Table 1 Notation.

Q = {Q^ul, Q^ur, Q^ll, Q^lr}

The set of quadrant images corresponding to the upper-left, upper-right, lower-left and lower-right quadrants, respectively.

T = {T^ul, T^ur, T^ll, T^lr}

The set of transformations of all 4 quadrant images, where each quadrant’s transformation stores the x-translation, y-translation and degrees of rotation.

D_pair(Q¹, Q²)

Pair-wise intensity-based dissimilarity computed on each quadrant pair (Q¹, Q²).

M_pair(Q¹, Q²)

Pair-wise distance-based misalignment computed on each quadrant pair (Q¹, Q²).

{V¹(k), V²(k)}

The k^th set of corresponding histogram vectors or pixel values V¹ and V² of a pair of quadrants, where V¹ belongs to Q¹ and V² belongs to Q².

The set of corresponding outer and inner corner points C¹ and C² of a pair of quadrants, where C¹ belongs to Q¹ and C² belongs to Q².

w₁, w₂

Empirically determined cost function component weights (w₁, w₂)

w₃, w₄

Inner- and outer-point weights (w₃, w₄)

m, n

m = Number of overhanging and n = number of corresponding pixels for a pair of adjacent edges

p, b

p = Size of rectangular patch and b = number of histogram bins for cost computation

ϕ

Dissimilarity for a non-corresponding edge pixel