Dear Ahmed Tarawneh,

Look the link. May be useful.

http://docs.opencv.org/3.0-beta/doc/py_tutorials/py_imgproc/py_contours/py_contours_more_functions/py_contours_more_functions.html

http://docs.opencv.org/2.4/modules/imgproc/doc/structural_analysis_and_shape_descriptors.html

https://www.youtube.com/watch?v=DEHk-5xbJhU

Regards,Shafagat

Thank you for replying me Prof. Shafagat, actually, I searched about convexity defects using open-CV but I have got nothing but a ready-made function that I can use as a black box, I really want an explanation of the theory behind these points (defects) and how I can found it theoretically, thus make me able to programmed it using any programming language, I saw some research papers that used defects, but unfortunately without any explanations.

sorry this is out my interest. I can help in this regard.

best wishes to you

walid  

You could calculate the angle between each successive line-segment pair. Depending on how the line-segments run (clockwise or anti-clockwise), angles greater than (or less than)180 degrees are concavities. However, you then get all concavities...

In this case, following heuristic might also work: evaluate all points that are between two successive convex-hull points. The point that has the longest perpendicular distance to the line connecting the two convex-hull points, probably is the point you are looking for. 

Finally, I think it works, I actually calculate the angle between two vectors (A,B) and (A,C) where B and C supposed to be the Convex-hull points and A represents the points neighbouring (under) convex-hull pair as shown in the Figure below, then theta is calculated using the equation: theta= acos((vector1 . vector2) / (Len(vector1)+Len(vector2))), theta is calculated for each point then I select the max theta, the point that has the max theta shown in figure as a green point.

Thank you Mr. Lambert Zijp, Please let me know if you have any comments on what you've done.

All appreciation and gratitude for all of you

The equation you use looks a lot like the dot-product of two vectors, except that the length of the two vectors should be multiplied; not added.

https://en.wikipedia.org/wiki/Dot_product

Yes, finding the smallest theta (not max theta) could work too.

The curvature measures in the following papers could also be of interest:

C. Zhang, C. Sun, R. Su, and T. D. Pham, Clustered nuclei splitting via curvature information and gray-scale distance transform, Journal of Microscopy, 259(1):36-52, July 2015.  http://dx.doi.org/10.1111/jmi.12246

C. Zhang, C. Sun, and T. D. Pham, Segmentation of Clustered Nuclei Based on Concave Curve Expansion, Journal of Microscopy, 251(1):57-67, July 2013. http://dx.doi.org/10.1111/jmi.12043

This is an excellent question.   Many thanks for posting it.

Also, the replies given so far are very helpful.

Sir, I  do not know if this helps but you could use corner detectors to detect all the corners. Harris corner detector is commonly used and you can look it up on wiki for the mathematical part.

Then for the finger tips you could use the fact that the finger tip is usually the highest in the locality of the curve connecting the nearest points. The roots can be found by assuming that they lie between two high corners and the difference in height is very pronounced.

The dot product approach is also simple  and can be very useful

Another better solution to find defects using Matlab:

step 1: Compute the convex hull to produce ConvHull as a binary image(as shown in the figure below  (this can be done easily in Matlab be using  bwconvhull() command

step 2: subtract the origin image (mask) from the convex hull mask that produced in the previous step, all defects will appear as a white regions (see the figure).

step 3: find the connected regions by using bwconncomp(), (discard the smallest regions).

step 4: for each region find the point that has the smallest distance from the centroid point e.g using ED or MD

Dear Mr. Tarawneh.

I have been trying to implement what you said (Sequence of steps you followed to find convexity defects on matlab) so far I failed at step 4 

Can you help me through?

Hi Ahmed,

Using bwconncomp() command, all white regions will be stored in a cell structure,

each cell element i.e cell(N) contains array of points that belonging to one region, So for each cell(N) points you should compute the distance between that points (each one) and the center point ( Center point of the shape in the first image ) using any one of distance metrics e.g Euclidean distance ED, Manhattan distance MD .. etc, now, the point that has the smallest distance is the point that you want (finger root). complete the procedure for all cell elements.

The bwconncomp returns either PixelIdxlist or NumObjects, which one of them

For more clarification:

d=c-b;    % b,c and d are the first, second and third im respectively

CC = bwconncomp(d);

reg=CC.PixelIdxList;    %reg regions cell

[~,I] = sort(cellfun(@length,reg),'descend');

reg = reg(I);

for i=1:5      % 5 is # of cell elements (regions) -problem dependent-

idx=reg{1,i};

[y,x] = ind2sub([re ce],idx);   % re # of row in the image and ce # of col

newidx=cat(2,x,y);                 % newidx points of region

for j=1:length(newidx)    %calculate the distance, cen is the center point

newidx(j,3)=abs(cen(1,1)- newidx(j,1))+abs(cen(1,2)- newidx(j,2)); %MD

end

[v,in]=min(newidx(:,3)); %value and index of the smallest distance

point(i,:)=[ newidx(in,1),newidx(in,2)]; %final points

end

Pls, let me Know if you face any problem.

best regards

Why did you assume it was 5 segments only

thank your very much for the code snippet but you did not mark them right?

If you want to send me the code

[email protected]

Dear Ahmed,

b,c and d are the first, second and third images respectively, the number 5 determine the number of regions ( defects ) you want ( in the code the largest five regions ), the code in the previous comment will work fine with you if you understood the idea.

I did understand the code and I wrote it down in my script the variable called (points) showed me  (x,Y) coordinates.

I guess this what I want, all I need now is to mark them in the figure, right?

Exactly .. 

what is [v, in] means? can I increase the regions i am working on  and how will it affect the code?

I have a problem Mr. Ahmed in labeling the convexity defects 

My Code in labeling

% preview it.

figure(3);

subplot(1,3,3);

imshow(Ch);

title('Convex Defects of Hand');

hold on

for i = 1 : length(point(:,1))

for j = 1 : length(point(1,:))

plot(point(i,j),'r+','MarkerSize',10);

end

end

:

Hi Ahmed,

You can simply plot array of point without needing a loop, I have tried to work on image you sent me, it works correctly with me, using the previous code, you should to handle with segmented image ( binary image ), try to add the following part at the end of the code :

subplot(2,2,1);

imshow(b);

subplot(2,2,2);

imshow(con);

subplot(2,2,3);

imshow(d);

subplot(2,2,4);

imshow(b); hold on; plot(point(:,1),point(:,2),'b*','MarkerSize',12);

plot(cen(:,1),cen(:,2),'r*','MarkerSize',12) 

the result of your image shown in the attached Figure.

best regards

After I used your above code, it showed me different results, is that okay?

What is your segmentation approach as I can see it is showing better results than mine

Of course, the segmentation result will affect the locations of the points (defects), I have used Kmeans for segmentation, it would be nice if you add an image of your results.

Results using Color Segmentation

can I have your email address Mr. Ahmed?