Detection Green Balls

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Detection Green Balls

In the following pictures, a green ball is photographed. Detection the green ball is our mission.

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Collect Data

In this problem, I want to map RGB data into HSV data to utilize the color as features.

I use matlab function roipoly to collect HSV data.

There are 19 images as training samples.

The data obtained is (8022,3 ) double array.

Its columns are H,S,V values respectively.

The code to collect HSV data.

close allimagepath = './train';Samples = [];for k=1:19    % Load image    I = imread(sprintf('%s/%03d.png',imagepath,k));        I = rgb2hsv(I);        H = I(:,:,1);    S = I(:,:,2);    V = I(:,:,3);        % Collect samples     disp('');    disp('INTRUCTION: Click along the boundary of the ball. Double-click when you get back to the initial point.')    disp('INTRUCTION: You can maximize the window size of the figure for precise clicks.')    figure(1),     mask = roipoly(I);     figure(2), imshow(mask); title('Mask');    sample_ind = find(mask > 0);        h = H(sample_ind);    s = S(sample_ind);    v = V(sample_ind);        Samples = [Samples; [h s v]]; % append Samples        disp('INTRUCTION: Press any key to continue. (Ctrl+c to exit)')    pauseend

visualization code:

figure, scatter3(Samples(:,1),Samples(:,2),Samples(:,3),'.');title('Pixel Color Distribubtion');xlabel('Red');ylabel('Green');zlabel('Blue');

Choose Model.

In this session, I choose Multivariate Gaussian Model.

$P(x|\mu,\Sigma)=\frac{1}{\sqrt{(2\pi)^{d}}|\Sigma|}e^{-\frac{1}{2}(x-\mu)^{T}\Sigma^{-1}(x-\mu)}$
where $x,\mu,\Sigma$ are matrices.

so, right now we need to use maximum likelihood estimation to learn the parameters $\mu,\Sigma$ .

Parameters Learning

Likelihood function $f(\mu,\Sigma)$ .

$f(\mu,\Sigma)=\sum_{i=1}^{N}ln(\frac{1}{(2\pi)^d|\Sigma|}e^{-\frac{1}{2}(x_{(i)}-\mu)^T\Sigma^{-1}(x_{(i)}-\mu)})$

$=\sum_{i=1}^{N}[-\frac{d}{2}ln(2\pi)-ln(|\Sigma|)-\frac{1}{2}(x_{(i)}-\mu)^T\Sigma^{-1}(x_{(i)}-\mu)]$

$=\sum_{i=1}^{N}[-\frac{d}{2}ln(2\pi)-ln(|\Sigma|)-\frac{1}{2}(x^{T}_{i}\Sigma^{-1}x_{(i)}-\mu^{T}\Sigma^{-1}x_{(i)}-x^{T}\Sigma^{-1}\mu+\mu^{T}\Sigma^{-1}\mu)]$

because $\Sigma^{-1}\Sigma = I$ ,so $\Sigma^{T}(\Sigma^{-1})^{T} = I$ ,and because $\Sigma^{T}=\Sigma$ ,

such that, $\Sigma(\Sigma^{-1})^{T} = I$ , then $(\Sigma^{-1})^{T}=\Sigma^{-1}$ .

$\frac{\partial f}{\partial \mu}=\sum_{i=1}^{N}[-0.5(-\Sigma^{-1}x_{(i)}-(\Sigma^{-1})^{T}x_{(i)}+\Sigma^{-1}\mu+(\Sigma^{-1})^{T}\mu)]$

$=\sum_{i=1}^{N}[-\Sigma^{-1}(x_{(i)}-\mu)]=-\Sigma^{-1}[\sum_{i=1}^{N}x_{(i)}-N\mu]=0$

$\mu=\frac{ \sum_{i=1}^{N}x_{(i)}}{N}$

$\Sigma=\frac{1}{N}\sum_{i=1}^{N}(x_{(i)}-\mu)(x_{(i)}-\mu)^T$

Results

In this example, I chose 0.95 as the threshold. Any pixels whose probability are greater than 0.95 are marked.

At last, the centers of all marked pixels are found by matlab function bwconncomp.

The detection function is displayed as the following:

function [segI, loc] = detectBall(I)% hsv datamu = [0.1565,0.6163,0.5992];sig = [0.0003,-0.0002,-0.0002;-0.0002,0.0191,0.0059;-0.0002,0.0059,0.0024];thre = 0.95;I = im2double(I);I = rgb2hsv(I);mage = reshape(I, 120*160,3);GMM = mvnpdf(mage, mu,sig);GMM = reshape(GMM, 120,160);mage = GMM > thre;bw_biggest = false(size(mage));% all zerosCC = bwconncomp(mage);numPixels = cellfun(@numel,CC.PixelIdxList);[biggest,idx] = max(numPixels);bw_biggest(CC.PixelIdxList{idx}) = true;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Compute the location of the ball center%S = regionprops(CC,'Centroid');loc = S(idx).Centroid; % find centersegI = bw_biggest;end

Thanks for reading, give me a comment if you have any doubts.

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