Fitting 3D morphable models using implicit representations

We consider the problem of approximating the 3D scan of a real object through an affine combination of examples. Common approaches depend either on the explicit estimation of point-to-point correspondences or on 2-dimensional projections of the target mesh; both present drawbacks. We follow an approach similar to [IF03] by representing the target via an implicit function, whose values at the vertices of the approximation are used to define a robust cost function. The problem is approached in two steps, by approximating first a coarse implicit representation of the whole target, and then finer, local ones; the local approximations are then merged together with a Poisson-based method. We report the results of applying our method on a subset of 3D scans from the Face Recognition Grand Challenge v.1.0.

Fully Automatic Segmentation of AP Pelvis X-rays via Random Forest Regression and Hierarchical Sparse Shape Composition

Knowledge of landmarks and contours in anteroposterior (AP) pelvis X-rays is invaluable for computer aided diagnosis, hip surgery planning and image-guided interventions. This paper presents a fully automatic and robust approach for landmarking and segmentation of both pelvis and femur in a conventional AP X-ray. Our approach is based on random forest regression and hierarchical sparse shape composition. Experiments conducted on 436 clinical AP pelvis x-rays show that our approach achieves an average point-to-curve error around 1.3 mm for femur and 2.2 mm for pelvis, both with success rates around 98%. Compared to existing methods, our approach exhibits better performance in both the robustness and the accuracy.

Propositional and situational representations of text

Two informationally equivalent texts were constructed which described a fictitious town, emphasizing its spatial layout. In one version (Survey text), spatial information was in geographic terms, while in the other version (Route text), the equivalent information was provided in the form of directions for driving through the town. Subjects recalled these texts and verified old as well as inference statements. In Experiment I, subjects were able to recall the texts quite well, while showing little ability to use the information they had acquired to make inferences about spatial relations in the town which had not been directly stated in the text. With simpler texts, subjects in Experiment II were able to make infereces, especially when the form of the question corresponded to the version of the text they had read. It was concluded that free recall depended on the construction of a propositional textbase during comprehension, while inferences required a situation model, either in the form of a mental map or a procedural representation of the town. It could be shown that the form of the situation model depended on both the representation invited by the text and subject biases.

Sensory and conceptual representations in memory: Motor images which cannot be imaged

The paper argues for a distinction between sensory-and conceptual-information storage in the human information-processing system. Conceptual information is characterized as meaningful and symbolic, while sensory information may exist in modality-bound form. Furthermore, it is assumed that sensory information does not contribute to conscious remembering and can be used only in data-driven process reptitions, which can be accompanied by a kind of vague or intuitive feeling. Accordingly, pure top-down and willingly controlled processing, such as free recall, should not have any access to sensory data. Empirical results from different research areas and from two experiments conducted by the authors are presented in this article to support these theoretical distinctions. The experiments were designed to separate a sensory-motor and a conceptual component in memory for two-digit numbers and two-letter items, when parts of the numbers or items were imaged or drawn on a tablet. The results of free recall and recognition are discussed in a theoretical framework which distinguishes sensory and conceptual information in memory.

Sparse computation for large-scale binary classification

Well-known data mining algorithms rely on inputs in the form of pairwise similarities between objects. For large datasets it is computationally impossible to perform all pairwise comparisons. We therefore propose a novel approach that uses approximate Principal Component Analysis to efficiently identify groups of similar objects. The effectiveness of the approach is demonstrated in the context of binary classification using the supervised normalized cut as a classifier. For large datasets from the UCI repository, the approach significantly improves run times with minimal loss in accuracy.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.