The Alignment of Objects With Smooth Surfaces: Error Analysis of the Curvature Method

The recognition of objects with smooth bounding surfaces from their contour images is considerably more complicated than that of objects with sharp edges, since in the former case the set of object points that generates the silhouette contours changes from one view to another. The "curvature method", developed by Basri and Ullman [1988], provides a method to approximate the appearance of such objects from different viewpoints. In this paper we analyze the curvature method. We apply the method to ellipsoidal objects and compute analytically the error obtained for different rotations of the objects. The error depends on the exact shape of the ellipsoid (namely, the relative lengths of its axes), and it increases a sthe ellipsoid becomes "deep" (elongated in the Z-direction). We show that the errors are usually small, and that, in general, a small number of models is required to predict the appearance of an ellipsoid from all possible views. Finally, we show experimentally that the curvature method applies as well to objects with hyperbolic surface patches.

Bit-Width Analysis for General Applications

It has been widely known that a significant part of the bits are useless or even unused during the program execution. Bit-width analysis targets at finding the minimum bits needed for each variable in the program, which ensures the execution correctness and resources saving. In this paper, we proposed a static analysis method for bit-widths in general applications, which approximates conservatively at compile time and is independent of runtime conditions. While most related work focus on integer applications, our method is also tailored and applicable to floating point variables, which could be extended to transform floating point number into fixed point numbers together with precision analysis. We used more precise representations for data value ranges of both scalar and array variables. Element level analysis is carried out for arrays. We also suggested an alternative for the standard fixed-point iterations in bi-directional range analysis. These techniques are implemented on the Trimaran compiler structure and tested on a set of benchmarks to show the results.