[cv] linearity and convolution

Linearity:

An operator or system H is linear if two properties hold:

1. Additivity:

    H(f1+f2) = H(f1) + H(f2)

2. scaling  multiplicative

    H(a*f1) = a*H(f1)

where f1, f2 are functions, a is a constant.

impulse function: 

an idealized function whose area is 1.

its width is near to 0, but its height is +inf.

impulse response:

correlation and convolution

if filter is symmetric, the correlation filter and convolution filter is the same.

shift invariant - property of convolution operation

also, convolution is a linear operation.

at sometimes, filter is separable.

Boundary issues

full : dimensions of  output image becames larger.

same: dimensions of output image remain the same.

valid: dimensions of output image decreased

% Explore edge options
pkg load image;

%% Load an image
img = imread('fall-leaves.png');  % also available: peppers.png, mandrill.png
imshow(img);


%% Create a Gaussian filter
height = 15;
sigma =  2;

filter_g = fspecial('gaussian', height, sigma);


%% 
out_img = imfilter(img,filter_g,'symmetric'); % 0 replicate, circular, symmetric
imshow(out_img);

fill zeros:

circular:

symmetric

sharpen filter

加倍的像素值减去周围像素信息可以将图片锐化。

unsharp mask makes picture sharper.

median filter

% Apply a median filter
pkg load image;

%% Read an image
img = imread('moon.png');  % also try: brooklyn-bridge.png, penny-farthing.png
imshow(img);

%% Add salt & pepper noise
noiseimg = imnoise(img, 'salt & pepper', 2);
imshow(noiseimg);
img1 = medfilt2(noiseimg); % add median filter
imshow(img1);