Given a point, locate 3 point in different 8 directions.

I'm working with images, and after that I've found a certain pixel, I have to consider 8 directions starting from this point, one direction for each 45 degrees counter-clockwise. On these directions, I have to locate 3 points (the ones for which there is a rapid variation in intensity with the adjacent pixel in that direction).

I really don't know how I can locate these directions and the points that belong to them, so any suggestion and help would be appreciated.

[jonas]

Could you provide an example input/output array?

[Francesco Argenziano]

I can provide you with an image about what I'm supposed to have in output. The + is the starting point, the square are the points I have to find

[jonas]

I dont understand. Are the squares present in the input image or do they display the "correct" points? What is the criteria for finding one of those points? Do you have to use this very specific technique?

[Francesco Argenziano]

The square only display the correct points, the original image is just the eye. To find those point, you move along one of the eight directions (starting from the starting point) and for each pair of adjacent pixel on that direction you measure the difference of intensity. The three pixels that have tha maxixum variation are the ones I have to found.

Calculating the variation isn't hard, the biggest problem is how I can move along one direction to calculate that, and how can i find those directions.

[J. Alex Lee]

What do you mean "how to find those directions"? Didn't you state that you want it to be every 45degrees? Based on the "target" result, it seems you want to start from horizontal or vertical, so in matlab's coordinates, 0:45:315

"Moving along a direction" and "calculating variations" seems to me to two aspects of one problem: calculating variation along some direction...so what exactly is your difficulty?

Based on how the question is posed, is this some kind of assignment?

Answer 1

[Matt J]

I'm not sure I understand what the how-to challenge is in the question, but the approach that I think you want is to calculate all differences along a specific direction at all pixels simultaneously. That will allow you to efficiently process all differences of a particular type in a highly vectorized manner.

For example, if I call your image A, all southwest to northeast differences can be calculated by,

k=[0 -1;
   1, 0];

SWNE=abs(conv2(A,k,'valid')); %southwest to northeast absolute differences

while all north-west to south-east differences can be calculated by

NWSE=abs(conv2(A,flipud(k),'valid'));%northwest to southeast absolute differences

[J. Alex Lee]

you could also construct rotated GoG kernels to smooth out any noise; it would also be the more generalizable solution than the kernels specific to 45deg.

alternatively you could probably use gradient components in the principal directions from simpler filters like sobel, and rotate them after the fact (i think)

and then it would still remain to take line scans of the gradient components and identify the "edges".

Answer 2

[Matt J]

Or maybe this is what you want. In the code below, A is your image and the result Neighbors(i,j,:) contains all 9 neighbors of A(i,j) including i,j itself. Likewise Differences(i,j,:) will contain all absolute differences of the neighbors.

z=zeros(3);
Neighbors=repmat(A,1,1,9); %pre-allocation
for i=1:9
    k=z;
    k(i)=1;
    
    Neighbors(:,:,i)=conv2(A,k,'same');
end

Differences=abs(Neighbors-A); %Difference from central pixel

Answer 3

[J. Alex Lee]

as long as we're guessing at the problem, an approach that would alleviate the need for line scans would be to rotate the source image itself about the "starting point" and take diff() of the image (or some smoothed version of it)

Answer 4

[J. Alex Lee]

Or since there is a built-in called improfile (with one toolbox or another), you can skip the convolutions for gradients, take the profiles of the image itself and just do a 1D diff() on them.