In this paper, we identify some of the limitations of current-day shape matching techniques. We provide examples of how contour-based shape matching techniques cannot provide a good match for certain visually similar shapes. To overcome this limitation, we propose a perceptually motivated variant of the well-known shape context descriptor. We identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties. We show that our method can easily be augmented with any other shape matching algorithm. We also show from our experiments that the use of our descriptor can significantly improve the retrieval rates.
Due to the diversity involved in shape-matching, it has become difficult to come up with a single measure that incorporates all the requirements. While the use of Euclidean distance is beneficial for identifying certain classes of objects, the use of inner distance favours some others. As a result, researchers have started to fuse two or more techniques while calculating the distance between two shapes. @cite_37 identified that the use of inner distance was overkill" for certain classes of objects and proposed a technique to balance deformability and discriminability. They calculate the cost between two shapes with the help of various distance measures, parameterised by an aspect weight, and retain the best" cost. However, they still use points sampled from the contour and their algorithm would therefore be susceptible to objects with strong base structures that have indentations in their contours.
@cite_37
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The matching of two-dimensional shapes is an important problem with applications in domains as diverse as biometrics, industry, medicine and anthropology. The distance measure used must be invariant to many distortions, including scale, offset, noise, partial occlusion, etc. Most of these distortions are relatively easy to handle, either in the representation of the data or in the similarity measure used. However rotation invariance seems to be uniquely difficult. Current approaches typically try to achieve rotation invariance in the representation of the data, at the expense of discrimination ability, or in the distance measure, at the expense of efficiency. In this work we show that we can take the slow but accurate approaches and dramatically speed them up. On real world problems our technique can take current approaches and make them four orders of magnitude faster, without false dismissals. Moreover, our technique can be used with any of the dozens of existing shape representations and with all the most popular distance measures including Euclidean distance, Dynamic Time Warping and Longest Common Subsequence. Part structure and articulation are of fundamental importance in computer and human vision. We propose using the inner-distance to build shape descriptors that are robust to articulation and capture part structure. The inner-distance is defined as the length of the shortest path between landmark points within the shape silhouette. We show that it is articulation insensitive and more effective at capturing part structures than the Euclidean distance. This suggests that the inner-distance can be used as a replacement for the Euclidean distance to build more accurate descriptors for complex shapes, especially for those with articulated parts. In addition, texture information along the shortest path can be used to further improve shape classification. With this idea, we propose three approaches to using the inner-distance. The first method combines the inner-distance and multidimensional scaling (MDS) to build articulation invariant signatures for articulated shapes. The second method uses the inner-distance to build a new shape descriptor based on shape contexts. The third one extends the second one by considering the texture information along shortest paths. The proposed approaches have been tested on a variety of shape databases, including an articulated shape data set, MPEG7 CE-Shape-1, Kimia silhouettes, the ETH-80 data set, two leaf data sets, and a human motion silhouette data set. In all the experiments, our methods demonstrate effective performance compared with other algorithms For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by: (1) solving for correspondences between points on the two shapes; (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; regularized thin-plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearest-neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits, and the COIL data set.