Measuring Shapes with Desired Convex Polygons.

In this paper we have developed a family of shape measures. All the measures from the family evaluate the degree to which a shape looks like a predefined convex polygon. A quite new approach in designing object shape based measures has been applied.

A new convexity measure for polygons.

Abstract-Convexity estimators are commonly used in the analysis of shape. In this paper, we define and evaluate a new convexity measure for planar regions bounded by polygons. The new convexity measure can be understood as a "boundary-based" measure and in accordance with this it is more sensitive to measured boundary defects than the so called "area-based" convexity measures.

Separating points by parallel hyperplanes--characterization problem.

This paper deals with partitions of a discrete set S of points in a d-dimensional space, by h parallel hyperplanes. Such partitions are in a direct correspondence with multilinear threshold functions which appear in the theory of neural networks and multivalued logic. The characterization (encoding) problem is studied.

The number of N-point digital discs.

A digital disc is the set of all integer points inside some given disc. Let {\cal D}_{N} be the number of different digital discs consisting of N points (different up to translation). The upper bound D(N) = O(N(2)) was shown recently; no corresponding lower bound is known.

On the orientability of shapes.

The orientation of a shape is a useful quantity, and has been shown to affect performance of object recognition in the human visual system. Shape orientation has also been used in computer vision to provide a properly oriented frame of reference, which can aid recognition. However, for certain shapes, the standard moment-based method of orientation estimation fails.

On encoding and enumerating threshold functions.

In this paper, we deal with encoding and enumerating threshold functions defined on n-dimensional binary inputs. The paper specifies situations in which the unique characterization of functions from a given class is preserved by usage of an appropriate set of discrete moments. Moreover, sometimes such a characterization (coding) is optimal with respect to the number of necessary bit rate per coded function.