Add and multiply implementation

[ahmadmughees]

Hello,

I have few questions regarding your add and multiply implementation (which is not super clear from the paper).

1. Why did you use canonical combination instead of convex? Do you have any specific reason?

def add(img1, img2, beta):
    a, b = get_ab(beta)
    img1, img2 = img1 * 2 - 1, img2 * 2 - 1
    out = a * img1 + b * img2
    out = (out + 1) / 2
    return out

2. In the add implementation: why did you renormalize to [-1, 1] range? any benefits in numerical stability which I am not aware of?

def multiply(img1, img2, beta):
    a, b = get_ab(beta)
    img1, img2 = img1 * 2, img2 * 2
    out = (img1 ** a) * (img2.clip(1e-37) ** b)
    out = out / 2
    return out

3. As per the paper multiply is the geometric mean, which I can say is the weighted geometric mean. it should follow the equation
   $$\text{GM}(x) = \left( \text{img1}(x)^{a} \times \text{img2}(x)^{b} \right)^{\frac{1}{a + b}}$$

this ${\frac{1}{a + b}}$ is missing from your implementation. Also here you normalize to [0, 2] range. can you help me understand this implementation? Thanks, a lot.