C. C. Chen. Improved moment invariants for shape discriminations. Pattern Recognition, 26(5):683--686, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of trademark images. The features used to describe shape can be classified into those that describe the boundary of the objects, like string encoding and Fourier descriptor co efficients, and those which describe the regions in the image like polygonal approximations [23] and invariant moments [3]. However, much of this work assumes that the object can be segmented from the background before the shape features can be computed. This may not be a problem for databases where the object is depicted against a plain background, but this is a serious problem for general image databases. In ....

C. C. Chen. Improved moment invariants for shape discrimination. Pattern Recognition, 26(5):683--686, 1993.

....object is translated or scaled. With appropriate normalization, central moments and normalized central moments are often used to overcome these problems. Hu proposed seven moment invariants, which are the linear combination of the central moments up to the third order to describe the object shape [29, 65]. These 7 shape descriptors are proven to be invariant to scaling, translation and rotation. The complex Zernike moments provide a = q p pq y x y x f dy dx m 23 general solution for rotation invariant property [143] In the language of linear algebra, Equation 2.7 is the projection of ....

C.C. Chen. Improved moment invariants for shape discrimination. Pattern Recognition 26(5), 1993, p. 683-686.

....object # # # # is given by # ### # # ####### # # # # ## ### For finite point sets the integral can be replaced by a summation. The infinite sequence of moments, ## # ### #####, uniquely determines the shape, and vice versa. Variations such as Zernike moments are described in [32] and [12]. Based on such moments, a number of functions, moment invariants, can be defined that are invariant under certain transformations such as translation, scaling, and rotation. Using only a limited number of low order moment invariants, the less critical and noisy high order moments are discarded. ....

C. C. Chen. Improved moment invariants for shape discrimination. Pattern Recognition, 26(5):683--686, 1993.

....2 IE 2 = f(x; y) x; y = 1; 2; Mg. Denote g = x; y) as the contour centroid. The central moment of the (p q)th order is p;q = X (x;y) X 2v i (x Gamma x) p (y Gamma y) q (6) The centre moments are invariant to translation. They can be normalized to scale invariance by [19] (a) contours (b) images Fig. 3. The contours (a) extracted from the corresponding images in (b) j pq = pq fl 00 where fl = p q 1, for p q = 2; 3; 7) Seven moment invariants based on the 2nd and 3rd order moments are computed as, OE 1 = j 20 j 02 (8) OE 2 = j 20 Gamma j ....

Chaur-Chin Chen.: Improved Moment Invariants for Shape Discrimination. Pattern Recognition, vol. 26, no. 5, pp. 683-86, 1993.

....binary [1; n] 1; m] image f : n X x=1 m X y=1 x p y q f(x; y) where the background pixels have value zero, and the object pixels have value one. The in nite sequence of moments, p; q = 0; 1; uniquely determines the shape, and vice verse. Variations are described in [KH90] and [Che93] Based on such moments, a number of functions, moment invariants, can be de ned that are invariant under certain transformations such as translation, scaling, and rotation. Using only a limited number of low order moment invariants, the less critical and noisy high order moments are discarded. A ....

C. C. Chen. Improved moment invariants for shape discrimination. Pattern Recognition, 26(5):683-686, 1993.

.... simple polygon or a chain code then efficient algorithms for com s x M 20 M 00 = M jk x x s x j y y s y k A = g x y , m pq x p y q g x y , dxdy = 78 puting moment invariants can be found in [Ch93], BF86] SNA90] and [Si93] 6. Moments for Preprocessing For a method of normalizing hand printed characters see [Ca70] 7. Generalizations of as Predictors of Discrimination Performance In a recent paper Ball [Ba73] proposed and investigated a generalization of the notion of . From the ....

Chen, C.-C., "Improved moment invariants for shape discrimination," Pattern Recognition, vol. 26, No. 5, 1993, pp. 683-686.

....of exact computation is discussed by examining the invariance of Hu s moments. A fast method for computing moments of regions in grey level image, using discrete Green s theorem, is also presented. 1 Introduction Moments have been widely used in shape analysis and pattern recognition [1][9]. The (p q) th order moment of an image is de ned as m pq = Z y Z x g(x; y)x p y q dxdy (1) where g(x; y) is the intensity as a function of spatial position. The double integral is often replaced by a double summation in discrete images m pq = X y X x g(x; y)x p y q (2) In ....

C.-C. Chen, Improved moment invariants for shape discrimination, Pattern Recogn. 26(5), 683 686(1993).

....p 0 and pN Gamma1 . The skewness, of the part, ae(C) is defined as ae(C) cos Gamma1 p 0 pN Gamma1 Delta pmpN=2 k p 0 pN Gamma1 kk pmpN=2 k Moment invariants: Moment invariants are well known in pattern recognition [23] Modified moments using only the curve boundary were defined in [9]. After experimenting with the use of several normalized moments, we settled on only one of them (denoted as OE 1 ) the sum of the two normalized second moments [10] Convexity: The codon representation is susceptible to spurious extrema resulting from noise, preventing it from being a ....

C.-C. Chen. Improved moment invariants for shape discrimination. Pattern Recognition, 26(5):683--686, 1993.

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C. C. Chen. Improved moment invariants for shape discriminations. Pattern Recognition, 26(5):683--686, 1993.

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