The outline of a shape can be described in many different ways, with various advantages and disadvantages. For instance, the description provided by a Fourier series has the advantage of being continuously defined, which makes it a good candidate for analysis; typically, the availability of such a description facilitates the determination of the moments of the outline of the shape, as well as those of the shape itself. But, in an image-processing context, shapes are not readily described using Fourier series. Instead, they are given by a collection of pixels, so that their natural description is a list of coordinates—those of the pixels on the boundary of the shape.

In this project, the student will design a Java plugin for ImageJ that takes a binary image as input, detects the outlines of the shapes found in the image, and approximates them by curve representations based on Fourier series. Issues like the adaptation of the number of terms in the series, the control of the quality of the approximation, or the prevention of self-intersections will need to be addressed. The statistics of a curve will then be computed and will give access to the moments of either the curve or the shape (i.e., the surface enclosed by the curve).

Requirements: to be following or to have followed the course on image processing taught by Michael Unser.