ....

R. J. Prokop and A. P. Reeves, "A survey of moment-based techniques for unoccluded object representation and recognition," Computer Vision, Graphics, and Image Processing. Graphical Models and Image Processing, vol. 54, no. 5, pp. 438--460, 1992.

....moments up to second order as region descriptors because the operations for adding pixels to a region or merging two regions are computationally fast and they are sufficient to describe position and size of the regions. Moments are often used in computer vision algorithms to describe image objects [2,3]. The definition of the moment M(p,q) of a region is as follows: M(p,q) Expy q (x.y) region We use the moments M(O,O) M(1, O) and M(1,1) They describe the number of pixels and the center of the region and are computational simple. Additionally we need the central moments C(p,q) of a region ....

R. J. Prokop and A. P. Reeves, "A survey of moment-based techniques for unoccluded object representation and recognition" Computer Vision, Graphics, and Image Processing. Graphical Models andImage Processing, vol. 54, pp. 438-460, Sept. 1992.

....representation and recognition is an important topic in the computer vision area. Moments of the intensity function of pixels are commonly used for representing an object or an image. The p = m n order moment (Mm;n ) of an array of pixels with values f(x; y) and size NM is defined by equation 1 [1, 2]. Mm;n y=1 f(x; y) 1) Low order moments are commonly used to extract features, such as area and center of gravity, and to find the location and orientation of objects in a image [1, 2, 3, 4] In contrast, high order moments are used for pattern recognition and image representation ....

.... order moment (Mm;n ) of an array of pixels with values f(x; y) and size NM is defined by equation 1 [1, 2] Mm;n y=1 f(x; y) 1) Low order moments are commonly used to extract features, such as area and center of gravity, and to find the location and orientation of objects in a image [1, 2, 3, 4]. In contrast, high order moments are used for pattern recognition and image representation [5, 6] A direct computation of equation 1 requires NM additions and (m n)NM multiplications. In the last years, several algorithms and architectures have been proposed to improve the speed of moments ....

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R. J. Prokop and A. P. Reeves, "A Survey of MomentBased Techniques for Unoccluded Object Representation and Recognition", Graphical Models and Image Processing, vol. 54, no. 5, September 1992, pp. 438-- 460.

....a large database [78] Finally, shapes have been indexed based on their statistical properties. The simplest approach represents objects with feature vectors [29] in a multidimensional space where the axes encode global geometric properties, such as circularity, eccentricity, or algebraic moments [68, 86]. Other methods have considered histograms of geometric statistics [1, 6, 15, 31, 62] For instance, Ankerst et al. 4] proposed shape histograms decomposing shells and sectors around a model s centroid. Besl [15] used histograms of the crease angle for all edges in a 3D triangular mesh. Osada et ....

.... skeletons [19, 37, 83] require a consistent model of the object s boundary and interior, which is difficult to reconstruct for highly degenerate computer graphics models [11, 36, 58] Other shape representations, such as Extended Gaussian Images [38] Spherical Attribute Images [27, 28] moments [68, 86], and wavelets [34] require a priori registration into a canonical coordinate system, which is difficult to achieve robustly. Finally, statistical shape descriptors, such as feature vectors [29] and shape distributions [62] are usually not discriminating enough to distinguish between similar ....

Richard J. Prokop and Anthony P. Reeves. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graphical Models and Image Processsing, 54(5):438--460, 1992.

....in momentbased schemes, calculating the moment directly entails a high computation cost. To overcome this diculty and allow moment techniques to be used in real time image processing and computer vision, various ecient implementation methods and special purpose architectures have been proposed [13]. In what follows, we develop an explicit computation procedure for s n;p . To this end, we distinguish the following four cases: When n = p = 0, the evaluation of (eq. 19) gives s 0;0 = 1. When p = 0 and n 0, so s n;0 = R 1 1 f n (x)dx = 0. 8 DMI, Universit e de Sherbrooke Technical ....

R.J. Prokop and A.P. Reeves. A Survey of Moment-Based Techniques for Unoccluded Object Representation and Recognition. CVGIP: Graphical Models and Image Processing, 54:438-460, 1992.

....invariants can be put into a feature vector, which can be used for matching. Algebraic moments and other global object features such as area, circularity, eccentricity, compactness, major axis orientation, Euler number, concavity tree, shape numbers, can all be used for shape description [9] [42]. 1.1.2 Modal matching Rather than working with the area of a 2D object, the boundary can be used instead. Samples of the boundary can be described with Fourier descriptors, the coefficients of the discrete Fourier transform [56] Another form of shape decomposition is the decomposition into an ....

R. J. Prokop and A. P. Reeves. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graphics Models and Image Processing, 54(5):438--460, 1992.

....shapes have been compared on the basis of their statistical properties. The simplest approach of this type is to evaluate distances between feature vectors [22] in a multidimensional space where the axes encode global geometric properties, such as circularity, eccentricity, or algebraic moments [45, 53]. Other methods have compared discrete histograms of geometric statistics. For example, Thackeretal[1,4,8,9,25,26,47,54] Huetetal. 33] and Ikeuchi et al. 34] have all represented shapes in 2D images by histograms of angles and distances between pairs of 2D line segments. For 3D shapes, Ankerst ....

....proposed in this paper. We fi nd t ha t D2 shape distributions outperform moments for classification of models in our tests. The differences are more significant for more stringent classification criteria (i.e. First Tier) and for higher order moments, which are known to be sensitive to noise [45]. Further studies are required to test whether D2 shape distributions perform better than moments for larger databases or for other shape matching applications. First Second Nearest Method Tier Tier Neighbor D2 49 66 66 M3 35 46 63 M4 41 52 64 M5 28 38 55 M6 34 44 54 M7 27 ....

R. J. Prokop and A. P. Reeves. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graphics Models and Image Processsing, 54(5):438--460, 1992.

....shapes have been compared on the basis of their statistical properties. The simplest approach of this type is to evaluate distances between feature vectors [22] in a multidimensional space where the axes encode global geometric properties, such as circularity, eccentricity, or algebraic moments [45, 53]. Other methods have compared discrete histograms of geometric statistics. For example, Thacker et al. [1, 4, 8, 9, 24, 25, 47, 54] Huet et al. 32] and Ikeuchi et al. 33] have all represented shapes in 2D images by histograms of angles and distances between pairs of 2D line segments. For 3D ....

Richard J. Prokop and Anthony P. Reeves. A survey of momentbased techniques for unoccluded object representation and recognition. CVGIP: Graphics Models and Image Processsing, 54(5):438-- 460, 1992.

....are considered. Color information has proven very useful in pattern recognition, e.g. through the use of color histograms [5, 6, 8] or multiband correlation functions [7] Another strand of research has focussed on moment invariants under different types of geometric and or photometric changes [9, 10, 11, 12, 2, 13, 7, 1]. Color histograms do not exploit the spatial layout of the colors, whereas for moment invariants our experiments have shown that in order to increase the recognition performance, one may have to let grow the order of the moments beyond the point where they remain stable. These problems are ....

R. Prokop and A. Reeves, A survey of moment-based techniques for unoccluded object representation and recognition, Computer Vision Graphics and Image Processing: Models and Image Processing, 1992; 54(5):438--460.

....r (I) ff (g I i Gamma g (I) fi (b I i Gamma b (I) fl (7) where ff; fi; fl 0 and ff fi fl = n. Roughly speaking low order moments give a coarse description of the distribution. More and more distribution details are unveiled as one progresses through the higher moments[11]. Two observations stem from this. First, for color based object recognition low order moments capture the most useful information. For example, low order moments are less effected by confounding processes such as image noise or highlights. Stricker and Orengo[12] have presented experimental ....

R.J. Prokop and A.P. Reeves. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graphical Models and Image Processing, 54(5):438--460, 1992.

....moments; Hu s moments; Li s moments; Rotation invariant; Feature selection; nearest neighbor classifier; Character classification; Document analysis and recognition 1. Introduction The use of moment invariants as features for identification and inspection of 2D shape has received much attention [1]. Since Hu [2] presented the first paper on the use of image moments for 2D pattern recognition, momentbased techniques have found wide applications [3, 4] Resis [5] revised some of the theoretical proofs in [2] By Corresponding author. Tel. 0085227888641; Fax: 0085227888614; E mail: ....

R.J. Prokop, A.P. Reeves, A survey of moment-based techniques for unoccluded object representation and recognition, CVGIP: Graphical Models Image Process, Vol. 54(5) (1992) 438---460.

....and labeling in this case. A wide range of shape recognition approaches have been proposed, such as structural (e.g. methods organizing local features into graphs [5] trees [6] or strings [7] fuzzy or probablistic (e.g. relaxation methods [8] statistical (e.g. methods based on moments [9]) methods that work on some transform domain (e.g. Fourier [10] or Hough [11] and methods based on Neural Networks [12, 13] An important class of contour tracking and matching methods relies on physical models of the deformation and is based on minimization of an energy function, without ....

Richard J. Prokop and Anthony P. Reeves. A Survey of Moment-based Techniques for Unoccluded Object Representation and Recognition. CVGIP: Graphical Models and Image Processing, 54(5):438--460, 1992.

....measures typically used to split a region are t he one dimensional moments of the image. Assuming that our document image is given by a function img(x, y) that maps each pixel coordinates #x, y# to the probability that the pixel is black 1 , the one dimensional moments of order p are defined as [2]: hm p (y) x p img(x, y) vm p (x) y p img(x, y) x y The zeroth order moment (p = 0) is commonly referred to as the projection profile and reflects the expected number of black pixels in each row column. From the first and secondorder moments, one can easily obtain the center of ....

....classification, but there are other alternatives. Two dimensional moments give a compact representation of the global geometrical properties of a shape such as size, aspect ratio, orientation, moments of inertia and kurtosis that can be used to distinguish between significantly different shapes [2]. They can be extended to our probabilistic framework as easily as one dimensional moments: E(m pq ) x p y q img(x, y) reg(x, y) xy Var(m pq ) x p ) 2 (y q ) 2 img(x, y) reg(x, y) 1 img(x, y) reg(x, y) xy When moments are insufficient to distinguish between shapes, ....

R. Prokop and A. Reeves. A Survey of Moment-Based Techniques for Unoccluded Object Representation and Recognition. Computer Vision, Graphics and Image Processing, 54(5):438-460, September 1992.

....moment invariants can be put into a feature vector, which can be used for matching. Global object features such as area, circularity, eccentricity, compactness, major axis orientation, Euler number, concavity tree, shape numbers, and algebraic moments can all be used for shape description [BB82] PR92] A number of such features are for example used by the QBIC system [NBE 93] 2.2.2 Modal matching Rather than working with the area of an object, the boundary can be used instead. Samples of the boundary can be described with Fourier descriptors, the coe cients of the discrete Fourier ....

Richard J. Prokop and Anthony P. Reeves. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graphics Models and Image Processing, 54(5):438-460, 1992.

....p y q (3) The moments can be used to compute many useful shape features. From the 10 low order moments (p q 3) we can compute shape features like the area, centroid, radius of gyration, orientation, bounding rectangle and image ellipse, and invariant geometric moments including Hu s moments [16]. Direct evaluation of the double sum in Eq. 3) will require a signi cant amount of computation. There exist fast methods for the moment computation. By using the discrete Green s theorem, we have proposed a new method [15] which is faster than earlier methods, and gives exactly the same results ....

R. J. Prokop and A. P. Reeves, A survey of moment-based techniques for unoccluded object representation and recognition, CVGIP: Graphical Models and Image Processing 54(5):438460, 1992.

....of the pattern [3, 5, 6, 7, 17, 18] Color histograms, however, do not exploit the spatial distribution of the colors within the pattern. Another strand of research has focussed on moment invariants for greyvalue intensity patterns under different types of geometric and or photometric changes [1, 4, 8, 10, 15, 16, 19]. A limitation of this approach is that one may have to let grow the order of the moments beyond the point where they remain stable in order to create sufficient discriminant power for distinguishing between different patterns. These problems are remedied in this paper by introducing powers of the ....

R. Prokop and A. Reeves, A survey of moment-based techniques for unoccluded object representation and recognition, CVGIP: Models and Image Processing, Vol. 54 (1992), pp. 438 -- 460.

.... boundary [17, 18, 19, 20, 21, 22, 23, 24] and various Fourier transforms of the boundary [25, 26, 27, 28, 29] Examples of global methods include the medial axis (also called symmetric axis) transform (MAT) proposed by Blum and described in [30, 31, 32, 17, 33, 34, 20, 22] moment based approaches [35, 36, 37, 38], and methods of shape decomposition into other primitive shapes [39, 40, 41, 42] Another classification of shape analysis algorithms can be made on the basis of whether the result of the analysis is numeric or non numeric. For example, the MAT produces another image (containing a symmetric axis) ....

....the MAT produces another image (containing a symmetric axis) and is therefore called a space domain technique. On the other hand, scalar transform techniques produce numbers (scalars or vectors) as results. Examples of later methods include various Fourier [25, 26, 27, 28, 29] and moment based [35, 36, 37, 38] procedures for shape analysis. A third classification of shape analysis methods can be made on the basis of information preservation. Methods which allow for the accurate (or at least sufficiently accurate) reconstruction of a shape from its descriptor are called information preserving methods, ....

[Article contains additional citation context not shown here]

R. J. Prokop and A. P. Reeves. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graphical Models and Image Processing, 54:438--460, 1992.

....performance. 2.3 Moments Traditionally, moments have been widely used in pattern recognition applications to describe the geometrical shapes of different objects. They provide fundamental geometric properties (e.g. area, centroid, moment of inertia, skewness, kurtosis) of a distribution [18]. The moments can also be used to represent the pdf of pixel intensities of the image [8] We note that the pdf of pixel intensities is the same as the histogram except for a scale factor that normalizes the total area under the pdf to be 1. Hence, we use the term pdf and histogram interchangeably ....

R. J. Prokop and A. P. Reeves, "A survey of moment-based techniques for unoccluded object representation and recognition," CVGIP: Graphical Models and Image Processing 54(5), 438-460, (Sep. 1992).

....p y q (3) The moments can be used to compute many useful shape features. From the 10 low order moments (p q 3) we can compute shape features like the area, centroid, radius of gyration, orientation, bounding rectangle and image ellipse, and invariant geometric moments including Hu s moments [16]. Direct evaluation of the double sum in Eq. 3) will require a signi cant amount of computation. There exist fast methods for the moment computation. By using the discrete Green s theorem, we have proposed a new method [17] which is faster than earlier methods, and gives exactly the same results ....

R. J. Prokop and A. P. Reeves, A survey of moment-based techniques for unoccluded object representation and recognition, CVGIP: Graphical Models and Image Processing 54(5):438460, 1992.

....scaling invariant shape feature. Kulpa s method [4] has been used to compute the cell perimeter. See [14] for an evaluation of several area and perimeter estimators. Cartesian geometric moments of binary regions have been eOEciently computed [13] in order to obtain moment based shape features [9] such as area, centroid, radius of gyration, orientation, and image ellipse. The elongation has been measured as the ratio of the lengths of the semimajor and semiminor axes of the image ellipse. 3.3 The Evaluation Method The manual segmentation as shown in Figure 1(right) is used as the ....

Prokop, R. J., Reeves, A. P.: A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graphical Models and Image Processing 54 (1992) 438460

....methods mostly take local features of the characters into account only, making the recognition of Chinese characters that are very close in shapes very difficult. Moment descriptors of various forms have been developed following Hu[7] 8] as the extracted features of an image in pattern recognition [15]. Describing an image with moments instead of other traditional methods of image processing means that global properties of the image are used rather than local ones. The moment method is different from other feature extraction methods used in Chinese character recognition in that, carefully ....

R.J. Prokop and A.P. Reeves, A survey of moment-based techniques for unoccluded object representation and recognition, Graphical Models And Image Processing, Vol. 54, No. 5, September, pp. 438-460, 1992.

....are obtained by the normalization j pq = pq ( 00 ) fl ; fl = p q 2 1; p q 2: 2) 3. 1 Invariant Moment Features A number of techniques have been used to derive invariant features from moments for object representation and recognition (see Belkasim et al. 1] and Prokop and Reeves [10] for a survey and comparison) The set of seven moment combinations by Hu [5] is representative of nonlinear combinations of low order two dimensional Cartesian moments. The radius of gyration of an object is de ned as the radius of a circle where we could concentrate all the mass of the object ....

....by Hu [5] is representative of nonlinear combinations of low order two dimensional Cartesian moments. The radius of gyration of an object is de ned as the radius of a circle where we could concentrate all the mass of the object without altering the moment of inertia about its center of mass [10]. This feature is inherently invariant to image orientation, and is therefore a simple and useful rotationally invariant feature for shape analysis. In terms of second order central moments, it is given by Theta R = r 20 02 00 (3) The object ellipse is also a simple, invariant ....

R. J. Prokop, and A. P. Reeves, A survey of moment-based techniques for unoccluded object representation and recognition, CVGPR: Graphical Models and Image Processing 54(5), 438460 (1992).

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PROKOP, R. J., AND REEVES, A. P. 1992. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graph. Models Image Process. 54, 5, 438--460.

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R. J. Prokop and A. P. Reeves. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graphics Models and Image Processsing, 54(5):438--460, 1992.

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R. J. Prokop and A. P. Reeves. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graphics Models and Image Processsing, 54(5):438--460, 1992.

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R.J. Prokop and A. P. Reeves. A survey of moments based techniques for unoccluded object representation. Graphical models and Image Processing, 54(5):438-460, Sep. 1992.

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R. J. Prokop and A. P. Reeves, "A survey of moment-based techniques for unoccluded object representation and recognition," in Proc. Computer Vision, Graphics, Image Processing Conf., vol. 54, Sept. 1992, pp. 438--460.

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R. J. Prokop and A. P. Reeves, "A survey of moment-based techniques for unoccluded object representation and recognition," CVGIP: Graph. Models Image Process., vol. 54, pp. 438--460, 1992.

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R. J. Prokop and A. P. Reeves. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graphical Models and Image Processsing, 54(5):438-- 460, 1992.

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R. Prolop and A. Reeves, "A Survey of Moment-Based Techniques for Unoccluded Object Representation and Recognition", CVGIP: Graphical Models and Image Processing, Vol. 54, No. 5, pp. 438--460, 1992.

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R.J. Prokop, A.P. Reeves, A survey of moment-based techniques for unoccluded object representation and recognition, Computer Vision, Graphics and Image Processing, 54(5), 1992, 438-460.

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R.J. Prokop and A. P. Reeves. A survey of moments based techniques for unoccluded object representation. Graphical models and Image Processing, 54(5):438--460, Sep. 1992.

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R. J. Prokop and A. P. Reeves, "A survey of moment-based techniques for unoccluded object representation and recognition," Comput. Vis., Graph., Image Process., vol. 54, no. 5, pp. 438--460, 1992.

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R. J. Prokop and A. P. Reeves. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP GMIP, 54(5):pp. 438--460, 1992.

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R.J. Prokop, A.P. Reeves, A survey of moment-based techniques for unoccluded object representation and recognition CVGIP: Graphical Models and Image Processing, Vol. 54, 1992, pp. 438}460

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R. J. Prokop, and A. P. Reeves, A survey of momentbased techniques for unoccluded object representation and recognition, CVGPR: Graphical Models and Image Processing 54(5), 438460(1992).

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