[cv]edge detection: gradients

最新推荐文章于 2024-11-22 17:20:11 发布

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本文介绍了如何使用图像处理技术来检测图片中的边缘。主要内容包括理解边缘的基本概念、梯度的数学表示及其在边缘检测中的应用。通过Matlab示例展示了如何实现Sobel算子进行边缘检测，并给出了具体步骤。

部署运行你感兴趣的模型镜像

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
change-boundary

detection edges

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

derivative and edges
differential operator

image gradient
image-gradient

the gradient direction is given by : $tan^{-1}(\frac{\partial f}{\partial y} / \frac{\partial f}{\partial x})$
The amount of change is given by the gradient magnitude: $\left \| \bigtriangledown f \right \|=\sqrt{(\frac{\partial f}{\partial x})^{2}+(\frac{\partial f}{\partial y})^{2}}$
这里写图片描述

finite difference

$\frac{\partial f}{\partial x} \approx \frac{f(x+1 ,y)-f(x,y)}{1}$
it was called right derivative.
finite-difference

differential operator

discrete gradient

sobel 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,_)

sobel-operator0
well-known-gradient

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

corr-gradient

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