Patrice Koehl Department of Computer Science Genome Center Room 4319, Genome Center, GBSF 451 East Health Sciences Drive University of California Davis, CA 95616 Phone: (530) 754 5121 koehl@cs.ucdavis.edu

## Tutorial 2: How to describe a shape: Biological shape descriptors

### Overview

The problem of describing, measuring and comparing shapes arises in image processing when searching for or recognizing objects in an image or a video. This problem is now surfacing in many more disciplines that are generating increase amounts of quantitative and visual information. Biology occupies a central place among these fields of applications. In cellular biology, the measurements of cell morphology and dynamics by imaging techniques such as light or fluorescent microscopy yield large numbers of 2D and 3D images that need to be segmented and quantified. In molecular biology the common assumption that the structure (or shape) of a protein is a major determinant of its function has stimulated the development of many methods for representing, measuring and comparing protein structures. The description of a shape increases in complexity as the object departs from regularity. The objective of most scientists is not necessarily to describe such shapes completely but to identify a small set of attributes of the shape that are information-rich with respect to the problem at hand. We will explore different options for defining such attributes.

### Simple Spherical Harmonics viewer

The viewer below generates at random spherical harmonics of the form:

$$r = \sin(m_0\phi)^{m_1} + \cos(m_2\phi)^{m_3} + \sin(m_4\theta)^{m_5} + \cos(m_6\theta)^{m_7}$$

where $$(r,\theta,\phi)$$ are spherical coordinates. Just press "Generate New" in the Control Panel to generate a new spherical ahrmonics, with the constants m chosen at random, as positive (possible 0) integer values. Wireframe allows you to toggle between "wireframe" and "solid" representation for the spherical harmonics. Your mouse allows you to rotate the image, and zoom in the control panel allows you to change the scale.

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