Lecture Digital image processing: Image transforms - Nguyễn Công Phương

Nguyễn Công Phương DIGITAL IMAGE PROCESSING Image Transforms Contents I. Introduction to Image Processing & Matlab II. Image Acquisition, Types, & File I/O III. Image Arithmetic IV. Affine & Logical Operations, Distortions, & Noise in Images V. Image Transform VI. Spatial & Frequency Domain Filter Design VII. Image Restoration & Blind Deconvolution VIII. Image Compression IX. Edge Detection X. Binary Image Processing XI. Image Encryption & Watermarking XII. Image Classification & Segmentation XIII. Image – Based Object Tracking XIV. Face Recognition XV. Soft Computing in Image Processing sites.google.com/site/ncpdhbkhn 2 Image Transforms 1. Discrete Fourier Transform (DFT) in 2D 2. Wavelet Transform 3. Hough Transform sites.google.com/site/ncpdhbkhn 3 DFT (1) F(u,v) = 1 M −1 N−1 N2 m=0 n=0 um vn f (m,n)e  M N  f (m,n) = 1 N2 M −1 N−1 um vn F(u,v)e  M N  m=0 n=0 • For an image of size M×N. • f(m,n): the image in the spatial domain. • F(u,v): in the Fourier space. sites.google.com/site/ncpdhbkhn 4 DFT (2) • DFT FFT (Fast Fourier Transform). • F(0,0) represents the DC component of the image, which corresponds to the average brightness. • F(N – 1, N – 1) represents the highest frequency. • DFT is used to access the geometric characteristics of a spatial domain image. • In most implementation, the Fourier image is shifted in such a way that the DC value (the image mean), F(0,0), is displayed in the center of the image. The further away from the center an image point is, the higher is its corresponding frequency. sites.google.com/site/ncpdhbkhn 5 ... - tailieumienphi.vn