Siddiqi, K., & Kimia, B. B. (1995). Parts of visual form: computational aspects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17, 239--251.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....proceeds by substituting two consecutive line segments with a single line segment joining their endpoints. However this approach is very sensitive to the order of point substitution. Malladi and Sethian [55] developed a level set approach to curve evolution and decomposition. Siddiqi et al. [50] proposed a theory of shape based on a reaction diffusion equation to produce a hierarchical decomposition of shape into parts and protrusions. The main drawback with the multi scale approach is that the procedure of curve evolution is very slow. For example in [56] a convolution with the ....

....body part shapes and geometric relationships. Zhu and Yuille [23] developed a similarity measure to compare silhouettes based on both the local shapes of parts and the topology but the method can not handle shape degeneration or resolution changes very well. Several curve evolution approaches [50, 54, 55] have been proposed to model shapes of an object at different scales, but the related similarity measure is sensitive to occlusion and is not invariant under scaling. Leung et al. 27, 28, 29] have proposed a method which combines the intensity pattern and the spatial relationships between the ....

K. Siddiqi, B. B. Kimia, "Parts of Visual Form: Computational Aspects," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 17, No. 3, pp. 239-251, 1995.

....arcs are not taken from the original contours, but from their simplified versions. Significant maximal convex arcs on simplified contours correspond to significant parts of visual form [9] whose importance and relevance for object recognition is verified by numerous cognitive experiments [5, 6, 16, 18]. For P298 a single simplified contour is used as a shape descriptor. This contour is optimally determined by a novel process of contour simplification called discrete curve evolution in [11] This process allows to reduce the influence of noise without changing the overall appearance of objects. ....

K. Siddiqi and B. B. Kimia. Parts of visual form: Computational aspects. IEEE Trans. PAMI, 17:239--251, 1995.

....points of minimal negative curvature (Hoffman and Richards [4] This is the case when the endpoints of convex arcs are located near the points of minimal negative curvature. Also for many objects, the resulting parts of objects correspond to limbs and necks in the theory of Siddiqi and Kimia [17]. For boundaries of continuous objects, the endpoints of maximal convex arcs correspond to inflection points (e.g. inflection points are used for shape description in Freeman [18] The correspondence of the endpoints of maximal convex arcs to different kinds of critical points (in the sense of ....

K. Siddiqi and B. B. Kimia. Parts of visual form: Computational aspects. IEEE Trans. PAMI, 17:239-251, 1995.

....g. A variation of this approach that makes the combin ation of in terior an d exterior in) rmation more explicit is presen ted by Abe et al. 1] who segmen t the axes based on domin n t poin ts detected alon g the boun( ry. Based on psychophysical an d ecological con sideration s Siddiqian d Kimia [15] described a partitio nio schemein volvin two types of parts:n ecks an d limbs. Necks were determinF by diameters of locallyminyS3 in36L1 ed circles in the region while limbs werelin0 through pairs ofn3 ative curvatureminLJ havin co circular bounL ry ta nen ts (i.e. they join smoothly) Competin ....

K. Siddiqi and B.B. Kimia. Parts of visual form:C omputational aspects. IEEE Trans . PAMI , 17(3):239--251, 1995.

....on the boundary of the object, iii) minimum description length criterion, iv) primitives cycles, and v) perceptual grouping and geometric relationships. We review them briefly and explain why none is appropriate as such for our problem. 4 3.1. Approaches based on symmetry axes Several works ( 2] [3], 4] 5] have used symmetry axes to segment objects into parts. After edge detection, the object symmetry axes are detected. The axes are usually computed by taking the midpoint between two black pixels, and by linking these midpoints. The result is a collection of axes in which some are relevant ....

Siddiqi, K. and B.J. Kimia, Parts of Visual Form: Computational Aspects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995. 17(3): pp. 239-251.

....sophisticated methods, like annular operators [6] Although these methods work fine on images without textures, their use on textured objects would give a large number of axes (most of them irrelevant) and it might be quite difficult to interpret the resulting data as parts. In another method [3][4], parts are found by computing distances and curvatures on the boundaries and shocks on the symmetry axes of the object to obtain neck based and limb based parts. This method is capable of dealing very well with occlusions. The parts obtained appear quite similar to what a human would find. Since ....

K. Siddiqi and B.J. Kimia, Parts of Visual Form: Computational Aspects, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 17, No. 3, March 1995, pp. 239-251.

....contour tracker. Unlike the FORMS, in our system no model is required when comparing two shapes to derive the correspondences. 2 Shape Representation We adopt the shape representation framework developed in [9] leading to a unique SA tree. The advantages over other related representations [3, 10, 1, 4, 11, 13, 15, 16] are that (i) we are not seeking a symmetry axis representation but rather, a set of correspondences along the shape contour structured in a tree graph, and (ii) we use a variational approach to establish a measurement on how good the representation of a contour shape is (see Figure 1) 2.1 Shape ....

K. Siddiqi and B. B. Kimia. Parts of Visual Form: Computational Aspects. IEEE PAMI, Vol. 17, No. 3, pp. 239-251, March, 1995.

....spite of the human ease in visually identifying it. Multiscale representations of shape are considered the most promising, due to their ability to take into account the evolution of shape as it is subjected to more and more smoothing. Different forms of scale space descriptions have been proposed [6, 10, 11, 12, 13]. One class of contour tracking and matching methods relies on physical models of the deformation and is based on minimization of an energy function, without first extracting a symbolic representation of the shapes [14, 15, 16, 17] More recently, matching of contours has been addressed with ....

K. Siddiqi and B. Kimia. Parts of Visual Form: Computational Aspects. IEEE Trans. on Pattern Analysis and Machine Intelligence, 17(3):239--251, 1995.

....and merging. A variation of this approachthatmakes the combination of interior and exterior information more explicit is presented byAbeet al... 1]who segment the axes based on dominantpoints detected along the boundary. Based on psychophysical and ecological considerations Siddiqi and Kimia [15] described a partitioning scheme involving twotypes of parts: necks and limbs. Necks were determined by diameters of locally minim al inscribed circles in the region while limbs were lines through pairs of negativecurvature minimahaving co circular boundary tangents (i.e. they join smoothly) ....

K. Siddiqi and B.B. Kimia. Parts of visual form: Computational aspects. IEEE Trans. PAMI, 17(3):239--251, 1995.

.... body of literature on the segmentation of objects, and on representation of object based on part decomposition (see, e.g. 1] for a fairly complete set of references) typically by de ning a set of elementary shapes (generalized cylinders, geons, superquadrics) 13, 15, 5] Siddiqi and Kimia [17] developed a framework for partitioning schemes for shape decomposition and presented a hierarchical partitioning scheme which combines a boundary based and a part based approach. There exist, however, very few proposals working on mesh based representations. An example is the recent work by ....

K. Siddiqi, B.B. Kimia, Parts of Visual Form: Computational Aspects, PAMI, 17(3): 239-251,

....minima of the principal curvatures are mapped to concave cusps in a 2D silhouette. Hence the 3D partitioning rule can be modified for 2D planar curves by dividing 27 an object boundary along the minima of negative curvature, if the boundary is traced counterclockwise. 16 Siddiqi and Kimia [134] argued that proper object partition must involve both object boundary and interior. Therefore, they extended Hoffman and Richard s partition scheme and introduced the concept of part lines, which are curved lines located completely within the interior of the object and terminated on the ....

....of curve segments with 0, 1 or 2 curvature extrema. Leyton [91, 92] constructed symmetric axes by bisecting concave and convex segments from their tips. He further suggested that deformation forces could act on these tip points in the direction of the symmetric axes. Siddiqi and Kimia s [134] neck based and limb based approach of object decomposition also put the terminals of part lines at the concave tips. We exploit local curvature extrema to divide the border into a set of indentation protrusion segments (see Figure 4.2) An indentation protrusion segment is defined as a curve ....

K. Siddiqi and B.B. Kimia. Parts of visual form: computational aspects. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(3), 1995, p. 239251.

....concludes this paper in section 5. 2 Determination of global similarity of 2D object contours According to Ullman [8] there are three main approaches in visual recogniton: the use of invariant properties that are common to all of their views, the use of parts and structural descriptions ( 3] 5] [7]) and the alignment approaches. The presented method belongs primarily to the latter approaches. The basic idea is to find that transformation between two contours, that possesses minimum cost. In [6] we presented a method for the determination of global similarity of 2 different 2D object ....

K. Siddiqi, B.B. Kimia, "Parts of Visual Form: Computational Aspects" , IEEE Transactions On Pattern Analysis and Machine Intelligence (PAMI), Vol. 17, pp. 239-251, 1995.

....and otherwise decompose data into patches. Our view of parts is that they are simply chunks of 2D curves or 3D surfaces that can be found reliably in any data in which they are visible and irrespective of sensor viewing direction. Among the bases for doing this are: a) general shape features [20]; b) geometric primitives [21, 22, 23] c) features pertinent to the restricted set of objects under consideration in a particular application; d) area or volume scale [24] e) complexity [1, 25, 22, 23] 3.1.2 Fast Determination of Patches and Parts Patches are chunks of data which are ....

K. Siddiqi and B. Kimia, "Parts of visual form: computational aspects," IEEE Transactions on Pattern Analysis and Machine Intelligence, May 1995.

....discrimination task used in our experiments requires a representational scheme which is at least two dimensional. There are many models of two dimensional shape representation which are consistent with our results (e.g. Blum (1973) Hoffman and Richards (1985) Biederman (1988) Leyton (1989) Kimia and Siddiqi (1995)) Burbeck, Pizer, Morse, Ariely, Zuberman, and Rolland (1996) have found recent evidence that the medial axis representation first proposed by Blum (1973) is consistent with psychophysical width discrimination experiments. However, as we have demonstrated above, width judgements do not seem to be ....

Kimia, B., & Siddiqi, K. (1995). Parts of visual form: computational aspects. IEEE Trans. Pattern Anal. Machine Intell., 17, 239--51.

....(Hoffman and Richards [9] see Figures 3 and 4, for example. This is the case when the endpoints of convex arcs are located near the points of minimal negative curvature. Also for many objects, the obtained parts of objects correspond to limbs and necks in the theory of Siddiqi and Kimia [16]. For boundaries of continuous objects, the endpoints of maximal convex arcs correspond to inflection points (e.g. inflection points are used for shape description in Freeman [4] The correspondence of the endpoints of maximal convex arcs to different kinds of critical points (in the sense of ....

.... and the length that is normalized with respect to the total length of the boundary curve (see Section 4) Additionally, the relevance measure of visual parts is based on the levels of the shape hierarchy on which they are determined, similarly as it is the case in Kimia et al. 11] see also [16]) Thus, we can obtain a relevance measure together with object parts. In contrary, part decomposition based on points of minimal negative curvature is binary, i.e. the obtained parts cannot be distinguished according to their salience. Our shape decomposition corresponds to the hierarchy of ....

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K. Siddiqi and B. B. Kimia. Parts of Visual Form: Computational Aspects. IEEE Trans. Pattern Analysis and Machine Intelligence 17, 239--251, 1995.

....geiger cs.nyu.edu. 1 2 IAN JERMYN, DAVID JACOBS, AND DAVI GEIGER We use images consisting of closed contours, and try to move to a higher level representation by grouping the interior into parts. This problem has been much studied and is the principle subject of, for example [2, 3, 14, 17, 21, 22, 27]. Much of this work is aimed at understanding shape, because of the fundamental role that this seems to play in object recognition: psychological work, for example [20] suggests that basicor entry level classi cation is highly correlated with shape. Reaching such an understanding is a dicult ....

K. Siddiqi and B.B. Kimia, \Parts of Visual Form: Computational Aspects", IEEE PAMI, Vol. 17, No. 3, pp. 239-251, March, 1995.

....spite of the human ease in visually identifying it. Multiscale representations of shape are considered the most promising, due to their ability to take into account the evolution of shape as it is subjected to more and more smoothing. Different forms of scale space descriptions have been proposed [6, 10, 11, 12, 13]. One class of contour tracking and matching methods relies on physical models of the deformation and is based on minimization of an energy function, without first extracting a symbolic representation of the shapes [14, 15, 16, 17] More recently, matching of contours has been addressed with ....

K. Siddiqi and B. Kimia. Parts of Visual Form: Computational Aspects. IEEE Trans. on Pattern Analysis and Machine Intelligence, 17(3):239--251, 1995.

....hand, many region based methods like [ 3,5,23,13,20,16,24,18,25,26,7,29,14,31,30 ] that use area surrounded by boundary curves concentrated just on finding reliable axis of shapes, which is another type of shapes rather than description usable by computers directly. Other region based methods [ 4,11,22,32,28,27 ] aimed at driving numerical representation by partitioning shapes into their parts based on the psychological observation [21] These methods require an analysis of its axis connections to find branch points where shapes are partitioned into their parts. Zhu [ 32 ] and Sharvit [27] used ....

K. Siddiqi and B. B. Kimia. "parts of visual form: computational aspects". IEEE Trans. Pattern. Anal. Mach. Intell., PAMI-17(3):239--251, 1995.

....spite of the human ease in visually identifying it. Multiscale representations of shape are considered the most promising, due to their ability to take into account the evolution of shape as it is subjected to more and more smoothing. Different forms of scale space descriptions have been proposed [7, 5, 8]. One class of contour tracking and matching methods relies on physical models of the deformation and is based on minimization of an energy function, without first extracting a symbolic representation of the shapes [9, 10] More recently, matching of contours has been addressed with dynamic ....

K. Siddiqi and B. Kimia. Parts of Visual Form: Computational Aspects. IEEE Trans. on Pattern Analysis and Machine Intelligence, 17(3):239--251, 1995.

....extracting a symbolic representation of the shapes [14, 15, 16, 17, 18] Multiscale methods are considered the most promising, due to their ability to take into account variations in shapes due to different degrees of smoothness. Various forms 2 of scale space descriptions have been proposed [19, 20, 21]. In an earlier approach [22] matching is performed through interval trees which are computed by tracking the Curvature Scale Space (CSS) representation [19] from coarser to finer scales. In [23] only the maxima of the CSS curves are used. In [24] it is demonstrated, however, that small shape ....

K. Siddiqi and B. Kimia. Parts of Visual Form: Computational Aspects. IEEE Trans. on Pattern Analysis and Machine Intelligence, 17(3):239--251, 1995.

....a lizard (after [36] neglecting the paws, the dashed lines are curves that represent codons and the small circles are the intersections between them. It can be seen that the intersections naturally identify part joints. Most part segmentation approaches found in the literature (e.g. 9] 1] and [33]) somehow by pass an explicit detection of significant codons by leaping directly to the determination of convex dominant points, which are then used to infer part decomposition. But convex dominant points have a local nature and do not express relationships to other Join point between parts ....

K. Siddiqi and B.B. Kimia. Parts of visual form: computational aspects. IEEE Transaction on Pattern Analysis and Machine Intelligence, 17(3):239--251, March 1995.

....to increase the robustness of the skeleton pyramid construction must take into account the 11 properties of set N . Third, skeleton nodes are often associated with negative curvature minima along the boundary (Symmetry Curvature Duality Theorem[18] Recent publications on shape analysis [35, 39] postulate that decomposition of compound shapes into subparts should take place at negative curvature minima. Consequently, the analysis of skeleton nodes can provide valuable additional information for the shape interpretation task. According to Section 6, the least significant component of the ....

....considered here, the above theorem can be simplified: Boundary segments bounded by negative curvature minima yield symmetry axes which terminate at positive curvature maxima. As has been mentioned before, shape partitioning at negative curvature minima has been repeatedly suggested in literature [35, 39]. Parts and protrusions typically generate branch segments and skeleton nodes associated with boundary sections of negative curvature y . For the time being, the investigation can be thus restricted to the typical shape of a part protrusion as shown in Fig. 11(a) The boundary segment S ....

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K. Siddiqi and B. Kimia, Parts of visual form: Computational aspects, IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-17(3):239--251, 1995.

....active contour tracker. Unlike the FORMS, in our system no model is required when comparing two shapes to derive the correspondences. 2 Shape Representation We adopt the shape representation framework developed in [9] leading to a unique SA tree. The advantages over other related representations [3, 10, 1, 4, 11, 13, 15, 16] are that (i) we are not seeking a symmetry axis representation but rather, a set of correspondences along the shape contour structured in a tree graph, and (ii) we use a variational approach to establish a measurement on how good the representation of a contour shape is (see Figure 1) 2.1 Shape ....

K. Siddiqi and B. B. Kimia. Parts of Visual Form: Computational Aspects. IEEE PAMI, Vol. 17, No. 3, pp. 239-251, March, 1995.

....between object parts [10] It is used when classifying objects into classes and hierarchies. A variation of the task of form segmentation has been applied in motion tracking [14] 13] Form segmentation is a relatively new area of research. Most techniques are applicable only to binary images [26]. The developed approaches face problems of noise sensitivity. Some produce intuitive results which depend on the local object properties [10] The main contibution of this paper is to propose a novel approach that performs the task of form segmentation. The proposed approach is based on the ....

....protrusions, are described as other objects. An advantage of this method is that it detects neck based parts of the object. For a more detailed description consult [12] A difficult problem with current form segmentation approaches is the ability to detect the bottom up top down bottleneck parts [26]. Many approaches do not study the behaviour of the segmentation process under different scales. According to Siddiqi and Kimia [26] a partitioning scheme should be stable with respect to changes in resolution. When moving from a fine to a coarse scale, parts are only removed, not added. Little ....

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K. Siddiqi and B. B. Kimia. Parts of visual form: Computational aspects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(3):239--251, 1995.

....are useful object features for shape recognition or indexing. 3.1 Maximum Invariant Patches and Parts There is not general agreement on the concept of patches and parts, but there are a number of different approaches to the problem. Among the bases for doing this are: a) general shape features [9]; b) geometric primitives; c) features pertinent to the restricted set of objects under consideration in a particular application; d) area or volume scale ; e) complexity. Our view of patches and parts is that they are simply chunks of 2D curves or 3D surfaces that can be found reliably in any ....

K. Siddiqi and B. Kimia, "Parts of visual form: computational aspects," IEEE Transactions on Pattern Analysis and Machine Intelligence, May 1995.

....of maximal trapezoids that is found at the beginning of the process corresponds to narrow trapezoids with almost parallel contour sides, in other words, contour sections that are near each other and almost parallel. Notice the similarity with the concept of neck defined for part segmentation [6]. A neck describes a narrow section of a shape which is a natural part separation. In our case, a narrow trapezoid discards associations between contours parts situated one on one side of the narrow trapezoid and the other part on its other side. This fact may be useful for efficient ....

K. Siddiqi and B. Kimia. Parts of visual form: Computational aspects. IEEE trans. on PAMI, 17(3):239--251, Mar 1995.

....space. In this representation the classical Euclidean scale space corresponds to the special case ff 0 = 0. The authors applied these principles to derive shape descriptors; the generation and classification of different types of singularities, i.e. shocks, provides the shape s fingerprints [50, 74, 75, 94, 95, 51]. In [75] the authors studied a possible extension of these principles to three dimensional shapes. There has also been much interest in the analysis of other scale spaces, which are invariant under certain transformation groups [38] The most important such groups in computational vision (object ....

....other techniques [102] see also Section 3.3) The construction of morphogenetic sequences from a shape attempts to describe and decompose the shape by means of a differential description of these sequences as filter outputs. One of these approaches implements curvature based contour evolution [48, 50, 94, 75, 95, 51], while others use morphological filtering [82] The principles of this approach are relatively simple; however, the interpretation and evaluation of the results is quite limited. Skeleton based decomposition techniques have proved their usefulness in two dimensional shape decomposition and ....

K. Siddiqi and B.B. Kimia. Parts of visual form: Computational aspects. Technical Report LEMS-114, Brown University, Providence, RI, 1994.

....of the objects that are invariant over a wide range of viewing conditions. These include methods that extract global features of the objects and clus ter the images according to these features [16, 7] A second family of methods relies on the part structure of objects for categorization [5, 4, 18, 6, 20, 27, 10]. The underlying assumption of these methods is that objects that belong to the same perceptual category maintain roughly the same set of parts. Finally, there are methods which seek to interpret the perceived shapes in terms of their function [33, 13, 22, 28] Unfortunately, it has been proven ....

K. Siddiqi and B.B. Kimia, 1995. Parts of visual form: computational aspects. PAMI, 17(3):239--251.

....snakes with shapes have previously been discussed, e.g. 6] Differently from their work, we model the deformations explicitly accounting for articulations. Moreover, we claim, our formulation can provide a foundation for object recognition. Interesting new ideas on recognition appeared in [1, 5, 18, 19, 21, 24] with related aspects to our approach. To reduce the computation complexity of our method, we adopt an optimization by parts technique to approximately solve the global optimization problem. Our rational is that the shape similarity measure [2] prefers deformations that preserve the part ....

K. Siddiqi and B. Kimia, "Parts of Visual Form: Computational Aspects," IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-17, March 1995.

....the data base. For 3D range data, the segmentation is often relatively easy to do. For 2D image data, the segmentation is often a major part of the object recognition problem. We feel that in the more complicated situations, the segmentation would either be done with basic existing methods such as [20, 8, 19], or with a partially model based approach which would involve using some of the model recognition methodology from the present paper. The direct approach to the solution of the recognition of the L stored object recognition problem is to take each of the L stored models, transform it (i.e. ....

K. Siddiqi and B. B. Kimia. Parts of visual form: Computational aspects. IEEE Trans. on Pattern Analysis and Machine Intelligence, 17(3):239--251, March 1995.

....are the most sensitive internal regions of the skeleton. 10 However, these graphs are topologically identical. 20 5 Interpretation: Parts from Growth Boundary glitches were considered as noise in x1, but syntactically similar configurations could also denote parts such as limbs or tails [29, 31]. This suggests a closer look at how limbs might arise. In particular, let us consider how objects grow. In Fig. 13, the early development of the amphibious plant Proserpinaca palustris clearly shows an outward branching from an initial body . Notice how negative curvature zones are present at ....

.... the boundary and the perception of parts was first noted by Hoffman and Richards [14] Related work which incorporates properties of the shape s interior includes part definitions in terms of skeleton junctions [6] second order shocks [17] degenerate waves 11 [32] part lines (limbs and necks) [29], and partcuts [15] The latter two proposals advocate a strict partitioning of a shape into disjoint regions, and suggest a number of criteria by which the salience of the constituent parts may be evaluated. Here we depart from the view that that parts should be disjoint sets, as the principle of ....

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K. Siddiqi and B. B. Kimia. Parts of visual form: computational aspects. PAMI, 17(3):239--251, 1994.

....immensely impractical without the use of parts, each of which can be described independently. When an articulated object moves, it is chiefly the configuration of the parts that changes, not their shape; occlusion and alterations affect only particular parts, not the entire object representation [19, 35]. Part representations can therefore support more robust recognition. In computer vision, primitives or boundary induced divisions are two ways of defining the parts of a shape. Some classes of shape primitives that have been considered are superquadrics [31] and geons [5] in which parts are ....

....units from a fixed and standard table of geometrical atoms. Boundary induced divisions have been proposed at orientation discontinuities [2, 16] and negative curvature minima [19] Region based part definitons in terms of skeleton junctions [9] second order shocks [23] neck and limb partlines [35], and degenerate waves [39] have also been proposed. 3.2 Parts from growth Perhaps our motivation for parts needs a biological basis. Siddiqi et al. suggested an ecological characterization of the part problem with a notion of form from function: objects specialize function through their ....

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K. Siddiqi and B. B. Kimia. Parts of visual form: computational aspects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(3):239--251, 1994. 28

....of forming high level object centered models from low level image based features, parts can serve as an intermediate representation. Evidence for part based representations in human vision is strong [1, 11] The computer vision literature is also rich with approaches to partitioning shape, see [14, 13] for a review. For example, Koenderink and van Doorn observe that as evidenced in works of art, elliptic (concave or convex) regions in three dimensional (3D) objects have a thing like character whereas hyperbolic (saddle shaped) regions act only as the glue that holds them together [9] The ....

....this argues for a role for interaction of a shape s boundary points through its region. Third, observe that when the boundaries associated with a negative curvature minima pair do not show evidence for continuation , Figure 3 (top) the decomposition suggested by the minima rule is not intuitive [13]. Again, note the necessary role for regional 1 2 3 Figure 3: Top: In the absence of good continuation , a decomposition based on a pair of negative curvature minima may not be intuitive. Bottom: When a portion of the boundary of a shape is shifted with respect to another portion, narrow ....

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K. Siddiqi and B. B. Kimia. Parts of visual form: Computational aspects. IEEE Trans. Pattern Analysis and Machine Intelligence, To Appear, 1994.

....can be found in [11] 4 Shock Labels Depict Part Anatomy Partitioning prior to figure ground segregation can aid in the segmentation process. It is now argued that shock labels provide evidence for parts in the result of low level processes. A theory for partitioning visual form was proposed in [8] leading to two types of parts: one at necks, or certain locally shortest lines through the shape, and limbs, or curves through two negative curvature minima that smoothly interpolate (a) 4 3 2 1 0 1 2 3 4 (b) 4 0 3 2 1 (c) Rarefaction Regular Initial Orientation Element Figure 8: a) Ideal ....

....meeting a regular wave. c) degenerate shocks arise from two degenerate (rarefaction) waves. the tangent at one point to the tangent at another, Figure 11. The computation of each candidate partline involves computing a measure of salience which is then used to resolve conflicts when they arise [8]. While this framework is developed for partitioning segmented shape, the computations are local with respect to the part line size and can thus be computed prior to figure ground segmentation. We now suggest that a reformulation of this approach in the shock language using shock labels allows ....

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K. Siddiqi and B. B. Kimia. Parts of visual form: Computational aspects. PAMI, 17(3):239--251, March 1995.

....while necks result from narrowings for articulation, e.g. the neck that often exists between a turret and the main body of a tank. These part types are highly correlated with how people break shapes into parts [3] In addition, they satisfy a number of computational constraints for recognition [4]. In particular, they are robust to occlusion, Figure 2, stable with changes in viewing geometry, and are designed to yield functional three dimensional parts. Further, note that parts can cover a range of scales, with small parts being attached to larger ones. For example, at the coarse level a ....

Kaleem Siddiqi and Benjamin B. Kimia. Parts of visual form: Computational aspects. IEEE Trans. on Pattern Analysis and Machine Intelligence, 17(3):239--251, March 1995.

....become neighbors in a deformation process and therefore are similar. In summary, solutions of equation (46) satisfying the entropy condition 1 are the proper physical solutions in the viscosity sense. Although this is not the paper to discuss numerical implementations, we do observe that Sethian [87] proved that simple, Lagrangian, difference approximations require an impractically small time step in order to achieve stability for Hamilton Jacobi equations. The algorithm proposed by Osher Sethian [65, 85] which is based on Hamilton Jacobi theory (and therefore optimal control) has provided ....

K. Siddiqi and B. B. Kimia. Parts of visual form: Computational aspects. IEEE Trans. Pattern Analysis and Machine Intelligence, To Appear, 1994.

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Siddiqi, K., & Kimia, B. B. (1995). Parts of visual form: computational aspects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17, 239--251.

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Siddiqi, K., & Kimia, B. B. (1995). Parts of visual form: computational aspects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17, 239 -- 251.

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Siddiqi, K., & Kimia, B.B. (1995). Parts of visual form: Computational aspects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17, 239--251.

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K. Siddiqi, B., and B. Kimia, "Parts of visual form: Computational aspects," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 3, pp. 239-- 251, 1995.

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K. Siddiqi and B.B. Kimia. Parts of visual form: Computational aspects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(3):239--251, 1995.

No context found.

K. Siddiqi and B.B. Kimia. Parts of visual form: computational aspects. IEEE Transaction on Pattern Analysis and Machine Intelligence, 17(3):239-- 251, March 1995.

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K. Siddiqi and B.B. Kimia. Parts of visual form: Computational aspects. 17(3):239--251, 1995.

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K. Siddiqi, B. B. Kimia, "Parts of Visual Form: Computational Aspects," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 17, No. 3, pp. 239-251, 1995.

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K.Siddiqi and B.B. Kimia, "Parts of visual form: Computational aspects," in Proc. IEEE Conf. on Computer Vision and Pattern Recognition, 1993.

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