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.
@cite_33 identified that though the use of inner distance provided invariance to articulations, it could not be directly applied to non-ideal" 2-D projections of 3-D objects. If the projection took place using a weak perspective, then not all parts of the 3-D model would get accurately projected onto the 2-D plane. In order to overcome this problem, they modeled an articulating object as a combination of approximate convex parts and performed affine normalization of these parts. They then use inner distance to perform shape matching on the normalized shapes. Their near-convex decomposition algorithm takes as input the contour of the object and splits the object into multiple convex parts. However, such an approach cannot be followed for shapes such as those shown in Figure , since the algorithm would split the object into multiple parts, yielding undesirable results.
@cite_33
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Given a set of points corresponding to a 2D projection of a non-planar shape, we would like to obtain a representation invariant to articulations (under no self-occlusions). It is a challenging problem since we need to account for the changes in 2D shape due to 3D articulations, viewpoint variations, as well as the varying effects of imaging process on different regions of the shape due to its non-planarity. By modeling an articulating shape as a combination of approximate convex parts connected by non-convex junctions, we propose to preserve distances between a pair of points by (i) estimating the parts of the shape through approximate convex decomposition, by introducing a robust measure of convexity and (ii) performing part-wise affine normalization by assuming a weak perspective camera model, and then relating the points using the inner distance which is insensitive to planar articulations. We demonstrate the effectiveness of our representation on a dataset with non-planar articulations, and on standard shape retrieval datasets like MPEG-7. 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 Many algorithms for both identifying and reconstructing a 3-D object are based on the 2-D silhouettes of the object. In general, identifying a nonconvex object using a silhouette-based approach implies neglecting some features of its surface as identification clues. The same features cannot be reconstructed by volume intersection techniques using multiple silhouettes of the object. This paper addresses the problem of finding which parts of a nonconvex object are relevant for silhouette-based image understanding. For this purpose, the geometric concept of visual hull of a 3-D object is introduced. This is the closest approximation of object S that can be obtained with the volume intersection approach; it is the maximal object silhouette-equivalent to S, i.e., which can be substituted for S without affecting any silhouette. Only the parts of the surface of S that also lie on the surface of the visual hull can be reconstructed or identified using silhouette-based algorithms. The visual hull depends not only on the object but also on the region allowed to the viewpoint. Two main viewing regions result in the external and internal visual hull. In the former case the viewing region is related to the convex hull of S, in the latter it is bounded by S. The internal visual hull also admits an interpretation not related to silhouettes. Algorithms for computing visual hulls are presented and their complexity analyzed. In general, the visual hull of a 3-D planar face object turns out to be bounded by planar and curved patches. > One of the long-standing tasks in computer vision is to use a single 2-D view of an object in order to produce its 3-D shape. Recovering the lost dimension in this process has been the goal of classic shape-from-X methods, but often the assumptions made in those works are quite limiting to be useful for general 3-D objects. This problem has been recently addressed with deep learning methods containing a 2-D (convolution) encoder followed by a 3-D (deconvolution) decoder. These methods have been reasonably successful, but memory and run time constraints impose a strong limitation in terms of the resolution of the reconstructed 3-D shapes. In particular, state-of-the-art methods are able to reconstruct 3-D shapes represented by volumes of at most 323 voxels using state-of-the-art desktop computers. In this work, we present a scalable 2-D single view to 3-D volume reconstruction deep learning method, where the 3-D (deconvolution) decoder is replaced by a simple inverse discrete cosine transform (IDCT) decoder. Our simpler architecture has an order of magnitude faster inference when reconstructing 3-D volumes compared to the convolution-deconvolutional model, an exponentially smaller memory complexity while training and testing, and a sub-linear run-time training complexity with respect to the output volume size. We show on benchmark datasets that our method can produce high-resolution reconstructions with state of the art accuracy.