Extracting subimage with a specified aspect ratio - c++

Question

I need to extract an object from an image. I know the location of the object inside the image, ie the region where the object is located: this region is provided as a pair of coordinates [xmin, ymin] and [xmax, ymax].
I would like to modify the coordinates of this region (thus increasing the height and width in a suitable way) in order to extract a subimage with a specified aspect ratio. So, we have the following constraints:
in order to avoid cutting the object incorrectly, the width and height of the region must not be reduced;
bounds checking: the adaptation of the region size must ensure that the new coordinates are inside the image;
the width/height ratio of the subimage should be approximately equal to the specified aspect ratio.
How to solve this problem?
UPDATE: one possible solution
The solution to my problem is mainly the algorithm proposed by Mark in this answer. The result of this algorithm is a new region wider or higher than the original and it is able to obtain a new aspect ratio very close to that specified, without moving the center of the original region (if this is feasible, depending on the position of the region within the original image). The region obtained from this algorithm could be further processed by the following algorithm in order to make the aspect ratio closer to that specified.
for left=0:(xmin-1), // it tries all possible combinations
for right=0:(imgWidth-xmax), // of increments of the region size
for top=0:(ymin-1), // along the four directions
for bottom=0:(imgHeight-ymax),
x1 = xmin - left;
x2 = xmax + right;
y1 = ymin - top;
y2 = ymax + bottom;
newRatio = (x2 - x1) / (y2 - y1);
if (newRatio == ratio)
rect = [x1 y1 x2 y2];
return;
end
end
end
end
end
Example... An image with 976 rows and 1239 columns; an initial region [xmin ymin xmax ymax] = [570 174 959 957].
First algorithm (main processing).
Input: the initial region and the image size.
Output: it produces new region r1 = [568 174 960 957],
width = 392 and height = 783, so the aspect ratio is equal to 0.5006.
Second algorithm (post-processing).
Input: the region r1.
Output: new region r2 = [568 174 960 958],
width = 392 and height = 784, so the aspect ratio is equal to 0.5.

Answer 1

obj_width = xmax - xmin
obj_height = ymax - ymin
if (obj_width / obj_height > ratio)
{
height_adjustment = ((obj_width / ratio) - (ymax - ymin)) / 2;
ymin -= height_adjustment;
ymax += height_adjustment;
if (ymin < 0)
{
ymax -= ymin;
ymin = 0;
}
if (ymax >= image_height)
ymax = image_height - 1;
}
else if (obj_width / obj_height < ratio)
{
width_adjustment = ((obj_height * ratio) - (xmax - xmin)) / 2;
xmin -= width_adjustment;
xmax += width_adjustment;
if (xmin < 0)
{
xmax -= xmin;
xmin = 0;
}
if (xmax >= image_width)
xmax = image_width - 1;
}

Answer 2

Let's start with your region: a w x h rectangle centered on a point p. You want to extend this region to have the aspect ratio r. The idea is to extend the width or the height:
(trivial case) If w / h == r, then return.
Compute w' = h x r.
If w' > w, then the resulting region is of width w', height h and center p.
Else, the resulting region is of width w, height h' = w / r, and center p.
Move the center p to follow the edges of the image if it has to be clipped, for example if the resulting region upper-left point is outside of the image: let u = upper-left point of the resulting region and d = (min(u.x,0), min(u.y,0)). Then, the final center will be p' = p - d. It is similar for the lower-right part of the region.
Clip the resulting region to the image.