Kenneth I. Joy

Sound graphs: A numerical data analysis method for the blind

A system for the creation of computer-generated sound patterns of two-dimensional line graphs is described. The objectives of the system are to provide the blind with a means of understanding line graphs in the holistic manner used by those with sight. A continuously varying pitch is used to represent motion in the x direction. To test the feasibility of using sound to represent graphs, a prototype system was developed and human factors experimenters were performed. Fourteen subjects were used to compare the tactile-graph methods normally used by the blind to these new sound graphs. It was discovered that mathematical concepts such as symmetry, monotonicity, and the slopes of lines could be determined quickly using sound. Even better performance may be expected with additional training. The flexibility, speed, cost-effectiveness, and greater measure of independence provided the blind or sight-impaired using these methods was demonstrated.

Piecewise optimal triangulation for the approximation of scattered data in the plane

Abstract We present an efficient algorithm to obtain a triangulated graph surface for scattered points (x i y i ) T , i=1,…,n, with associated function values fi. The maximal distance between the triangulated graph surface and the function values is measured in z-direction (z=f(x,y)) and lies within a user-defined tolerance. The number of triangles is minimized locally by adapting their shapes to different second-degree least squares approximations of the underlying data. The method consists of three major steps: 1. subdividing the given discrete data set into clusters such that each cluster can be approximated by a quadratic polynomial within a prescribed tolerance; 2. optimally triangulating the graph surface of each quadratic polynomial; and 3. “stitching” the triangulations of all graph surfaces together. We also discuss modifications of the algorithm that are necessary to deal with discrete data points, without connectivity information, originating from a general two-manifold surface, i.e., a surface in three-dimensional space that is not necessarily a graph surface.

Streaming Aerial Video Textures.

We present a streaming compression algorithm for huge time-varying aerial imagery. New airborne optical sensors are capable of collecting billion-pixel images at multiple frames per second. These images must be transmitted through a low-bandwidth pipe requiring aggressive compression techniques. We achieve such compression by treating foreground portions of the imagery separately from background portions. Foreground information consists of moving objects, which form a tiny fraction of the total pixels. Background areas are compressed effectively over time using streaming wavelet analysis to compute a compact video texture map that represents several frames of raw input images. This map can be rendered efficiently using an algorithm amenable to GPU implementation. The core algorithmic contributions of this work are methods for fast, low-memory streaming wavelet compression and efficient display of wavelet video textures resulting from such compression.