select a region from an image satisfying a condition

How to select a region from an orientation image satisfying the following condition

Answer 1

[Image Analyst]

See the FAQ: http://matlab.wikia.com/wiki/FAQ#How_do_I_create_a_circle.3F

[Walter Roberson]

Create a circle and crop it. Use the resulting mask for whatever it is you are doing, such as conv2 or as a structuring element for erosion.

[Walter Roberson]

Why not just take the one time hit of creating a matrix with the appropriate mask of 1 and 0?

[Walter Roberson]

 [
0 1 1 1 1 1 1 1 0;
1 1 1 1 1 1 1 1 1;
0 1 1 1 1 1 1 1 0;
0 1 1 1 1 1 1 1 0;
0 0 1 1 1 1 1 0 0;
0 0 0 0 1 0 0 0 0]

[Image Analyst]

I have no idea how you got the underlying image beneath your circular mask. I assume you had that already. What formula or operations are you using to get those values? Or do you not have them already? If you don't have those numbers yet, what distances are they measuring displacement from? Like do you have two images and are tracking some object (e.g. a car, a ball, a laser spot) and the object moved from location 1 in image 1 to location 2 in image 2?

[Walter Roberson]

You need to read the caption more carefully. The dx and dy are the horizontal and vertical displacement of the element's position relative to the center. The formulas show simply define a truncated circle as a mask, without in any way talking about the content of the image.

(j.^2) > -1

Incorrect: in the original it is dy, not dy^2.

If you must construct the mask computationally then:

KR = 4;
[row, col, p] = size(IMG);
xc = col/2; yc = row/2; 
if xc ~= floor(xc) || yc ~= floor(yc)
   error('cannot handle images with odd numbers of rows or columns')
end
[X, Y] = ndgrid(1:col, 1:row);
mask = (X-xc).^2 + (Y-yc).^2 <= KR.^2 & (Y-yc) >= -1;

The reason for ruling out images with odd dimensions is that the centre of those would be in-between pixels, which would lead to masks of slightly different shape than you need.