We introduce a systematic approach to designing summarizing abstract numeric domains from existing numeric domains. Summarizing domains use summary dimensions to represent potentially unbounded collections of numeric objects. Such domains are of benefit to analyses that verify properties of systems with an unbounded number of numeric objects, such as shape analysis, or systems in which the numb...

Shape analysis of simple closed plane curves is an important subject including many chances of application to industry, especially when the curves are apparent contours of objects projected into the plane. A notion of panorama view is introduced, with presentations of some ideas of its application to the subject.

In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds and Lie groups. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull growth data of Bookstein as well as the analysis of the shape changes associated with aging of t...

We present a new method for morphing 2D and 3D objects. In particular we focus on the problem of smooth interpolation on a shape manifold. The proposed method takes advantage of two recent works on 2D and 3D shape analysis to compute elastic geodesics between any two arbitrary shapes and interpolations on a Riemannian manifold. Given a finite set of frames of the same (2D or 3D) object from a v...

This paper introduces the concept of discrete multidimensional size function, a mathematical tool studying the so-called size graphs. These graphs constitute an ingredient of Size Theory, a geometrical/topological approach to shape analysis and comparison. A global method for reducing size graphs is presented, together with a theorem stating that size graphs reduced in such a way preserve all t...

This paper describes the work that has been done during the first year of the 3-SHIRT project, which aims at developing innovative solutions in all the phases of content-based 3D shape retrieval, namely: shape analysis and segmentation, design of shape descriptors, shape indexing and matching, and evaluation.

In this paper I develop a theory of reasons that has strong similarities to Peter Klein’s infinitism. The view I develop, Framework Reasons, upholds Klein’s principles of avoiding arbitrariness (PAA) and avoiding circularity (PAC) without requiring an infinite regress of reasons. A view of reasons that holds that the ‘reason for’ relation is constrained by PAA and PAC can avoid an infinite regr...

How should we understand reasons-based knowledge? According to the counterfactual or modal account of conclusive reasons, famously defended by Dretske, R is conclusive for P just in case [R would not be the case unless P were the case]. I argue that while knowing is plausibly related to having conclusive reasons to believe, having such reasons cannot be understood in terms of the obtaining of t...

SECTION 2241. "ENFORCEMENT" SPECIFIC PURPOSE OF THE REGULATION. The proposed amendment to the regulation will institute a formal administrative review process to the Department of Transportation's permitting, licensing and enforcement decisions for outdoor advertising. NECESSITY. The proposed amendment to the regulation is necessary to reduce litigation expenses by resolving the issue at a low ...