  In Computer Vision, edge detection is one of the favored approaches for
feature and object detection in images since it provides information about
their objects boundaries. Other region-based approaches use probabilistic
analysis such as clustering and Markov random fields, but those methods cannot
be used to analyze edges and their interaction. In fact, only image
segmentation can produce regions based on edges, but it requires thresholding
by simply separating the regions into binary in-out information. Hence, there
is currently a gap between edge-based and region-based algorithms, since edges
cannot be used to study the properties of a region and vice versa. The
objective of this paper is to present a novel spatial probability analysis that
allows determining the probability of inclusion inside a set of partial
contours (strokes). To answer this objective, we developed a new approach that
uses electromagnetic convolutions and repulsion optimization to compute the
required probabilities. Hence, it becomes possible to generate a continuous
space of probability based only on the edge information, thus bridging the gap
between the edge-based methods and the region-based methods. The developed
method is consistent with the fundamental properties of inclusion probabilities
and its results are validated by comparing an image with the probability-based
estimation given by our algorithm. The method can also be generalized to take
into consideration the intensity of the edges or to be used for 3D shapes. This
is the first documented method that allows computing a space of probability
based on interacting edges, which opens the path to broader applications such
as image segmentation and contour completion.
