I am having issues getting the correct translation values after rotating my image. The code I have so far calculates the bounding box for a given rotation using basic trigonometry, it then applies a translation to the rotation matrix. The issue I am having however is that my translation always seems to be 1 pixel out, by that I mean I get a 1-pixel black border along the top or sides of my rotated image.
Here is my code:
def rotate_image(mat, angle):
height, width = mat.shape[:2]
image_center = (width / 2.0, height / 2.0)
rotation_mat = cv2.getRotationMatrix2D(image_center, angle, 1.0)
# Get Bounding Box
radians = math.radians(angle)
sin = abs(math.sin(radians))
cos = abs(math.cos(radians))
bound_w = (width * cos) + (height * sin)
bound_h = (width * sin) + (height * cos)
# Set Translation
rotation_mat[0, 2] += (bound_w / 2.0) - image_center[0]
rotation_mat[1, 2] += (bound_h / 2.0) - image_center[1]
rotated_mat = cv2.warpAffine(mat, rotation_mat, (int(bound_w), int(bound_h)))
return rotated_mat
Here is the original image for reference and some examples of the image using that code:
coffee.png – Original
coffee.png - 90° - Notice the 1px border across the top
coffee.png - 180° - Notice the 1px border across the top and left
I am not so hot on my math, but I hazard a guess that this is being caused by some rounding issue as we’re dealing with floating point numbers. I would like to know what methods other people use, what would be the simplest and most performant way to rotate and translate an image about its centre point please?
Thank you.
EDIT
As per @Falko's answer, I was not using zero-based calculation. My corrected code is as follows:
def rotate_image(mat, angle):
height, width = mat.shape[:2]
image_center = ((width - 1) / 2.0, (height - 1) / 2.0)
rotation_mat = cv2.getRotationMatrix2D(image_center, angle, 1.0)
# Get Bounding Box
radians = math.radians(angle)
sin = abs(math.sin(radians))
cos = abs(math.cos(radians))
bound_w = (width * cos) + (height * sin)
bound_h = (width * sin) + (height * cos)
# Set Translation
rotation_mat[0, 2] += ((bound_w - 1) / 2.0 - image_center[0])
rotation_mat[1, 2] += ((bound_h - 1) / 2.0 - image_center[1])
rotated_mat = cv2.warpAffine(mat, rotation_mat, (int(bound_w), int(bound_h)))
return rotated_mat
I'd still appreciate seeing alternative methods people are using to perform rotation and translation! :)
