Face image abstraction by Ford-Fulkerson algorithm and invariant feature descriptor for human identification

This paper discusses a face image abstraction method by using SIFT features and Ford-Fulkerson algorithm. Ford-Fulkerson algorithm is used to compute the maximum flow in a flow network drawn on SIFT features extracted from a face image. The idea is to obtain an augmenting path which is a path from the source vertex to destination vertex with the available capacities on all edges along a set of paths and flow is calculated along one of these paths. The process is repeated until it is obtained more paths with the available capacities. At the initial stage, face image is characterized by SIFT (Scale Invariant Feature Transform) features and the keypoints descriptor information is taken as features set for further processing. Keypoints descriptor is used to generate several face representations by using a series of matrix operations which are further used to determine a Directed Acyclic Graph (DAG). The resultant directed graph contains sparse and distinctive face characteristics of a subject from which the face image is captured. We then apply the Ford-Fulkerson algorithm on the directed graph to maintain the capacity constraints, skew symmetry and flow conservation to obtain an augmenting path with available capacities (relation between SIFT points). Finally, we obtain a mathematical representation of a face image and this representation is further encoded to be used as a set of distinctive features for matching. The time complexity of the proposed face abstraction algorithm is found to be O(VE²) where V is the set of vertices and E is the set of edges in a directed graph.