By Keith Hubbard

An Investigation of Random Number Generation

April 2000

Advisor: Dr. Maria Zack

Abstract:

From nuclear physics simulations to customer response sampling, from data encryption to the Monte Carlo method, computer generated pseudo-random numbers are a necessity for the information age. Many algorithms, both simple and complex, have been created for this purpose with diverse results. The challenge of the modern mathematician in this area is to test these algorithms for the pertinent aspects of randomness that are required in a particular problem. Thus a wide variety of tests have been developed to evaluate the randomness of pseudo-random number generators. The purpose of this project is three fold: first, to research and program various algorithms and tests that have been used in the field; second, to evaluate specific algorithms and classes of algorithms to find the relative strengths and weaknesses of each; and third, to use that information to design a random number generator.

 

By Scott Thompson

Improving Stereo Vision Models Using Genetic Algorithms

April 2000

Advisor: Dr. Jeff McKinstry

Abstract:

Given two pictures of the same scene taken from slightly different points of view (i.e. a stereogram), it is possible to determine the distance from the camera for each point in the scene that is visible in both pictures. This is the basis for human binocular vision, or stereo vision. Much research has been done in the field of computer vision to develop computer software that will take a stereogram and reproduce the three dimensional scene show in the stereogram. Unfortunately, the stereo vision problem has not been solved satisfactorily. Our approach to this problem has been to use the recently proposed techniques of genetic search to automatically find an optimal, biologically based model to perform the task of stereo analysis. The models are modular, multilayered, neural network models with feedback connections, based on the known anatomy of the primate visual system. Neural models are evaluated based on performance on a test suite of artificial stereograms generated using 3D computer graphics which provides the correct depth estimate at each pixel in the stereogram. The performance of our model will be compared against an existing stereo vision model will be compared against an existing stereo vision model on both artificial images with ground-truth, and natural images used in the computer vision literature.

 

By Eric Byrd

Memory Based Models for Stereo Vision

November 1999

Advisor: Dr. Jeff McKinstry

Abstract:

Given two pictures of the same scene taken from slightly different points of view (i.e. a stereogram), it is possible to determine the distance from the camera for each point in the scene that is visible in both pictures. This is the basis for human binocular vision, or stereo vision. Much research has been done in the field of computer vision to develop computer software that will take a stereogram and reproduce the three dimensional scene shown in the stereogram.

Unfortunately, the stereo vision system has not been solved satisfactorily. Our approach to this problem has been to use information gleaned from biological vision systems in order to develop an improved stereo vision algorithm. One remarkable feature of the primate visual system is the vast number of neurons in the primary visual cortex devoted to analyzing each small patch of the visual scene. This number is estimated to be 800,00 neurons per patch. It is known that these neurons respond selectively to visual patterns with different orientation, spatial frequency, and binocular depth. This suggests a memory-based model for stereo vision in which each neuron memorizes a pattern that it has seen before. If each neuron memorizes a different pattern, it would be possible to store a very large number of patterns. If we associate with each memorized pattern the depth of the object that generated the visual pattern, then we could automatically reconstruct the correct depth of similar patterns in the future, thus solving the stereo vision problem. Is it possible to perform accurate stereo analysis with a memory-based model? We tested four different memory based models on the task of stereo vision: nearest neighbor, k-th nearest neighbor, voting, and population coding. We found through empirical measurements that the biologically inspired method of population encoding performed the best on our suite of artificial, gray-scale test images. However, we found that none of these methods performed as well as human perception. In fact, none performed as well as another biologically inspired model of stereo vision found in the literature, the energy model. If primate stereo vision is memory-based as the biological evidence suggest, then a more complex model than those used in this study is required to explain its superior performance.