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My intention is to append all the LBPs to get the LBP of my image that is having 200 channels.

why not write into the resp. channel in the 1st place ?

# this will hold our final result:
height, width, channels = hsi_data.shape
lbp_final = np.zeros((height, width, channels),np.uint8)

for k in range(0, channels):
     image_gray = hsi_data[:,:,k]
     for i in range(0, height):
        for j in range(0, width):
            lbp_final[i, j, k] = lbp_calculated_pixel(img_gray, i, j)

(untested, i don't have python)