The label set is $\$ where 0 means the original pixels should be used and 1 means the computed average should be used.
The energy functional decomposes into a dataterm $\phi$ and a smoothness term $\psi$: A hard threshold on $D^i_$ can be achieved by using some appropriate set of $\alpha, \beta_0, \beta_1$.
On the reference frame, we detect features using SURF feature detector, then we track those feature points throughout the video sequence using Lucas-Kanade tracking method.
These tracked features will provide sparse correspondences between each frame and the reference.
When taking photos under low-light environments such as indoor or at night, one of the two undesirable outcomes can happen: The photos can be blurry due to camera's or subjects' motion taken with long exposures or they can contain high level of noise because of short exposures and high sensor sensitivity.
One approach that can overcome this problem is to capture a short video sequence or multiple high-noise photos and computationally combine them to produce a single low-noise photo.Given a short video sequence (10-30 frames) taken from a hand-held camera, recover a low-noise still image.The algorithm should be robust to both camera's and scene motions and should be fast enough to provide a practical experience on mobile phones / cameras.In order to handle larger motions with Farneback's algorithm, we therefore perform a global alignment using homography before running the dense optical flow as in our current pipeline.This hugely improves the alignment quality as shown below.This gives us a baseline quality for denoising algorithms.The runtime however turns out to be impractical for real-time applications as the algorithm took 23 minutes to process 15 frames at resolution 960 x 540 pixels.The smoothness term is only non-zero when $\psi(x_i, x_j \neq x_i) = \gamma$ which penalizes different adjacent labels.This binary segmentation problem is solved using graph-cut which gives us a global-optimal labeling $X: \mathbb^d \rightarrow $.We then erode this labeling function and apply Gaussian blur to transform 0-1 labeling into a continuous alpha mask.The final low-noise composite is computed using a simple interpolation $(1-x_i)I^0 x_i\widetilde$.