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In this paper we study the regularity of the solution of an elliptic partial di erential equation with discontinuous coe cients. This result is used to establish the continuous Fr echet di erentiability of a shape functional arising in the optimal shape design of an electromagnet.

We present a novel approach of shape matching and recognition of 3D objects using arti"cial potential "elds. The potential model assumes that boundary of every 3D template object of identical volume is uniformly charged. An initially small input object placed inside a template object will experience repulsive force and torque arising from the potential "eld. A better match in shape between the ...

Shape context descriptors have been a valuable tool in shape description since their introduction. In this paper we examine the performance of shape context descriptors in the presence of noisy human silhouette data. Shape context descriptors have been shown to be robust to Gaussian noise in the task of shape matching. We implement four different configurations of shape context by altering the ...

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Points P1, . . . , Pn in the unit square define a convex n-chain if they are below y = x and, together with P0 = (0, 0) and Pn+1 = (1, 1), they are in convex position. Under uniform probability, we prove an almost sure limit theorem for these chains that uses only probabilistic arguments, and which strengthens similar limit shape statements established by other authors. An interesting feature i...

J. Keesling has shown that for connected spaces X the natural inclusion e : X → βX of X in its Stone-Čech compactification is a shape equivalence if and only if X is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.