Characterizing finitely based abelian Mal’cev varieties

The purpose of this paper is to recover dense correspondence between non-rigid shapes for anatomical objects, which is a key element of disease diagnosis and analysis. We proposed a shape matching framework based on Markov random fields to obtain non-rigid correspondence. We constructed an energy function by summing up two terms where one was a unary term and the other was a binary term. By using this formulation, shape matching was represented as an energy function minimisation problem. Loopy belief propagation (LBP) was then used to minimize the energy function. We adopted a new sparse update technique for LBP update to increase computational efficiency. At the same time, we also proposed to use a novel clamping technique, an expectation-maximization (EM) like approach, to enhance matching accuracy. Experiments with the hippocampal data from OASIS and PATH showed that the sparse update was 160 times faster than standard BP. By iteratively running the EM-like clamping procedure, we were able to obtain high quality non-rigid correspondence results to achieve 97% matching rate between two hippocampi. Our shape matching based approach overcomes the flip problem of first-order ellipsoid and does not assume pre-alignment unlike iterative closest point.

Clustering as physically inspired energy minimization

We formulate the pigmented-skin-lesion (PSL) matching problem as a relaxed labeling of an association graph. In this graph labeling problem, each node represents a mapping between a PSL from one image to a PSL in the second image and the optimal labels are those optimizing a high order Markov Random Field energy (MRF). The energy is made up of unary, binary, and ternary energy terms capturing the likelihood of matching between the points, edges, and cliques of two graphs representing the spatial distribution of the two PSL sets. Following an exploration of various MRF energy terms, we propose a novel entropy energy term encouraging solutions with low uncertainty. By interpreting the relaxed labeling as a measure of confidence, we further leverage the high confidence matching to sequentially constrain the learnt objective function defined on the association graph. We evaluate our method on a large set of synthetic data as well as 56 pairs of real dermatological images. Our proposed method compares favorably with the state-of-the-art.

Water-fat separation incorporating spatial smoothing is robust to noise

Abstract. We propose a real time indoor corridor layout estimation method based on visual Simultaneous Localization and Mapping (SLAM). The proposed method adopts the Manhattan World Assumption at indoor spaces and uses the detected single image straight line segments and their corresponding orthogonal vanishing points to improve the feature matching scheme in the adopted visual SLAM system. Using the proposed real time indoor corridor layout estimation method, the system is able to build an online sparse map of structural corner point features. The challenges presented by abrupt camera rotation in the 3D space are successfully handled through matching vanishing directions of consecutive video frames on the Gaussian sphere. Using the single image based indoor layout features for initializing the system, permitted the proposed method to perform real time layout estimation and camera localization in indoor corridor areas. For layout structural corner points matching, we adopted features which are invariant under scale, translation, and rotation. We proposed a new feature matching cost function which considers both local and global context information. The cost function consists of a unary term, which measures pixel to pixel orientation differences of the matched corners, and a binary term, which measures the amount of angle differences between directly connected layout corner features. We have performed the experiments on real scenes at York University campus buildings and the available RAWSEEDS dataset. The incoming results depict that the proposed method robustly performs along with producing very limited position and orientation errors.

We introduce the binary discriminator and the dual binary discriminator and the corresponding universal algebras with 0. The latter are related to permutability and distributivity at 0. For A finite the dual binary discriminator is in the intersection of all maximal subclones of the clone of all f satisfying f (0,...,0) = 0 (except certain maximal subclones if A is of prime power cardinality). An algebra with a special binary term function and a special unary term function is a dual binary discriminator algebra if and only if it is ideal-free. Finally we characterize binary and dual binary discriminator varieties.