摘要
20世纪70年代初,图像处理已经形成了较完善的学科体系。它的研究内容主要包括：图像分割、图像去噪、图像配准、图像融合、目标检测、图像压缩、图像重建以及模式识别等。图像处理已经成功的应用到军事、刑侦、商业、医学、艺术、家庭娱乐等领域,并且范围仍在扩大。
本文回顾了基于变分和水平集方法的活动轮廓分割模型,并详述了参数活动轮廓模型、曲线演化理论、水平集方法和Chan-Vese模型。在这些工作基础上,很多学者都从不同角度提出了各种各样的改进,但由于模型本身或求解方法的缺陷,都存在各自的不足,其中计算速度慢是普遍存在的问题；另外,本文详述了人脸识别中基于子空间的四种方法——PCA、LDA、MMC、MFA,并将前三种方法与我们要改进的SRC方法进行比较,均不同程度的存在识别率低、速度慢等缺点。
本文介绍了求解凸泛函极值的经典Bregman迭代方法和将其应用于求解带约束优化问题的详细过程,在深刻理解其原理的基础上,详细论述了Tom Goldstein等人提出的分裂Bregman方法,并将其应用在经典的Chan-Vese模型的求解过程中,得到了很好的效果,极大的提高了分割效率。自此,很多学者都对该类方法给予了极大的关注,先后将其应用在ROF去噪、加权GCS模型、CCD图像修复等模型中。本文将分裂Bregman方法应用到人脸识别中,对SRC模型进行求解,通过大量的数值试验表明,在保证原有甚至更高识别率基础上,识别效率大大提高,验证了该方法在求解类似L1正则化问题的高效性和准确性,进一步扩大了该方法的应用范围。
In the early 1970s, image processing has already developed relatively complete system of academic disciplines. It mainly includes:image segmentation, image denoising, image registration, image fusion, target detection, image compression, image reconstruction and pattern recognition, etc. Image processing have been successfully applied to the military, criminal investigation, business, medicine, art, home entertainment and other fields, and the application area is still expanding.
This paper reviews the active contour model based the variation calculus and level set, and detailed the parametric active contour model, curve evolution theory, the level set method and the Chan-Vese model. Based on this work, many scholars made a variety of improvements from different the angles, but because of the drawback of the model itself or computing approach, there are shortages of their own, in which computing speed is a common problem; In addition, this paper expounds the four face recognization methods via the subspace-based, PCA, LDA, MMC, MFA. Compared with SRC method which we will improve, These four methods have the defects of low recognization rate and poor computing speed to varying degrees.
This paper describes the classical Bregman iteration method commonly used for solving the convex functional extremum problem, and apply it to solve the constrained optimization problems with detailed steps. With a deep understanding of its principles, We show the Split Bregman method proposed by Tom Goldstein in detail, applied it to the process of solving the classical Chan-Vese model and got good results, greatly improved the segmentation efficiency. Since then, many scholars paid great attention to this method, and successfully extend its applications to ROF denoising, weighted GCS model, CCD image restoration model and other ones. This paper utilizes the Split Bregman method to the face recognition for the first time, to solve the SRC model. Based on a large number of numerical experiments, it shows that the recognition efficiency is remarkably improved with a similar or even higher recognition rate, verifies this method to be a efficient tool for solving large scale problems similar to the L1 regularizations problems, and further expand the scope of application of the method.
引文
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