WIP: Context-Adaptive Interpolator (CAI)

algorithms/context-adaptive_interpolator.py

@@ -43,19 +43,28 @@ for m in range(1, IImage.size[0] - 1):
             r[m - 1, n - 1] = round(newPixel)
 
 Q = 3
+# $\sigma_0^2$ is the noise variance.
+sigma_0 = sqrt(9)
 
-def wienerFilter():
+# Wiener filter.
+def h_w(i, j):
     # Equation (7)
-    hw[i, j] = h[i, j] * sigma(i, j) / (sigma(i, j) + sigma_0 ** 2)
+    return h[i, j] * sigma(i, j) / (sigma(i, j) + sigma_0 ** 2)
 
+# Minimum of the considered variances.
 def sigma(i, j):
     # Equation (9)
     return sigma_q(i, j, Q)
 
+def getPixelIndexesAround(i, numberOfPixelsInEachDirection):
+    return range(i - numberOfPixelsInEachDirection, i + numberOfPixelsInEachDirection)
+
+# Local variance obtained by Maximum A Posteriori (MAP).
 def sigma_q(i, j, q):
     # Equation (8)
-    # TODO:
-    pass
+    numberOfPixelsInEachDirection = (q - 1) // 2
+    B_q = [(x, z) for x in getPixelIndexesAround(i, numberOfPixelsInEachDirection) for z in getPixelIndexesAround(j, numberOfPixelsInEachDirection)]
+    return max(0, (1 / q ** 2) * sum([h[x, z] ** 2 - sigma_0 ** 2 for (x, z) in B_q]))
 
 # Why need to rotate the image? See #14.
 rImage.rotate(-90).show()