Spatial Domain Filtering

Fourier Transform

2-D Fourier Transform

Spatial Frequency

Fourier Transform Shift

Fourier Transform Rotation

Sample 2-D Fourier Transforms

Power Spectra

Image Enhancement in the

Frequency Domain

2-D Fourier Transform

2-D High- & Low-Pass Filters

2-D Notch Filter

Low-Pass Filtering in Frequency Domain

Non-linear Filtering

1D Convolution

2D Convolution

Computation Requirements

2D Transforms as 1D Computations

Sample C Code for Spatial Processing

Spatial Derivatives

Edge Processing

More Edge Processing

Second Order Derivatives

2D Edge Finding

Edge Location

Sharpening

Digital Image Processing, 2nd ed.www.imageprocessingbook.com

Chapter 2: Digital Image Fundamentals

MATLAB/Image Processing Toolbox

function [rt, f, g] = twodsin(A,u0, v0, M, N)% TWODSIN Compares for loops vs. vectorization.% The comparison is based on implementing the function% f(x,y)=Asin(u0x+v0y) for x=0,1,2,…,M-1 and% y=0,1,2,…,N-1. The inputs to the function are% M and N and the constants in the function.% GWE, Example 2.13, p.57

% First implement using for loopstic %start timingfor r=1:M u0x=u0*(r-1); for c=1:N v0y=v0*(c-1); f(r,c)=A*sin(u0x+v0y); endendt1=toc; % End timing

% Now implement using vectorizationtic %start timingr=0:M-1;c=0:N-1;[C,R]=meshgrid(c,r);%special MATLAB function for fast 2D function evaluations% creates all the (x,y) pairs for function evaluationg=A*sin(u0*R+v0*C);

t2=toc; %End timing

%compute the ratio of the two timesrt=t1/(t2+eps); %use eps in case t2 is close to zero.

>> [rt,f,g]=twodsin(1, 1/(2*pi), 1/(4*pi), 512, 512);>> rt rt = 34.2520 % I only got ~19 on my old machine.>>g=mat2gray(g);>> imshow(g) %show in separate window.

imshow (f)%f is an image array

imwrite(f, ‘filename’)% filename MUST contain a recognized file format extension% .tif or .tiff identify TIFF% .jpg identifies JPEG% additional parameters for tiff and jpeg identify compression, etc.

imfinfo filename% returns all kind of useful file information such as size

g=imread(‘filename’)% filename MUST contain an appropriate extension

indexed

intensity

RGBbinary

General matrix

rgb2ind

rgb2gray

mat2gray

ind2graygray2ind

ind2rgb

bw2ind

One pixel

1 2 3 N

>> h=imhist(f) %any previously loaded image % must be gray scale image>> h1=h(1:10:256) %create bins for horiz axis>> horz=1:10:256; %>> bar(horz, h1) %>> axis([0 255 0 15000]) %expand lower range of y-axis>> set(gca, ‘xtick’, 0:50:255) %gca means ‘get current axis’>> set(gca, ‘ytick’, 0:2000:15000) %lab h & v ticks

See GWE, p.77-78

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