# Transform Methods in Image Processing

S. Allen Broughton

MHC Faculty Seminar in Mathematics
Spring Term 2001 @ Mount Holyoke College

### Abstract

This web page contains the notes and supporting scripts for a series of lectures on transform methods in image processing. The talks focus on various vector and matrix  models of processing with a view towards:
• discretely and finitely sampled signals such as audio clips and images
• computational methods, employing chiefly Matlab tools

### Lectures

#### Lecture 1: Introduction to signal and image processing and various transform examples

• Lecture Notes in pdf format - printout of power point file: (32 pages 121K) MHCSemLect1.pdf
• Matlab Scripts used - Image processing toolbox used, all scripts are small text files.
• Edge detection script  edgedet.m
• Blurring 8-bit color vs monochrome  eightbit.m
• Denoising a signal via truncation of the DFT dftdemo.m
• 1D analysis and synthesis wave forms for the DFT  waveformsDFT.m
• 1D analysis and synthesis of signal with the Discrete Cosine Transform analsynDCT.m
• 1D analysis and synthesis of signal with the Discrete Wavelet Transform analsynDWT.m
• DFT performance fftperform.m
• Split a matlab image with color index map into its three components RGBOpic.m
• Split a jpeg image into three three RGB colour matrices jpg2rgb.m
• Maple Scripts
• Various model waveforms, periodic exponential, discrete exponential waveforms on ZN, windowed exponential waveforms, and continuous wavelets  modelwaveforms.mws  (99K)
• The Windowed Fourier Transform wft.mws (550K)
• The Continuous Wavelet Transform cwt.mws (401K)
• Images from Demos

#### Lecture 2: The discrete Fourier transform  (DFT) and filtering/convolution (signal and images)

• Lecture Notes  pdf format - printout of LaTeX  (24 pages 345K) MHCSemLect2.pdf
• Matlab Scripts
• Visualization of  "frequency contributions" of model wave forms to a signal and the associated DFT dft1demo3.m
• Polar decomposition of 2D waveforms  wavefft2cband.m
• High and low pass frequency filtering demo (smoothing and differencing) hilopassdemo.m
• Demonstration of smoothing an image with a moving mask. smoothimage.m
• 1D and 2D implementations of circular convolution circconv.m, circconv2.m
• Frequency response demonstration - filtering a pure wave form filterwavedemo.m
• Plot magnitude and phase  frequency response for a filter freqrespplot.m
• Restoration script  ansmid3.m
• Maple Scripts

#### Lecture 3: Finish up Lecture 2

• Image discussed after seminar on fft performace as a functionof  N =datasize (fftperform.pdf )