针对室外光照条件下阴影的快速高效检测问题，提出了基于正交分解的阴影检测算法。利用室外场景图像中阴影区域内外的线性模型建立线性方程组，对该线性方程组的解空间进行正交分解，得到一幅彩色光照不变图像和一幅光照变化图像。通过K-means算法将彩色光照不变图像分类为几个区域，每个区域具有一致的反照率。根据分类结果，对光照变化图像采用EM算法进行高斯混合建模，提取阴影区域。最后采用形态学算子对提取的阴影区域进行优化。该算法不需要复杂的特征算子学习过程，大大降低了计算的时间复杂度，而且不需要任何先验知识，可以直接应用到实时场景处理中。

For detecting the shadow in outdoor illumination conditions rapidly and efficiently, a shadow detection approach based on pixel-wise orthogonal decomposition is proposed. Based on linear model in and out of shadows in an outdoor scene image, a linear equation set is built for each pixel value vector and orthogonally decomposed. By the decomposition of the linear equation solution space, a color illumination invariant image and an illumination variation image are obtained. The color illumination invariant image is classified into some regions using K-means algorithm, each region has the same spectral albedo. According to the classification results, a Gaussian mixture model with expectation maximization algorithm is proposed for modeling the illumination variation image, and then the shadow areas are extracted. The extracted shadow areas are optimized with morphological operator. The proposed method does not need complex learning process of feature operators and greatly reduces the time complexity of computation. It also does not require any prior knowledge and can be directly applied to the real-time scene processing.