Padding scipy affine_transform output to show non-overlapping regions of transformed images-CodePudding

The

The displacement search

The first thing is to compute the correlation of the image

def compute_correlation(a1, a2): A1 = np.fft.rfftn(a1, axes=(0,1)) A2 = np.fft.rfftn(a2, axes=(0,1)) C = np.fft.irfftn(np.sum(A1 * np.conj(A2), axis=2)) return C

Then, let's create an example without rotation and confirm that the with the index of the maximum correlation we can find the displacement that fit one image to the other.

displacement, _ = random_transform() a1, a2 = image_pair(im, 521, 512, displacement, angle=0) C = compute_correlation(a1, a2) np.unravel_index(np.argmax(C), C.shape), displacement a3 = np.roll(a2, np.unravel_index(np.argmax(C), C.shape), axis=(0,1)) assert np.all(a3 == a1)

With rotation or interpolation this result may not be exact but it gives the displacement that will give us the closest possible alignment.

Let's put this in a function for future use

def get_aligned(a1, a2, angle): a1_rotated = ndimage.rotate(a1, angle, reshape=False) C = compute_correlation(a2, a1_rotated) found_displacement = np.unravel_index(np.argmax(C), C.shape) a1_aligned = np.roll(a1_rotated, found_displacement, axis=(0,1)) return a1_aligned

Searching for the angle

Now we can do something in two steps,

in one we compute the correlation for each angle, then with the angle that gives maximum correlation find the alignment.

displacement, angle = random_transform() a1, a2 = image_pair(im, 521, 512, displacement, angle) C_max = [] C_argmax = [] angle_guesses = np.arange(0, 360, 5) for angle_guess in angle_guesses: a1_rotated = ndimage.rotate(a1, angle_guess, reshape=False) C = compute_correlation(a1_rotated, a2) i = np.argmax(C) v = C.reshape(-1)[i] C_max.append(v) C_argmax.append(i)

Let's see how the correlation looks like

plt.plot(angle_guesses, C_max);

We have a clear winner looking at this curve, even if a sunflower has some sort of rotation symmetry.

Let's apply the transformation to the original image and see how it looks like

a1_aligned = get_aligned(a1, a2, angle_guesses[np.argmax(C_max)]) plt.subplot(121) plt.imshow(a2) plt.subplot(122) plt.imshow(a1_aligned)

Great, I wouldn't have done better than this manually.

I am using a sunflower image for beauty reasons, but the procedure is the same for any type of image. I use RGB showing that the image may have one additional dimension, i.e. it uses a feature vector, instead of the scalar feature, you can use reshape your data to (width, height, 1) if your feature is a scalar.