结合显性与隐性空间光滑的高效二维图像判别特征抽取

A Fast Discriminant Feature Extraction Framework Combining Implicit Spatial Smoothness with Explicit One for Two-Dimensional Image

图像具有固有的二维空间结构,空间上邻近的像素点通常具有相近的灰度值,意味着图像具有局部光滑性.为对其特征抽取,传统方法常将原始图像拉成向量,造成空间结构的破坏,由此直接基于图像的2D特征抽取法应运而生.典型的如2DLDA,2DPCA,相比向量方法,计算复杂度显著降低,但其操作针对的是图像整行(或整列),导致空间光滑度过粗.为此,空间正则化通过在向量化空间中显式地施加局部空间光滑弥补这一不足,由此获得了比2D抽取法更优的分类性能,但其遗传了向量法的高计算代价.最近,隐性空间正则化方法(implicit spatial regularization,ISR)提出利用图像划分与重组隐性地体现图像局部光滑性,而后再利用现有2D方法抽取特征,使典型双边2DLDA性能优于SSSL(一种典型的显性空间正则化方法),但是,仅隐性地光滑缺乏显式的强制约束力,其特征空间依然欠光滑,同时双边2DLDA由非凸问题获得,计算耗时却不能保证解的全局最优性.鉴于此,提出一种结合显性与隐性空间光滑的高效二维图像判别特征抽取框架(2D-CISSE).其关键步骤是预先对图像显性地全局光滑,紧接着进行ISR,既继承了ISR的隐性光滑又强化了图像局部光滑的显式约束力,不仅可直接获得全局最优投影,同时该框架具有一般性,即现有大部分图像光滑方法与2D特征抽取法均可嵌入其中.最后,通过在人脸数据集Yale,ORL,CMU PIE,AR以及手写数字数据集MNIST和USPS上的对比实验验证了2D-CISSE框架性能的优越性与计算的高效性.

Images have two-dimensional inherent spatial structures, and the pixels spatially close to each other have similar gray values, which means images are locally spatially smooth. To extract features, traditional methods usually convert an original image into a vector, resulting in the destruction of spatial structure. Thus 2D image-based feature extraction methods emerge, typically, such as 2DLDA and 2DPCA, which reduce time complexity significantly. However, 2D-based methods manipulate on the whole raw （or column） of an image,leading to spatially under-smoothing. To overcome such shortcomings, spatial regularization is proposed by explicitly imposing a Laplacian penalty to constrain the projection coefficients to be spatially smooth and has achieved better performance than 2D-based methods, but sharing the genetic high computing cost with ID methods. Implicit spatial regularization （ISR） constrains spatial smoothness within each local image region by dividing and reshaping image and then executing 2D-based feature extraction methods, resulting in a performance improvement of the typical bi-side 2DLDA over SSSL （a typical ESR method）. However, ISR obtains the spatial smooth implicitly but has lack of explicit spatial constraints such that the feature space obtained by ISR is still not smooth enough. The optimization criteria of bi-side 2DLDA are not jointly convex simultaneously, resulting in high computing cost and globally optimal solution cannot be guaranteed. Inspired by statements above, we introduce a novel linear discriminanmodel called fast discriminant feature extraction framework combining implicit spatial smoothnesswith explicit one for two-dimensional image recognition （2D-CISSE）. The key step of 2D-CISSE is topreprocess spatial smooth for images, then ISR is executed. 2D-CISSE not only retains spatial smoothexplicitly, but also reinforces the explicit spatial constraints. Not only can it achieve globally optimasolution, but it also have generality, i. e. any out-of-shelf image smoothing methods and 2D-basedfeature extraction methods can be embedded into our framework. Finally,experimental results onfour face datasets （Yale, ORL, CMU PIE and AR） and handwritten digit datasets （MNIST andUSPS） demonstrate the effectiveness and superiority of our 2D-CISSE.