A new approach for face detection using the maximum function of probability density functions
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A new approach for face detection using the maximum function of probability density functions Ha Che-Ngoc1 · Thao Nguyen-Trang2,3 · Tran Nguyen-Bao4 · Trung Nguyen-Thoi5,6 · Tai Vo-Van7 Accepted: 2 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This article establishes some theoretical results about the maximum function of probability density functions ( f max ) and the integration of f max (I f max ). Using the probability density function extracted from the image as a relatively stable feature of the image and I f max as a measure the similarity between a “face” candidate region and a group of training face images, we propose a new face detection method, one of the most challenging tasks related to image analysis. The experiments demonstrate the competitiveness of the proposed method, especially in the case of rotated images. It also shows potential in real application of the researched problem. Keywords Density function · Face detection · Maximum function · Rotated image
1 Introduction Face detection is the task of detecting all human faces, of any size, in a given image. It is also a pre-processing step for other tasks such as face recognition, emotion recognition, etc.
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Tai Vo-Van [email protected] Ha Che-Ngoc [email protected]
1
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
2
University of Science, Ho Chi Minh City, Vietnam
3
Vietnam National University, Ho Chi Minh City, Vietnam
4
Video and Image Processing Lab, Information and Telecommunication Engineering, Soongsil University, Seoul, Korea
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Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam
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Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
7
College of Natural Science, Can Tho University, Can Tho, Vietnam
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Annals of Operations Research
Hence, the face detection recently has received much attention from the statisticians (Zhang and Zhang 2014; Li et al. 2015; Triantafyllidou and Tefas 2016). It is also the challenging research topic in statistics, pattern recognition, artificial intelligence, computer vision, etc. (Li et al. 2015; Günther et al. 2017). In terms of methodology, well-known methods for face detection, such as Template Matching (or Prototype matrix method, PMM), Cascade Classifier, Convolutional Neural Network, etc. were almost based on image intensity matrices, Red Green Blue matrices, then transformed them using filters, through a sequences of stages and hidden layers. The above methods, in general, have the following disadvantages: (i) They require the same size images in performing. The existing methods often extracted the character of an image by the matrix which depends on the size of images. As a result, the same image with different sizes gives the different extracted matrices. Therefore, they often have to be resized before implementing, which leads to loss of information. (ii) They are limited
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