Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Color Image Enhancement by a Forward-and-Backward Adaptive Beltrami Flow
AFPAC '00 Proceedings of the Second International Workshop on Algebraic Frames for the Perception-Action Cycle
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
A Non-Local Algorithm for Image Denoising
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Manifold models for signals and images
Computer Vision and Image Understanding
Efficient Beltrami flow using a short time kernel
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Non-local image smoothing by applying anisotropic diffusion PDE's in the space of patches
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
A general framework for low level vision
IEEE Transactions on Image Processing
On the origin of the bilateral filter and ways to improve it
IEEE Transactions on Image Processing
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
IEEE Transactions on Image Processing
Digital restoration of damaged mural images
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
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The Beltrami framework treats images as two dimensional manifolds embedded in a joint features-space domain. This way, a color image is considered to be a two dimensional surface embedded in a hybrid special-spectral five dimensional $\left\{ x,y,R,G,B\right\} $ space. Image selective smoothing, often referred to as a denoising filter, amounts to the process of area minimization of the image surface by mean curvature flow. One interesting variant of the Beltrami framework is treating local neighboring pixels as the feature-space. A distance is defined by the amount of deformation a local patch undergoes while traversing its support in the spatial domain. The question we try to tackle in this note is how to perform patch based denoising accurately, and efficiently. As a motivation we demonstrate the performance of the Beltrami filter in patch-space, and provide useful implementation considerations that allow for parameter tuning and efficient implementation on hand-held devices like smart phones.