How warp an image without cv2.remap cropping it.

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Related question: https://stackoverflow.com/questions/5...

I want to deform an image using the process described in the section 3 of this paper.

I'm using the following to generate a randomly deformed mesh:

def mesh_perturb(image):
    rows = image.shape[0]
    columns = image.shape[1]
    xx = np.arange(0, rows, 1)
    yy = np.arange(0, columns, 1)
    [Y, X] = np.meshgrid(xx, yy)
    ms = np.transpose(np.asarray([X.flatten('F'), Y.flatten('F')]), (1, 0))

    perturbed_mesh = ms
    nv = np.random.randint(20) - 1
    for k in range(nv):
        # Choosing one vertex randomly
        vidx = np.random.randint(np.shape(ms)[0])
        vtex = ms[vidx, :]
        # Vector between all vertices and the selected one
        xv = perturbed_mesh - vtex
        # Random movement
        mv = (np.random.rand(1, 2) - 0.5) * 20
        hxv = np.zeros((np.shape(xv)[0], np.shape(xv)[1] + 1))
        hxv[:, :-1] = xv
        hmv = np.tile(np.append(mv, 0), (np.shape(xv)[0], 1))
        d = np.cross(hxv, hmv)
        d = np.absolute(d[:, 2])
        d = d / (np.linalg.norm(mv, ord=2))
        wt = d

        curve_type = np.random.rand(1)
        if curve_type > 0.3:
            alpha = np.random.rand(1) * 50 + 50
            wt = alpha / (wt + alpha)
        else:
            alpha = np.random.rand(1) + 1
            wt = 1 - (wt / 100)**alpha
        msmv = mv * np.expand_dims(wt, axis=1)
        perturbed_mesh = perturbed_mesh + msmv

    return perturbed_mesh

I used cv2.remap function with coordinates generated by the above function. But the generated images are cropped, they go out of bounds. So I used cv2.copyMakeBorder and to pad the image before passing the image to mesh_perturb function but the problem here is I have to use the coordinates as ground truth for a neural network and training a neural network with very large images is impossible with my current hardware and unnecessary. And if I crop the generated image, I have to crop the ground truth deformed mesh values too and they are unusable if I crop them.

Can someone suggest me a way to do deform the image without needing to crop the image.