Ce Liu Thesis

The two latter errors however are not important in our task because we only care about image similarity.Suppose these aligned frames are $I^1, I^2, \dots, I^n$ and $I^0$ is the reference, we compute $D^i = G * (I^0 - I^i)$ where $G$ is a truncated Gaussian kernel of size 3 x 3 and $*$ is the convolution operator.The smoothness term is only non-zero when $\psi(x_i, x_j \neq x_i) = \gamma$ which penalizes different adjacent labels.

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In such case, it is sometimes more desirable to retain the noisy original pixels.

One way to solve this problem is to apply a threshold to the color difference and retain original pixels when the sum is too large.

Then we weight the contribution from each pixel in each frame based on color similarity.

A noise-reduction version of $I^0$ is given by: $Z$ is the normalization factor and $D^i_$ is a vector that encodes RGB values for pixel $uv$. This similarity-based weight can handle small scene motions, but for large motions, there can be cases where the average pixels are close to those of $I^0$ but represent different objects such as when the exact pose of a person in the reference frame, for example, appears in only a few frames and the average converges to a different value but close to the true value.

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 an attempt to make it faster, we tried different approaches and experimented with bilateral filtering on Permutohedral Lattice that spans across multiple frames in the video without doing any motion estimation.The amount of noise in uniform-color regions is reduced but when compared to a result using a high-quality dense optical flow, the image edges that are corrupted due to noise cannot be recovered or denoised properly.We studied some techniques used in related work and tried different combinations of the algorithms, but given a limited period of time, we were not able to experiment with full implementations of the reference papers.However, we came up with a reasonable compromise between algorithm's runtime, complexity, and quality.Again, to make the algorithm more robust against noise, the sum of color differences around a Gaussian patch is used instead.(Assuming zero-mean noise, the sum of differences around the same patch should be close to zero.) This threshold alone can cause noisy artifacts, so we simply enforce spatial smoothness using Markov random field defined on a standard 4-connected grid.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 $(1-x_i)I^0 x_i\widetilde$.The following is a full description of our algorithm.The first frame in the video sequence will be used as a reference frame for which we try to reduce the noise.