Digital Image Processing

Introduction to digital images, applications of digital image processing. Elements of visual perception, image acquisition, sampling and quantization. Intensity transformations, histogram processing, spatial filtering, smoothing and sharpening filters, fuzzy set techniques for intensity transformation. Filtering in the frequency domain, 2D sampling and 2D Fourier transform, 2D convolution, aliasing, 1D and 2D discrete Fourier transform (DFT), circulant matrices and convolution. Image restoration, noise models, inverse and pseudo-inverse filter, Wiener filter, regularized least squares filter. Tomographic image reconstruction, the Radon transform, the Fourier-slice (central slice) theorem, reconstruction by filtered back-projections. Color image processing, RGB, CMY, CMYK color models, smoothing and sharpening of color images, color edge detection, noise in color images, Grassman’s laws, chromaticity diagram, color perception and reproduction. Wavelets and multiresolution processing, image pyramids, the Haar transform, sub-band coding, scaling functions, wavelet functions, wavelet series, discrete wavelet transform, continuous wavelet transform, fast wavelet transform, wavelet packets. Morphological image processing, dilation and erosion, opening and closing, the hit-or-miss transform, basic morphological algorithms, morphological image reconstruction, grey-scale morphology.

Objectives

The course aims to introduce the students to digital images and their applications. An extension of 1D fundamental topics to 2D is presented (sampling, convolution, Fourier transform, DFT and circular convolution) and the operation of filtering in the spatial and frequency domains is thoroughly analyzed. The student is also introduced to noise removal as well as to computerized tomography through the Radon transform and the filtered backprojection reconstruction of sinograms. Important part of the course is given to circulant matrices and how they are involved in the formulation of linear and circular convolutions and their application to developing advanced filters (regularized least squares filter, Wiener filter). The student is also introduced to colour spaces and the colour reproduction. Finally, the student is given an overview of 1D and 2D wavelet transform. Significant attention is given to guide the students to program the algorithms presented in the lectures.

Prerequisites

Syllabus

• Introduction to digital images • Intensity transformations and spatial filtering • Filtering in the frequency domain • Image restoration • Tomographic image reconstruction • Color image processing • Morphological image processing • Image segmentation