In order to handle pose variation problem in face recognition, Generic Elastic Models (GEMs) was proposed as a low computational and efficient 3D face modeling method, which generates 3D face model from single frontal face image by elastically deforming a generic 3D depth map based on 2D observations of the input face image. In this paper, we extend GEMs to Multi-Depth GEMs (MD-GEMs) by utilizing multiple generic depth maps which merely vary in depth linearly in process of 3D face modeling, taking the assumption that face depth variation across individuals can be modeled by a linear transformation of generic depth map. Multiple 3D models are generated for each input frontal face. In recognition, the galleries are the 3D models constructed from the frontal face of each ID while the probe is a non-frontal face. The pose of input non-frontal face is estimated by a linear regression method and 3D models in the constructed database are rotated and rendered at the estimated pose. Corresponding 2D images are synthesized after 2D projection. After face alignment, the distances between the input image and synthesized images are calculated by a normalized correlation measure and thus the corresponding identity in the database is matched. Experiments on Multi-PIE verify the effectiveness of MD-GEMs on handling pose variation problem in face recognition.
Based on comparative studies on correlation coefficient theory and utility theory, a series of rules that utility functions on dual hesitant fuzzy rough sets (DHFRSs) should satisfy, and a kind of novel utility function on DHFRSs are proposed. The characteristic of the introduced utility function is a parameter, which is determined by decision-makers according to their experiences. By using the proposed utility function on DHFRSs, a novel dual hesitant fuzzy rough pattern recognition method is also proposed. Furthermore, this study also points out that the classical dual tool is suitable to cope with dynamic data in exploratory data analysis situations, while the newly proposed one is suitable to cope with static data in confirmatory data analysis situations. Finally, a medical diagnosis and a traffic engineering example are introduced to reveal the effectiveness of the newly proposed utility functions on DHFRSs.
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