Order of Fourier Descriptor Effect on Geometrical Shapes

Shape descriptors are one of the tools commonly used in image processing applications. To enable a computer to be able to tell what the camera sees, the objects in the image need to be described in a systematic computer description. In this paper, the methodology proposed is based on Fourier Descriptor to study features for different geometric shapes (triangle, square, pentagon, and hexagon) with different sizes and different degrees of Fourier transformation. To do that, the shape image is converted to a binary form. The complement image is found for that binary image. Finally, the Fourier descriptor is got for the complemented image. Our work focuses on studying the effect of changing the order of Fourier descriptors when analyzing geometric shapes to study the extent of convergence of the edges of the same shape at different sizes and different order (number of coefficients) of Fourier descriptors. Experiments have proved the stability of the algorithm and its stability with the change in the size of the geometric shape. It is also proved to be stable and unaffected by the order adopted for the Fourier transform. The numerical results have been achieved using MATLAB software.