crf.py

"""
 Assumes:
 Zmin = 0
 Zmax = 255
 Arguments:
 Z(i,j) is the pixel values of pixel location number i in image j
 B(j) is the log delta t, or log shutter speed, for image j
 l is lamdba, the constant that determines the amount of smoothness
 w(z) is the weighting function value for pixel value z
 Returns:
 g(z) is the log exposure corresponding to pixel value z
 lE(i) is the log film irradiance at pixel location i
"""

import numpy as np


def crf_solve(Z, B, lambda_, w, Zmin, Zmax):
    n = Zmax + 1
    num_px, num_im = Z.shape
    A = np.zeros((num_px * num_im + n, n + num_px))
    b = np.zeros((A.shape[0]))

    # include the data fitting equations
    k = 0
    for i in range(num_px):
        for j in range(num_im):
            wij = w[Z[i, j]]
            A[k, Z[i, j]] = wij
            A[k, n + i] = -wij
            b[k] = wij * B[j]
            k += 1

    # fix the curve by setting its middle value to 0
    A[k, n // 2] = 1
    k += 1

    # include the smoothness equations
    for i in range(n - 2):
        A[k, i] = lambda_ * w[i + 1]
        A[k, i + 1] = -2 * lambda_ * w[i + 1]
        A[k, i + 2] = lambda_ * w[i + 1]
        k += 1

    # solve the system using LLS
    output = np.linalg.lstsq(A, b)
    x = output[0]
    g = x[:n]
    lE = x[n:]

    return [g, lE]