[cv]edge detection: gradients

usually, filter is used to find a specific pattern in the pictures.
If we want to find lines and edges in the picture, firstly we think about gradients.
画图的时候，光画出线条就可以表达很多信息。
不要轻视线条，其中包含了太多的信息。

edges

线条的成因：
1. 物体表面的不连续，形状变化
2. 表面颜色不连续
3. 光照强度不连续
4. depth discontinuity，物体与背景的差异

detection edges

recall images as functions.
each location (x,y) has a value.

in the above picture, edges like the steep cliffs.
so, our basic idea: find a neighborhood with strong signs of change.
But, there are two problems:
1. neighborhood size
2. how to detect changes

derivative and edges

differential operator

image gradient

the gradient direction is given by : tan−1(∂f∂y/∂f∂x)
The amount of change is given by the gradient magnitude:∥▽f∥=(∂f∂x)2+(∂f∂y)2−−−−−−−−−−−√

finite difference

∂f∂x≈f(x+1,y)−f(x,y)1
it was called right derivative.

differential operator

sobel operator

in matlab, there is a function imgradientxy which uses sobel operator but isn’t divided by 8.
So you need add a step to get that output divided by 8.

imgradientxy - Directional gradients of an image
This MATLAB function returns the directional gradients, Gx and Gy, the same size
as the input image I.
[Gx,Gy] = imgradientxy(I)
[Gx,Gy] = imgradientxy(I,method)
[gpuarrayGx,gpuarrayGy] = imgradientxy(gpuarrayI,_)

filter = fspecial('sobel'); % y direction
res = imfilter(double(img), filter);
imagesc(res);
colormap gray;
imshow(res);

imfilter function use correlation by default.

% 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