本征图像分解的可变尺度局部分析与集成方法

针对自然图像与磁共振图像,提出本征图像分解的统一的数学模型与算法,解决这两类图像中的重要问题:1)自然图像的光照和反射图像的估计,2)磁共振图像中的偏移场估计与分割.文中数学模型只需要一个基本的假设,即观察到的图像可近似为两个具有不同特性的本征图像的乘积:一个光滑的图像,简称为S-图像;一个近似为分片常量的图像,简称为L-图像.为了充分利用本征图像的特性,提出可变尺度局部分析与集成的方法.由于S-图像的光滑性,使用低阶泰勒展开式或更一般的光滑基函数的线性组合以局部逼近.得到的局部光滑逼近可通过整个感兴趣区域(ROI)的局部区域覆盖及其对应的单位分解扩展成整个ROI上的光滑图像,同时得到图像分割结果和L-图像.实验表明,文中方法对图像的两个本征因子的假设较弱,适用于更广泛的图像.目前方法已在磁共振图像及自然图像中进行测试,得到较优结果.

A Scalable Local Analysis and Integration Approach to Intrinsic Image Decomposition

A unified mathematical model and an algorithm are proposed to solve the problems of the estimation of illumination and reflectance images of a natural image and the segmentation and bias field estimation of a magnetic resonance image(MRI). The proposed model only requires a basic assumption that the observed image can be approximated by the product of two intrinsic images with different properties. One of the two intrinsic images is a smooth image, S-image, and the other is a piece-wise approximately constant image, L-image. To fully exploit the properties of the intrinsic images, a scalable local analysis and integration(SLAI) approach is proposed for the problem of intrinsic image estimation. Due to the smoothness of the S-image, a low order Taylor expansion or a linear combination of general smooth basis functions is utilized to locally approximate the S-image. The obtained local smooth approximation of the S-image can be extended to a smooth image on the entire region of interest(ROI) using partition of unity subordinate to a cover of ROI. Meanwhile, the segmentation result and the estimation of the L-image are obtained. The proposed method is based on a weaker assumption than the methods in the literature, and therefore it is applicable to more images. The proposed method produces satisfactory results on MR images and natural images.