Detecting shortest path on binary image

I'm trying to detect the shortest path from certain point on the image P in certain radius of searching, as shown on the picture. I was using linear equation y=ax+b,

x=400;
y=600;
switch direction
     case 'right'
                while(impixel(image,x,y)==[0,0,0])
                    x=x+1;
                    %y=600 stays the same
                end
     case 'left'
                while(impixel(image,x,y)==[0,0,0])
                    x=x-1;
                end
    %(...)
end

which is easy to use with horizontal line (a=0,b=x), but problem appears when I want to rotate the line with point P as origin. Since the pixel P is not the origin (0,0) of the image, its not enough to just change the 'a' parameter, but also somehow calculate 'b' for full linear equation.

Maybe there is some helpfull command that allows to detect the clostest binary object in given direction? If not, I'd appreciate any suggestions how can I calculate a and b parameters for the line equations.

[KALYAN ACHARJYA]

The question is:

Are you looking for the distance between yellow point and nearest white pixel towards right hand side?

Right?

[sooljex]

yes

Answer 1

[Image Analyst]

Steve Eddins has a whole blog series on this. I suggest you read it: Exploring shortest paths

To detect the boundary point closest to (x1, y1) you'll need to do this:

mask = bwareafilt(mask, 1); % Make sure there is only one blob.
boundaries = bwboundary(mask);
boundaries = boundaries{1}; % Extract from cell.  Data is [rows, columns], not [x, y]
% Find rows
yRows = boundaries(:, 1);
% Find columns (x)
xColumns = boundaries(:, 2);
% Find distances from (x1, y1) to all other points.
distances = sqrt((xColumns - x1).^2 + (yRows - y1).^2);
% Find the closest
[minDistance, indexOfMin] = min(distances);
% Find the coordinates
xColumnClosest = xColumns(indexOfMin)
yRowClosest = yRows(indexOfMin)

[sooljex]

This definitely seem to be working, thanks! Other part of my question was- can I somehow limit the area (give direction) in which it will try detect an object? (for example; give a cone shaped area of searching like on first picture)