A novel groupwise registration framework, called Atlas Building by Self-Organized Registration and Bundling (ABSORB), is proposed in this paper. In this framework, the global structure of relative subject image distribution is preserved during the registration by constraining each subject to deform locally within the learned manifold. A self-organized registration is employed to deform each subject towards a subset of its neighbors that are closer to the global center. Some subjects close enough in the manifold will be bundled into a subgroup during the registration, and then deformed together in the subsequent registration process. This framework performs groupwise registration in a hierarchical way. Specifically, in the higher level, it will perform on a much smaller dataset formed by the representative subjects of all subgroups generated in the previous levels of registration. The atlas image can be eventually built once the registration arrives at the upmost level. Experimental results on both synthetic and real datasets show that the proposed framework can achieve substantial improvements, compared to the other two widely used groupwise methods, in terms of both registration accuracy and robustness.

Support vector machines (SVM) are one of the most useful techniques in classification problems. One clear example is face recognition. However, SVM cannot be applied when the feature vectors defining our samples have missing entries. This is clearly the case in face recognition when occlusions are present in the training and/or testing sets. When k features are missing in a sample vector of class 1, these define an affine subspace of k dimensions. The goal of the SVM is to maximize the margin between the vectors of class 1 and class 2 on those dimensions with no missing elements and, at the same time, maximize the margin between the vectors in class 2 and the affine subspace of class 1. This second term of the SVM criterion will minimize the overlap between the classification hyperplane and the subspace of solutions in class 1, because we do not know which values in this subspace a test vector can take. The hyperplane minimizing this overlap is obviously the one parallel to the missing dimensions. However, this condition is too restrictive, because its solution will generally contradict that obtained when maximizing the margin of the visible data. To resolve this problem, we define a criterion which minimizes the probability of overlap. The resulting optimization problem can be solved efficiently and we show how the global minimum of the error term is guaranteed under mild conditions. We provide extensive experimental results, demonstrating the superiority of the proposed approach over the state of the art.

The task of finding a low-rank (r) matrix that best fits an original data matrix of higher rank is a recurring problem in science and engineering. The problem becomes especially difficult when the original data matrix has some missing entries and contains an unknown additive noise term in the remaining elements. The former problem can be solved by concatenating a set of r-column matrices that share a common single r-dimensional solution space. Unfortunately, the number of possible submatrices is generally very large and, hence, the results obtained with one set of r-column matrices will generally be different from that captured by a different set. Ideally, we would like to find that solution that is least affected by noise. This requires that we determine which of the r-column matrices (i.e., which of the original feature points) are less influenced by the unknown noise term. This paper presents a criterion to successfully carry out such a selection. Our key result is to formally prove that the more distinct the r vectors of the r-column matrices are, the less they are swayed by noise. This key result is then combined with the use of a noise model to derive an upper bound for the effect that noise and occlusions have on each of the r-column matrices. It is shown how this criterion can be effectively used to recover the noise-free matrix of rank r. Finally, we derive the affine and projective structure-from-motion (SFM) algorithms using the proposed criterion. Extensive validation on synthetic and real data sets shows the superiority of the proposed approach over the state of the art.

Partial occlusions in face images pose a great problem for most face recognition algorithms. Several solutions to this problem have been proposed over the years - ranging from dividing the face image into a set of local regions to sophisticated statistical methods. In the present paper, we pose the problem as a reconstruction one. In this approach, each test image is described as a linear combination of the training samples in each class. The class samples providing the best reconstruction determine the class label. Here, ldquobest reconstructionrdquo means that reconstruction providing the smallest matching error when using an appropriate metric to compare the reconstructed and test images. A key point in our formulation is to base this reconstruction solely on the visible data in the training and testing sets. This allows to have partial occlusions in both the training and testing samples, while previous methods only dealt with occlusions in the testing set. We show extensive experimental results using a large variety of comparative studies, demonstrating the superiority of the proposed approach over the state of the art.