reconstruction of image shows either black either square borders

I have trained two models (forward and backward).

(The input to the models are images of type uint8, so I am dividing by 255)

After predicting on each model, I receive two arrays:

forward = np.load('f.npy')backward = np.load('b.npy')

I also must use an image tiles_M in order to follow these equations:

p1 = ( 1.0 / abs(forward - tiles_M/255.) ) / ( (1.0 / abs(forward - tiles_M/255.)) + (1.0 / abs(backward - tiles_M/255.)) )p3 = ( 1.0 / abs(backward - tiles_M/255.) ) / ( (1.0 / abs(forward - tiles_M/255.)) + (1.0 / abs(backward - tiles_M/255.)) )

Note, that, I divide tiles_M by 255 (the same I did in inputs for training the models) since it is an uint8 image.

Then, the prediction must use this equation:

pred = p1 * forward + p3 * backward

The problem, is when I try to reconstruct the image, I receive a black image (all zero values).

If I normalize pred : pred = normalize_arr(pred)I receive this image

I have tried various ways to normalize either pred or p1, p2, forward, backward but now works as expected.

Now the interesting part comes from this.

If I use this equation (which is wrong and I accidentally typed at some point!):

p1 = ( 1.0 / abs(forward ) ) / ( (1.0 / abs(forward - tiles_M)) + (1.0 / abs(backward - tiles_M)) )p3 = ( 1.0 / abs(backward) ) / ( (1.0 / abs(forward - tiles_M)) + (1.0 / abs(backward - tiles_M)) )

so, no tiles_M scaling and no subtraction from tiles_M in the numerator, I receive this correct image!!!

The equation is:

You can find the data here.

This is the code:

import numpy as npimport cv2from PIL import Imagedef normalize_arr(arr):  the_min = arr.min()  the_max = arr.max()  the_max -= the_min  arr = ((arr - the_min)/the_max) * 255.  return arr.astype(np.uint8)def extract_tiles(size, im):    im = im[:, :, :3]    w = h = size    idxs = [(i, (i + h), j, (j + w)) for i in range(0, im.shape[0], h) for j in range(0, im.shape[1], w)]    tiles_asarrays = []    count = 0    for k, (i_start, i_end, j_start, j_end) in enumerate(idxs):        tile = im[i_start:i_end, j_start:j_end, ...]        if tile.shape[:2] != (h, w):            tile_ = tile            tile_size = (h, w) if tile.ndim == 2 else (h, w, tile.shape[2])            tile = np.zeros(tile_size, dtype=tile.dtype)            tile[:tile_.shape[0], :tile_.shape[1], ...] = tile_        count += 1        tiles_asarrays.append(tile)    return np.array(idxs), np.array(tiles_asarrays)IMG_WIDTH = 32# Load arraysforward = np.load('f.npy')backward = np.load('b.npy')tiles_M = np.load('tiles_M.npy')# Weighting paramsp1 = ( 1.0 / abs(forward - tiles_M/255.) ) / ( (1.0 / abs(forward - tiles_M/255.)) + (1.0 / abs(backward - tiles_M/255.)) )p3 = ( 1.0 / abs(backward - tiles_M/255.) ) / ( (1.0 / abs(forward - tiles_M/255.)) + (1.0 / abs(backward - tiles_M/255.)) )# works but wrong equation and no tiles_M scaling# p1 = ( 1.0 / abs(forward ) ) / ( (1.0 / abs(forward - tiles_M)) + (1.0 / abs(backward - tiles_M)) )# p3 = ( 1.0 / abs(backward) ) / ( (1.0 / abs(forward - tiles_M)) + (1.0 / abs(backward - tiles_M)) )pred = p1 * forward + p3 * backward#pred = normalize_arr(pred)# Load original imageimg = cv2.imread('E2.tif',                 cv2.IMREAD_UNCHANGED)img = cv2.resize(img, (1408, 1408), interpolation=cv2.INTER_AREA)img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)# create tiles idxs, tiles = extract_tiles(IMG_WIDTH, img)# Initialize reconstructed arrayreconstructed = np.zeros((img.shape[0],                          img.shape[1],                           img.shape[2]),                          dtype=np.uint8)# reconstructfor tile, (y_start, y_end, x_start, x_end) in zip(pred, idxs):    y_end = min(y_end, img.shape[0])    x_end = min(x_end, img.shape[1])    reconstructed[y_start:y_end, x_start:x_end] = tile[:(y_end - y_start), :(x_end - x_start)]# create image from arrayim = Image.fromarray(reconstructed)im = im.resize((1429, 1416))im.show()