Visuelle Wahrnehmung: computergestützte Experimente, mathematische Modelle und Simulationen

• Visual perception : computer-based experiments, mathematical models and simulations

Schüller, Anne; Walcher, Sebastian (Thesis advisor)

Aachen : Publikationsserver der RWTH Aachen University (2011)
Dissertation / PhD Thesis

Aachen, Techn. Hochsch., Diss., 2011

Abstract

Depth perception is a very significant and important aspect of human perception. In particular for a person participating in traffic, his or her ability to recognize depth differences is of great importance to their safety as it facilitates assessing the distances to other vehicles or pedestrians. Moreover in many sports a good depth perception is a considerable advantage. Thus, for example, the distance between a ball and the net can be estimated properly. Beyond its significance in everyday life, in the age of 3D movies the topic is of great interest. For students interested in mathematics or biology this topic is rich in content. In the present thesis the topic is made accessible to students with varying background and prior knowledge. The aim of this work is to create authentic learning material which can be applied in schools and first semester courses in college. The material builds on everyday experience, draws on present curricular knowledge, expands and deepens this knowledge, and is relevant in the field of biology. The work is divided into three parts, which can be read separately. The first part deals with experiments on depth perception. The aim is to measure an individual's depth perception. As a first result, subjects create an initial set of data, which shows an s-shaped curve when charted into a coordinate system. For the evaluation of the experiments, the data is fitted with a logistic function. The parameters of the fitted curve provide a threshold from which a measure of the depth perception can be calculated. The data fit is performed on different levels, thus readers with little mathematical knowledge as well as readers who have advanced mathematical knowledge from secondary school can carry out the experiments. A new computer program has been written for conducting the experiments and analysing the data. In addition, worksheets and interactive applets have been created that contribute to the understanding of the data analysis. The second part deals with the geometry of depth perception, with the goal to establish a model of binocular depth perception and analyze it. There are two different approaches to the model analysis, which require different amounts of prior knowledge of the reader. On the one hand, the model is analyzed experimentally by means of interactive applets on the basis of a dynamic geometry system. On the other hand, fundamental formulas and mapping rules are derived by which the model is investigated analytically. Finally, it is shown how appropriate approximation methods greatly simplify the equations and formulas. The third part provides readily usable educational material in the form of a guided program ("Leitprogramm"). It features topics from the first two parts of the work adequately edited for direct application in class.

Institutions

• Chair of Mathematics A [114110]
• Department of Mathematics [110000]
• Mathematics Teaching and Research Area [114220]