Applet in Java for the Representation of Shapes Using Fourier Series

Lukas De Oliveira Prestes

Semester Project

Section of Microtechnics, EPFL

July 2013

Abstract

This page presents two demonstration of the use of Fourier Descriptors for shape representation. The shape boundary is represented by N pixels of coordinates x[n] and y[n], the complex sequences z[n] is then formed and the DFT of z[n] is computed. The coefficients of the DFT are called the fourier descriptors of the shape. Any set of FD's corresponds to a closed curve and one can reconstruct the shape by taking a subset of the coefficients. The reconstructed shape will be a smoothed version of the original one and the more coefficients we take into account, the closer we get from the input image. Fourier Descriptors have properties such has invariance in translation, rotation or homothetic that makes them a good tool for the problem of shape classification and shape recognition. Two versions of the demonstration were implemented and are available below.
APPLET
This applet presents an implementation of the FD's for shape representation in Java. The user can choose between for examples of shape to reconstruct, the image takes a few seconds to load due to the preprocessing computations. The scrollbar can be used to change the amount of coefficients used for the shape reconstruction, this amount can be seen in the GUI as well as the gravity center and the area of the shapes. The method for filtering the coefficients can be chosen between 5 methods : low frequencies, high frequencies, largest modulus, smallest modulus and random.
HTML5
This is a simpler implementation of the software to show the possibility of running image processing programs in browsers using javascript. The two images are the input image and it's reconstruction with the amount of coefficients used in the text bar below. The user can modify the number using the arrows around the text field.