To solve this problem, we build a codebook from P and Q composed of two different data structures used to perform a fast search of possibly corresponding points (as described in Section 3.1) and point pairs (as described in Section 3.2).
For example, the genome of an individual that consists of 50% population X, 25% population Y, and 25% population Z can be represented by the corresponding point T as a convex combination: T = 0. 5 X + 0. 25 Y + 0. 25 Z, where each population is represented by a vector of K admixture coefficients, for example: X = [ 0. 1, 0. 15, 0. 25, 0, 0, 0. 5, 0, 0, 0 ].
Similarly to P i,k j, let us define the conditional probabilities pertaining to the first experimental class, P i, k j 0 = P r (X i = k | P a i = j, C = 0 ) and let P ^ i, k j 0 be the corresponding point estimators as in (2), that is, P ^ i, k j 0 = n i, k j 0 / n i, j 0, where n i, k j 0 ≡ ∑ s = 1 n 1 { x i s = k, p a i s = j, c s = 0 }.
As usual in combinatorial topology, we consider a discretization of the space, and represent it by a graph G, where two vertices are defined to be close to each other if and only if they belong to the same edge (the corresponding points can be as close as desired, by considering a subdivision of the space as fine as needed).
If the reliability, i.e., the peak value of BLPOC function, is below the threshold, the corresponding point pair is removed as outliers.
Equation (26) is further rearranged as an equation of the epipolar line constraint in image plane for two corresponding points [22], as shown in Figure 5 Figure 5 Epiploar plane of two camera views.
The cutoff value of AMH to discern between fertile and non-fertile ewes at first mating was chosen as the corresponding point of the ROC curve that maximized the Youden index, a prevalence-independent criterion [ 28].
However, the SSD value can still produce erroneous corresponding point pairs because of conditions such as lighting and occlusion.
Highlighted boxes denote points that are significantly different from the corresponding SCOW point, as determined by McNemar's χ-test.
