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標題: | 稀疏低秩模型於被遮擋人臉辨識與非凸數值優化方法 Sparse and Low-Rank Model for Occluded Face Recognition and Nonconvex Numerical Optimization |
作者: | Cho-Ying Wu 吳卓穎 |
指導教授: | 丁建均 |
關鍵字: | 遮擋物人臉辨識,稀疏低秩模型,非凸函數最佳化,ADMM,對偶性,衝量, Occluded face recognition,sparse and low-rank model,nonconvex optimization,ADMM,duality,momentum, |
出版年 : | 2017 |
學位: | 碩士 |
摘要: | 人臉辨識是長期在電腦視覺領域研究的主題。然而在真實世界中,遮擋物是經常發生且對辨識能力造成阻礙。在有遮擋物的情形下,人臉有效的資訊部分減少。近來,有基於稀疏表示的分類方法被提出於強健性人臉辨識的問題,於隨機像素破壞的人臉影像辨識上有不凡的表現,然而此方法對於真實世界的遮擋情形卻是缺乏效率及有效性。
基於壓縮感知的發展如L1 norm最小化問題以及矩陣的秩最小化問題,我們採用一種稀疏低秩模型,對人臉影像取廣義的梯度方向後,將其套用於此回歸模型上。我們採用總共三階的梯度方向當作人臉影像的特徵,透過alternating direction method of multipliers (ADMM)我們可以將此稀疏低秩模型將以最佳化。我們觀察到梯度方向圖並不符合低秩矩陣的假設,然而最佳化方法仍可以成功的適用,我們稱此為弱低秩最佳化問題。實驗上,我們證明透過弱低秩問題的最佳化,我們會喪失還原上的空間資訊,但是對於辨識能力有大幅的提升。與近年來的最先進的方法比較,我們提出的方法有最好的效能。 接著,我們研究凸優化與非凸優化方法的行為於一些稀疏低秩模型上,Robust Principal Component Analysis (RPCA) 與 Low-Rank Representation (LRR) 是兩個著名的稀疏低秩模型。他們都可以透過ADMM步驟與凸函數代理來做優化。然而凸函數代理有時無法有效的近似原始問題,所以我們引入了非凸函數來做更佳的近似。首先我們提出一個新的非凸函數代理,於矩陣補完的問題上有更佳的表現。接著我們將此代理函數用於RPCA與LRR問題,形成非凸的稀疏低秩模型。於ADMM的步驟上,我們也提出了加上衝量項改良了對偶步驟的更新,我們稱此為對偶衝量,並利用此避免最佳化點卡於局部最佳值的問題,以及使收斂速度更快。我們寫出了完整的理論上的收斂性分析與證明了非凸方法的收斂率。實驗上我們也證明非凸方法與對偶衝量都能夠使最佳化的解收斂到更小的還原誤差的點上。在RPCA上我們以矩陣及影像去雜訊作為實驗,在LRR上我們以頻譜聚類與異常偵測作為實驗。我們也與其他基於RPCA及LRR的改良方法做比較,也以實驗證明我們的方法有最佳的表現。 Face recognition is a very popular research topic for computer vision. However, in the real-world scenario, occlusion is a frequently occurring obstacle for recognition. With the occlusion, the information for the face of an individual is diminished. Recently, sparse representation based classification has been proposed on robust the face recognition problem. They have extraordinary performance on randomly corrupted face images. However, for real-world occlusion, this method lacks efficiency and effectiveness. Inspired by the techniques related to compressive sensing, such as L1-norm minimization and the rank minimization, we propose a novel sparse and low-rank model in this thesis. It performs regression for face images on the generalized gradient direction domain. We adopt the three orders gradient direction as features. Through the alternating direction method of multipliers (ADMM) procedure, we can optimize the sparse and low-rank model. We observe that the gradient direction map does not satisfy the low-rank assumption spatially. However, the optimization method still works well on the “weak low-rankness” optimization problem. In experiments, we show that, with the proposed method for solving the weak low-rank problem, the recognition rate can be improved greatly. Compared to the state-of-the-art methods, proposed method has the best performance. Next, we study the behavior of the convex and nonconvex optimizations of different sparse and low-rank models. Robust Principal Component Analysis (RPCA) and Low-Rank Representation (LRR) are two well-known models. They can be optimized by ADMM with the convex surrogates. Nevertheless, the convex surrogates cannot approximate the original problem well. Therefore, we propose a nonconvex surrogate for better approximation. First, a novel nonconvex surrogate which has better performance on the matrix completion and image completion problem is proposed. Next, this surrogate is applied on the RPCA and LRR to form the nonconvex sparse and low-rank models. In the ADMM procedure, we proposed to revise the dual updates with the momentum term. We call this trick dual momentum, which can avoid the local optimal problem and boost the convergence speed. We give a complete theoretical convergence analysis and prove the convergence rate of the nonconvex approach. Experiments show that the nonconvex approach with dual momentum can converge to a point with a smaller recovery residual on extensive applications such as matrix and image denoising of RPCA and spectral clustering with outlier detection of LRR. We also compare proposed method to the other improvement methods based on the RPCA and LRR and show that proposed methods has the best performance. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/59463 |
DOI: | 10.6342/NTU201700976 |
全文授權: | 有償授權 |
顯示於系所單位: | 電信工程學研究所 |
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