Lossless image compression is particularly important in applications requiring high fidelity such as medical imaging, remote sensing and scientific imaging. These applications cannot tolerate the minute artifacts that are caused by lossy compression methods. We first describe a new predictor for lossless image compression based on plane fitting. Our main contribution is an adaptive model switching algorithm that locally selects the best predictor for each pixel based on context. Our experiments show that the new predictor substantially outperform common lossless methods such as CALIC, JPEG-LS, CCSDS SZIP and SFALIC for various medical images of different modalities (including CT and MR images) and bit depths. The simplicity and inherently parallel nature of the model switching algorithm makes a very fast implementation possible.

The RANdom SAmple Consensus (RANSAC) algorithm, as a robust parameter estimator, has been widely used to remove gross errors. However, there is less work on analyzing the uncertainty produced by the RANSAC. This paper fills this gap by presenting an uncertainty estimation algorithm for the RANSAC. Based on a thorough analysis on the uncertainty of the model parameters generated during the random hypothesis sampling process of the RANSAC, we derive the probability that each hypothesis is selected as the best hypothesis by the RANSAC. Using the probability of the best hypothesis, we characterize the error expectation and error covariance of the model parameter estimates and compute the probability of each data point being an inlier. Three models including line fitting, homography, and essential matrix are used to evaluate the performance of the uncertainty estimation algorithm. Results demonstrate that the uncertainty produced by the RANSAC is characterized successfully by the proposed algorithm.

Matrix factorization in the presence of missing data is at the core of many computer vision problems such as structure from motion (SfM), non-rigid SfM and photometric stereo. We formulate the problem of matrix factorization with missing data as a low-rank semidefinite program (LRSDP) with the advantage that: $1)$ an efficient quasi-Newton implementation of the LRSDP enables us to solve large-scale factorization problems, and $2)$ additional constraints such as ortho-normality, required in orthographic SfM, can be directly incorporated in the new formulation. Our empirical evaluations suggest that, under the conditions of matrix completion theory, the proposed algorithm finds the optimal solution, and also requires fewer observations compared to the current state-of-the-art algorithms. We further demonstrate the effectiveness of the proposed algorithm in solving the affine SfM problem, non-rigid SfM and photometric stereo problems.