Edge detection :gradients

Derivatives(just like the theory of the smart car)

Edges in an image is really about the derivatives respect to the image function.As you can see:

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These edges correspond to these extrema of the derivatives.

parital derivatives of an image

First we just make make the derivatives of the x or y directions.As you can see,the different templates we you to get the detivatives.

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sobel operator

It not only watches the center of the op(operator),but also watches the nearby pixel.It is also the default op of the fun() in matlab:imgredientxy()

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And other ops are listed below:

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Matlab basically understand all of these:`

% Gradient Direction
function result = select_gdir(gmag, gdir, mag_min, angle_low, angle_high)
    % TODO Find and return pixels that fall within the desired mag, angle range
    result=gmag>=mag_min&gdir>=angle_low&gdir<=angle_high;
endfunction

pkg load image;

%% Load and convert image to double type, range [0, 1] for convenience
img = double(imread('octagon.png')) / 255.; 
imshow(img); % assumes [0, 1] range for double images

%% Compute x, y gradients
[gx gy] = imgradientxy(img, 'sobel'); % Note: gx, gy are not normalized

%% Obtain gradient magnitude and direction
[gmag gdir] = imgradient(gx, gy);
imshow(gmag / (4 * sqrt(2))); % mag = sqrt(gx^2 + gy^2), so [0, (4 * sqrt(2))]
imshow((gdir + 180.0) / 360.0); % angle in degrees [-180, 180]
%% Find pixels with desired gradient direction
my_grad = select_gdir(gmag, gdir, 1, 30, 60);% 45 +/- 15
%imshow(my_grad);  % NOTE: enable after you've implemented select_gdir

In the real world

What I'v said won't work without some extra handling!
The F(x) in the real word would be like this:

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The noise has cause us to have the positive and negative derivatives all over the place.

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So we basically apply smooth gradients somehow and look for some peaks.
And why we can do that?Because the linearity of the convolution as we can see below.We can apply the f before our derivatives.

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2-D derivatives to find the maximum

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