Region Matching with Missing Parts

Abstract

We present a variational approach to the problem of registering planar shapes despite missing parts. Registration is achieved through the evolution of a partial differential equation that simultaneously estimates the shape of the missing region, the underlying "complete shape" and the collection of group elements (Euclidean or affine) corresponding to the registration. Our technique applies both to shapes, for instance represented as characteristic functions (binary images), and to grayscale images, where all intensity levels evolve simultaneously in a partial differential equation. It can therefore be used to perform "region inpainting" and to register collections of images despite occlusions. The novelty of the approach lies on the fact that, rather than estimating the missing region in each image independently, we pose the problem as a joint registration with respect to an underlying "complete shape" from which the complete version of the original data is obtained via a group action.

Video-based descriptors for object recognition

“…(15), for the AmbientLambert case, has been discussed in [36], [37] and [38] in the presence of one or multiple occluding layers, respectively, and in particular in [39] it can be shown to be equivalent (under the Lambertian assumption) to image-to-image matching as described in Section 2.6. Once TST has been performed (yieldingĝ i ), and the residual computed (yieldinĝ ν i ), sample-based approximations for the nuisance distributions can be obtained, for instance…”

Prior-based Segmentation and Shape Registration in the Presence of Perspective Distortion

“…Expressing the planar-projective transformation within the energy functional (13) in terms of relative camera-object motion (R, t) and plane structure (n, d) rather than via the homography matrix is a considerable shortcut toward the recovery of these parameters. The cumbersome task of decomposing the homography matrix [15,18,27] is avoided.…”

“…In order to minimize the energy functional (13), one has to apply a gradient descent process that calls for the evaluation of φ simultaneously with the recovery of the transformation T p of the functionφ. We demonstrate this for transformations T p that consist of translation and rotation of the generalized cone, and correspond to scaling, translation, rotation and perspective distortion in the image.…”

“…Several works, for example [12,13,35,39], use the distance function as the level-set and the square difference between level-sets as the shape dissimilarity measure. A symmetric and unbiased modification of this shape distance (called pseudo distance) has been recently suggested by Cremers and Soatto [10].…”

Shape-Based Mutual Segmentation

“…Note that when more than two object instances are available, this ambiguity can be resolved by applying a majority rule [9]. Having only two images, we favor the image partitioning that minimizes a biased shape dissimilarity measure between the images.…”