该系列主要为上Udacity Computer Vision公开课所做的笔记，内容将会涉及一些公开课视频截图，如有侵权请联系删除

Image as A Funciton

Image as A Function

Impulse

面积为1，相当于图片中的基本单位

Correlation vs Convolution

Convolution的结果为Correlation作一次左右翻转再做一次上下翻转。
对于Impulse Image做Filter，Corelation将会得到一个左右、上下翻转后的Filter，而Convolution将会得到Filter本身。
对于对称的Filter,Correlation与Convolution的结果相同

Formula for Correlation and Convolution

Correlation

Convolution

Image Filter

Gaussian Filter

Influence of Sigma

Influence of Sigma in Gaussian Filter

Code

pkg load image;

img = imread('../../resource/sample_img.png');
imshow(img);


%% create a gaussian filter
filter_size = 21;
filter_sigma = 3;
filter = fspecial('gaussian', filter_size, filter_sigma);
smoothed = imfilter(img, filter, 0);

%0
%circular  
%replicate
%symmetric

smoothed = imfilter(img, filter, 'circular');

imshow(smoothed);

Edge Problem

clip filter(black) 0

clip filter

wrap around Circular

wrap around

copy edge Replicate

copy edge

reflect across edge Symmetric

reflect across edge

Unsharp Mask

Salt & Pepper Noise and Median Filter

Salt & Pepper Noise

Median Filter

Median Filter is not linear

Median Filter

Code in Matlab or Octave

noisy_img = imnoise(img, 'salt & pepper', 0.02);
imshow(noisy_img);
%median filter
median_filtered = medfilt2(noisy_img);
imshow(median_filtered);

Filter as Template

2A-L4

Template Matching

从Image中寻找Template

Normalized Correlation

Finding Template

Correlation Map

1-D Case

例如一维信号

onion = [1,2,3,4,5]
peppers = [2,3,4]

其normalized correlation为最大值处就是template所在位置

onion = [1,2,3,4,5]
peppers = [2,3,4]
normxcorr2(onion, peppers);
%-0.86603  -0.50000   1.00000   1.00000   1.00000  -0.50000  -0.86603
%其中结果第一位为
%  2, 3, 4
%        1,2,3,4,5
%第二位
% 2,3,4
%   1,2,3,4,5

2-D Case

function [yIndex xIndex] = find_template_2D(template, img)
    c = normxcorr2(template, img);
    [yRaw xRaw] = find(c == max(c(:)));
    yIndex = yRaw - size(template, 1) + 1;
    xIndex = xRaw - size(template, 2) + 1;
end

Edge Detection

Gradient

Image Gradient

Gradient Matrix

Well-Known Gradient Mask

Sobel Operator

因为大部分图片都是smooth的，所以在计算gradient时可以使用Sobel Operator

Sobel Operator Matrix

在Matlab中，Sobel Operator function没有系数1/8，因此结果为8倍

filt = fspecial('sobel')
% filt = [[1, 2, 1]; [0,0,0], [-1, -2, -1]];

[gx gy] = imgradientxy(img, 'sobel');
% gx gradient in x direction
% gy gradient in y direction
imshow((gx + 4) / 8);  %normalize
imshow(gx, [-4, 4]);

% magnitude and direction
[gmag, gdir] = imgradient(gx, gy);