Digital image processing assignment

Name:v.b.akilesh arigelaReg no:11bec0086Slot:c1Prof:arulmozhivarman p

Assignment no:20

Aim 1:To determine the lines of required length using Hough transform.Introduction:To manually extract the line information from an image can be very tiring and time-consuming especially if there are many lines in the image. An alternate method is preferable, but is not as trivial as edge detection since one has to determine which edge point belongs to which line, if any. The Hough-transform makes this separation possible and is the method we have used in our program for line detection.Theory of Hough transform:It transforms between the Cartesian space and a parameter space in which a straight line (or other boundary formulation) can be defined.Lets consider the case where we have straight lines in an image. We first note that for every point (x,y) in that image, all the straight lines passing through that point satisfy Equation 1 for varying values of line slope and intercept (m ,c) Y=mx+c ..eqn 1yx

Lines through a point in the Cartesian domain.At this point, it is easy to see that each different line through the point (x,y) corresponds to one of the points on the line in the (m c,c) space.Now, consider two pixels P1 and P2, which lie on the same line in the(x,y ) space. For each pixel, we can represent all the possible lines through it by a single line in the (m ,c ) space. Thus a line in the (x ,y ) space that passes through both pixels must lie on the intersection of the two lines in the (m ,c ) space, which represent the two pixels. This means that all pixels which lie on the same line in the (x ,y ) space are represented by lines which all pass through a single point in the (m ,c ) space, see Figures belowxyP1P2Line L

Points on the same line.mcP1P2Line L

The mapping of P1 and P2 from Cartesian space to the (m ,c ) space.

Algorithm:Following the above theory the below algorithm was developed to detect the lines in the image.1.Input the image2. Use the hough function to detect lines in an image.The function returns H, the Hough transform matrix. theta (in degrees) and rho are the arrays of rho and theta values over which hough generates the Hough transform matrix.3. Locate peaks in the Hough transform matrix H, generated by the hough function.4. Extract line segments in the image BW associated with particular bins in a Hough transform (with given requirements).5.Plot the beginning and ends of the lines.Matlab code:clc;I = imread('pea1.jpg');rotI = imrotate(I,360,'crop');bw_I = rgb2gray(rotI);BW = edge(bw_I,'canny');[H,T,R] = hough(BW);imshow(H,[],'XData',T,'YData',R,... 'InitialMagnification','fit');xlabel('\theta'), ylabel('\rho');axis on, axis normal, hold on;P = houghpeaks(H,120,'threshold',ceil(0.3*max(H(:))));x = T(P(:,2)); y = R(P(:,1));plot(x,y,'s','color','white');% Find lines and plot themlines = houghlines(BW,T,R,P,'FillGap',3,'MinLength',11);figure, imshow(rotI), hold onmax_len = 0;for k = 1:length(lines) xy = [lines(k).point1; lines(k).point2]; plot(xy(:,1),xy(:,2),'LineWidth',2,'Color','green'); % Plot beginnings and ends of lines plot(xy(1,1),xy(1,2),'x','LineWidth',2,'Color','yellow'); plot(xy(2,1),xy(2,2),'x','LineWidth',2,'Color','red');end

Results:Input image

Output image:

Transform bin image that represents number of peaks:

Conclusion:The classical Hough transform was concerned with the identification oflinesin the image, but later the Hough transform has been extended to identifying positions of arbitrary shapes, most commonly circles or ellipses.

Aim 2:To experiment hough circle detector.Algorithm:1.read the given image.2.set minimum amd maximum radii of circles to be detected.3. Find circles using circular Hough transform. (function is imfindcircles)4. draw circles with specified centers and radii on to the current axes.Matlab code:clc;A = imread('cir.jpg');imshow(A)Rmin = 8;Rmax = 60;[centersBright, radiiBright] = imfindcircles(A,[Rmin Rmax],'ObjectPolarity','bright');[centersDark, radiiDark] = imfindcircles(A,[Rmin Rmax],'ObjectPolarity','dark');viscircles(centersBright,radiiBright,'EdgeColor','b');viscircles(centersDark, radiiDark,'LineStyle','--');

Results:

Input image

Output image:

Similarly when another image that dont contain perfect circles is gives the results are as follows.Input image

Output image:

Limitations:The Hough transform is only efficient if a high number of votes fall in the right bin, so that the bin can be easily detected amid the background noise. This means that the bin must not be too small, or else some votes will fall in the neighboring bins, thus reducing the visibility of the main bin.Use of the Hough transform on noisy images is a very delicate matter and generally, a denoising stage must be used before.

References:Mathworks.comWikipediaJensen, Jeppe."Hough Transform for Straight Lines". Retrieved 16 December 2011.

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