This paper introduces a novel image filtering technique called the *guided filter*. Unlike traditional linear translation-invariant (LTI) filters, the guided filter incorporates additional information from a guidance image to enhance its performance. The filter is derived from a local linear model and can be applied to both grayscale and color images. It preserves edges better than the popular bilateral filter and has a fast, exact O(N) time algorithm, where N is the number of pixels. The guided filter is theoretically connected to the matting Laplacian matrix, making it a more versatile tool for various applications such as noise reduction, detail smoothing, HDR compression, image matting, haze removal, and joint upsampling. The paper also discusses the edge-preserving properties of the guided filter, its relation to the matting Laplacian matrix, and its efficient implementation. Experimental results demonstrate the effectiveness and efficiency of the guided filter in a wide range of computer vision and graphics tasks.This paper introduces a novel image filtering technique called the *guided filter*. Unlike traditional linear translation-invariant (LTI) filters, the guided filter incorporates additional information from a guidance image to enhance its performance. The filter is derived from a local linear model and can be applied to both grayscale and color images. It preserves edges better than the popular bilateral filter and has a fast, exact O(N) time algorithm, where N is the number of pixels. The guided filter is theoretically connected to the matting Laplacian matrix, making it a more versatile tool for various applications such as noise reduction, detail smoothing, HDR compression, image matting, haze removal, and joint upsampling. The paper also discusses the edge-preserving properties of the guided filter, its relation to the matting Laplacian matrix, and its efficient implementation. Experimental results demonstrate the effectiveness and efficiency of the guided filter in a wide range of computer vision and graphics tasks.