E. Milios. Shape Matching using Curvature Processes. Computer Vision, Graphics and Image Processing, 47:203--226, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... scheme for the scales used in the computation [11] Curvature has been considered to be one of the major perceptual properties of 2D shapes [2, 5, 10] It is invariant to rigid transformations and can be computed by our physiological system [3, 7] It has been used extensively in shape matching [8] and object recognition [6] as well as for shape modeling in both 2D [9] and 3D [1] From these observations regarding a 2D curve and its perception, the problem of 2D curve modeling can be formulated as a two stage process: first, the perception based selection of the local parts on the curve to ....

E. Milios. Shape matching using curvature processes. Computer Vision, Graphics, and Image Processing, 47:203--226, 1989.

....A feature is a region in a dataset that is of interest for its interpretation; feature extraction is the extrication of these regions for further analysis and visualization. Feature extraction has been investigated and utilized to solve a variety of problems, such as shape matching [47], image registration [59] solid modeling [46] edge detection [2] and data visualization [62] In most of its applications, feature extraction provides a compact representation of the relevant information embedded in the dataset. Researchers define different types of features for their ....

E. Milios, "Shape Matching Using Curvature Processes," Computer Vision, Graphics, and Image Processing, Vol. 47, pp. 203-226, 1989.

.... an image contour can be described at multiple scales, has led to such concepts as curvature space [87, 81] scale space primal sketch [72] curvature primal sketch [7] and curvature scales [67] Computation of Contours In order to make the structure of an image contour explicit, a geometric model [67, 80] of the contour needs to be computed from the image, which is also implemented by biological systems [32, 61] In computational vision, two methods are commonly employed: 1) local edge detection followed by global curve tracing [81, 84] and (2) global interpolation or energy optimization [57, ....

E. Milios. Shape matching using curvature processes. Computer Vision, Graphics, and Image Processing, 47:203--226, 1989. 197

.... when local distortions are present, exploits spatial relations between features [Hummel 83] Price 85] Ranade 80] Shapiro 90] Dynamic Programming Good efficiency for finding local transformations when an intrinsic ordering for matching is present [Guilloux 86] Maitre 87] Milios 89] Ohta 87] Generalized Hough Transform For shape matching of rigidly displaced contours by mapping edge space into dual parameter space [Ballard 81] Davis 82] Linear Programming For solving system of linear inequality constraints, used for finding rigid transformation for point ....

....calculations and pruning the search. This strategy can only be applied when an intrinsic ordering of the data problem exists. Several examples in which it has been applied include: signature verification [Pari 90] the registration of geographic contours with maps[Maitre 87] shape matching [Milios 89] stereomapping [Ohta 87] and horizontal motion tracking [Guilloux 86] Notice that in each of these examples, the data can be expressed in a linear ordering. In the shape matching example this was done using a cyclic sequence of the convex and concave segments of contours for each shape. In ....

E. E. Milios, "Shape Matching Using Curvature Processes," Computer Vision, Graphics, and Image Processing 47, 1989, pp203-226.

....is represented by a set of chained points. Several matching techniques for free form curves have been proposed in the literature. In the first category of techniques, curvature extrema are detected and then used in matching [4] However, it is difficult to localize precisely curvature extrema [5, 6], especially when the curves are smooth. Very small variations in the curves can change the number of curvature extrema and their positions on the curves. Thus, matching based on curvature extrema is highly sensitive to noise. In the second category, a curve is transformed into a sequence of ....

E. E. Milios, "Shape matching using curvature processes," Comput. Vision, Graphics Image Process., vol. 47, pp. 203--226, 1989.

.... dynamic programming is used to fit a closed curve template to an image (deformable template matching) Another class of matching methods relies on symbolic entities extracted from shape contours [21, 22, 23, 12] Dynamic programming has been a popular approach for matching such symbolic entities [24, 25, 26, 27]. In [24] the inability of dynamic programming to combine contour segments is mentioned, as well as the fact that differing resolutions in the matched contours will lead to reduced performance. In [26] deletions and insertions of features (corners in a polygonal representation) as well as ....

....reduced performance. In [26] deletions and insertions of features (corners in a polygonal representation) as well as smoothing of features (i.e. dropping corners) is incorporated in the dynamic programming scheme. This type of smoothing lends a primitive multiple scale character to the method. In [25] dynamic programming is used to guide the application of grammar rules that transform one shape into another, in the spirit of [7] In [27] matching proceeds both forward and backward from a support match between two features (landmark points) that are maximally similar. Features are extracted ....

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E. Milios. Shape Matching using Curvature Processes. Computer Vision, Graphics and Image Processing, 47:203--226, 1989.

....at various levels of shape detail by allowing matching of merged sequences of consecutive segments, if this leads to the minimization of a cost function. Each merging is a recursive application of the grammar rules CVC C and VCV V , where C and V denote convex and concave segments respectively [8]. The number of merged segments is always odd. A complete match is a correspondence between groups of consecutive segments in order, such that no segments are left unassociated. The goal is to find the best association of segments in shape A to segments in shape B. This is formulated as a ....

.... 1ji w ) in shape A and segments b(j w;1 1jj w ) in shape B respectively while, the last term is the cost of associating the merged a(i w;1 1jiw ) with the merged b(j w;1 1jj w ) Requirements for reliable cost computation are the following: ffl Merging should follow the process grammar rules [8] (i.e. each allowable merging should be a recursive application of the grammar rules CVC ) C and VCV ) V ) This is enforced by the DP algorithm. ffl Merging a visually prominent segment (i.e. a large segment with high curvature) into a merged segment of the opposite type (convex or concave) ....

E. Milios. Shape Matching using Curvature Processes. Computer Vision, Graphics and Image Processing, 47:203--226, 1989.

....b(j w;1 1jjw ) The role of merging cost is to restrict non promising merges. Constant represents the relative importance of the merging and dissimilarity costs. In this work was set to 1. Each allowable merging should be a recursive application of the grammar rules CVC ) C and VCV) V ) [3]. This is enforced by the DP algorithm. Next, we define geometric quantities (features) required in the definition of the cost functions as illustrated in Fig. 2. segment a tangent p area A i 1 tangent i rotation angle i i p Figure 2. Geometric quantities for defining the importance ....

E. Milios. Shape Matching using Curvature Processes. Computer Vision, Graphics and Image Processing, 47:203--226, 1989.

....at various levels of shape detail by allowing matching of merged sequences of consecutive segments, if this leads to the minimization of a cost function. Each merging is a recursive application of the grammar rules CVC C and VCV V , where C and V denote convex and concave segments respectively [11]. The number of merged segments is always odd. A complete match is a correspondence between groups of consecutive segments in order, such that no segments are left unassociated. The goal is to find the best association of segments in shape A to segments in shape B. This is formulated as a ....

.... 1ji w ) in shape A and segments b(j w;1 1jjw ) in shape B respectively while, the last term is the cost of associating the merged a(i w;1 1jiw ) with the merged b(j w;1 1jj w ) Requirements for reliable cost computation are the following: ffl Merging should follow the process grammar rules [11] (i.e. each allowable merging should be a recursive application of the grammar rules CVC ) C and VCV ) V ) This is enforced by the DP algorithm. ffl Merging a visually prominent segment (i.e. a large segment with high curvature) into a merged segment of the opposite type (convex or concave) ....

E. Milios. Shape Matching using Curvature Processes. Computer Vision, Graphics and Image Processing, 47:203--226, 1989.

.... dynamic programming is used to fit a closed curve template to an image (deformable template matching) Another class of matching methods relies on symbolic entities extracted from shape contours [21, 22, 23, 12] Dynamic programming has been a popular approach for matching such symbolic entities [24, 25, 26, 27]. In [24] the inability of dynamic programming to combine contour segments is mentioned, as well as the fact that differing resolutions in the matched contours will lead to reduced performance. In [26] deletions and insertions 4 of features (corners in a polygonal representation) as well as ....

....performance. In [26] deletions and insertions 4 of features (corners in a polygonal representation) as well as smoothing of features (i.e. dropping corners) is incorporated in the dynamic programming scheme. This type of smoothing lends a primitive multiple scale character to the method. In [25] dynamic programming is used to guide the application of grammar rules that transform one shape into another, in the spirit of [7] In [27] matching proceeds both forward and backward from a support match between two features (landmark points) that are maximally similar. Features are extracted ....

[Article contains additional citation context not shown here]

E. Milios. Shape Matching using Curvature Processes. Computer Vision, Graphics and Image Processing, 47:203--226, 1989.

.... In [13] dynamic programming is used to fit a closed curve template to an image (deformable template matching) Another class of matching methods relies on symbolic entities extracted from shape contours [14, 15] Dynamic programming has been a popular approach for matching such symbolic entities [16, 17, 18, 19]. Building upon the previously mentioned work, Ueda and Suzuki [14] propose a sophisticated dynamic programming (DP) algorithm, which can group segments together in order to come up with appropriate correspondences. For example, if one shape is slightly noisier than the other, it is possible for a ....

....merging an odd number of consecutive segments at the finest scale, if such a merging replacement can lead to the minimization of a cost function. Each merging should be a recursive application of the grammar rules CVC C and V CV V , where C and V denote convex and concave segments respectively [6, 17]. This is enforced by the algorithm. A complete match is a correspondence between groups of consecutive segments in order, such that no segments are left unassociated. The goal is to find the best association of segments in shape A to segments in shape B. The problem of finding the best ....

[Article contains additional citation context not shown here]

E. Milios. Shape Matching using Curvature Processes. Computer Vision, Graphics and Image Processing, 47:203--226, 1989.

.... dynamic programming is used to fit a closed curve template to an image (deformable template matching) Another class of matching methods relies on symbolic entities extracted from shape 4 contours [29, 30, 23] Dynamic programming has been a popular approach for matching such symbolic entities [31, 32, 33, 34]. In [31] the inability of dynamic programming to combine contour segments is mentioned, as well as the fact that differing resolutions in the matched contours will lead to reduced performance. In [33] deletions and insertions of features (corners in a polygonal representation) as well as ....

....reduced performance. In [33] deletions and insertions of features (corners in a polygonal representation) as well as smoothing of features (i.e. dropping corners) is incorporated in the dynamic programming scheme. This type of smoothing lends a primitive multiple scale character to the method. In [32] dynamic programming is used to guide the application of grammar rules that transform one shape into another, in the spirit of [35] In [34] matching proceeds both forward and backward from a support match between two features (landmark points) that are maximally similar. Features are extracted ....

[Article contains additional citation context not shown here]

E. Milios. Shape Matching using Curvature Processes. Computer Vision, Graphics and Image Processing, 47:203--226, 1989.

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E. E. Milios. Shape Matching Using Curvature Processes. Computer Vision, Graphics and Image Processing, 47:203--226, 1989.

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