7. Kernel Regression for Image Processing and Reconstruction
H.Takeda, S.Farsiu and P.Milanfar, IEEE transactions on image processing, vol.16, no.2, feb 2007
It is a Non-parametric approach that rely on the data itself to get the structure of the model and this is referred to as regression function. The kernel can be either a gaussian, exponential or other forms, in this paper gaussian kernel is chosen because of its low computational complexity. The kernel includes two important parameters such as the weighting and smoothing parameter.This method allows for tailoring the estimation problem to the local characteristics of the data,where the nearby samples are given higher weight than samples farther away from the center of the analysis window. Performance of the estimator also depends on the choice of the smoothing matrix(H),smaller kernels in the areas with more available samples, whereas larger kernels are suitable for more sparsely sampled areas in the image.
Choosing the order (N) is very important as it effectively increases more complex approximation of the signal.The low order approximates the result in smoother images.Experiments were conducted for different orders of approximation. For moderately noisy image, higher order interpolation results in better estimate and for heavily noisy image , the lower order regressors are better.
Classical Kernel Regression: It is nothing but local weighted averaging of data, where the order determines the type and complexity of the weighting scheme. For higher order regression the original kernel is modified to yield newly adapted equivalent kernel. This equivalently adapted kernel tend to adapt themselves to the density of the available samples. This method provides low quality of reconstruction in edge areas.
Data Adapted Kernel: This method relay not only on the sample location and density but also on the radiometric properties of these samples, where it adapts locally to the image features such as edges.
Steering Kernel: Measures a function of local gradient estimated between the neighboring values and to use this estimate to weight the respective measurements. It is based on two step approach, where the initial estimate of the image gradients is found with the help of some kind of gradient estimator . Then, this estimate is used to measure the dominant orientation of the local gradients in the image. In the second filtering stage , this orientation information is used to adaptively steer the local kernel , resulting in elongated, elliptical contours spread along the directions of the local edge.
With these locally adapted kernels, the denoising is effected most strongly along the edges resulting in strong preservation of details in the final output.
Software: http://alumni.soe.ucsc.edu/~htakeda/KernelToolBox.htm
Choosing the order (N) is very important as it effectively increases more complex approximation of the signal.The low order approximates the result in smoother images.Experiments were conducted for different orders of approximation. For moderately noisy image, higher order interpolation results in better estimate and for heavily noisy image , the lower order regressors are better.
Classical Kernel Regression: It is nothing but local weighted averaging of data, where the order determines the type and complexity of the weighting scheme. For higher order regression the original kernel is modified to yield newly adapted equivalent kernel. This equivalently adapted kernel tend to adapt themselves to the density of the available samples. This method provides low quality of reconstruction in edge areas.
Data Adapted Kernel: This method relay not only on the sample location and density but also on the radiometric properties of these samples, where it adapts locally to the image features such as edges.
Steering Kernel: Measures a function of local gradient estimated between the neighboring values and to use this estimate to weight the respective measurements. It is based on two step approach, where the initial estimate of the image gradients is found with the help of some kind of gradient estimator . Then, this estimate is used to measure the dominant orientation of the local gradients in the image. In the second filtering stage , this orientation information is used to adaptively steer the local kernel , resulting in elongated, elliptical contours spread along the directions of the local edge.
With these locally adapted kernels, the denoising is effected most strongly along the edges resulting in strong preservation of details in the final output.
Software: http://alumni.soe.ucsc.edu/~htakeda/KernelToolBox.htm
Results for MATLAB Code
(1)Image reconstruction from irregularly downsampled image by steering kernel regression.
(2) Image upscaling by steering kernel regression.
(3) Salt & Pepper Noise reduction.
(4) Compression artifact removal by using iterative steering kernel algorithm.
(5) Denoising for a color Image.