We consider the problem of computing large connected regions in a triangulated terrain of size n for which the normals of the triangles deviate by at most some small fixed angle. In previous work an exact near-quadratic algorithm was presented, but only a heuristic implementation with no guarantee was practicable. We present a new approximation algorithm for the problem which runs in O(n∈2) time and---apart from giving a guarantee on the quality of the produced solution---has been implemented and shows good performance on real data sets representing fracture surfaces consisting of around half a million triangles. Further we present a simple approximation algorithm for a related problem: given a set of n points in the plane, determine the placement of the unit disc which contains most points. This algorithm runs in linear time as well.

Chirp signal, a finite duration pulse with linear frequency modulation (LFM) is the signal waveform widely used for coherent image formation. Coherent imagery is derived essentially as a 2-dimensional correlation of received, delayed chirp waveform with a 2-dimensional matched filter. There is wide and active research interest in analyzing coherent imagery at multiple scales for multiresolution speckle reduction, clutter separation from desired targets and other low level vision requirements such as multiple scale segmentation, etc. This paper attempts to address these requirements during the image formation process; i.e., obtaining multiple resolution imagery by signal correlation at multiple scales. We derive a shift and scale invariant DWT algorithm, which functions as the cornerstone for such multiple scale correlation. We also briefly discuss implications of this image formation algorithm with particular attention to speckle reduction.