A Geometrical-Information-Assisted Approach for Local Feature Matching

Figure 1

An illustration of for Propositions 1 and 2, where the left side indicates that the probability of two points and being projected into the same circle centred at the referential point is zero under the Lebesgue measure on , whereas the right side shows that the counterpart may not be zero under the counting measure since there are points except (e.g., the 11 pink boxes above) that could be projected to.