Variational Image Segmentation Model Coupled with Image Restoration Achievements

Image segmentation and image restoration are two important topics in image processing with great achievements. In this paper, we propose a new multiphase segmentation model by combining image restoration and image segmentation models. Utilizing image restoration aspects, the proposed segmentation model can effectively and robustly tackle high noisy images, blurry images, images with missing pixels, and vector-valued images. In particular, one of the most important segmentation models, the piecewise constant Mumford-Shah model, can be extended easily in this way to segment gray and vector-valued images corrupted for example by noise, blur or missing pixels after coupling a new data fidelity term which comes from image restoration topics. It can be solved efficiently using the alternating minimization algorithm, and we prove the convergence of this algorithm with three variables under mild condition. Experiments on many synthetic and real-world images demonstrate that our method gives better segmentation results in comparison to others state-of-the-art segmentation models especially for blurry images and images with missing pixels values.Comment: 23 page

Uncertainty quantification for radio interferometric imaging: II. MAP estimation

Uncertainty quantification is a critical missing component in radio interferometric imaging that will only become increasingly important as the big-data era of radio interferometry emerges. Statistical sampling approaches to perform Bayesian inference, like Markov Chain Monte Carlo (MCMC) sampling, can in principle recover the full posterior distribution of the image, from which uncertainties can then be quantified. However, for massive data sizes, like those anticipated from the Square Kilometre Array (SKA), it will be difficult if not impossible to apply any MCMC technique due to its inherent computational cost. We formulate Bayesian inference problems with sparsity-promoting priors (motivated by compressive sensing), for which we recover maximum a posteriori (MAP) point estimators of radio interferometric images by convex optimisation. Exploiting recent developments in the theory of probability concentration, we quantify uncertainties by post-processing the recovered MAP estimate. Three strategies to quantify uncertainties are developed: (i) highest posterior density credible regions; (ii) local credible intervals (cf. error bars) for individual pixels and superpixels; and (iii) hypothesis testing of image structure. These forms of uncertainty quantification provide rich information for analysing radio interferometric observations in a statistically robust manner. Our MAP-based methods are approximately $10^5$ times faster computationally than state-of-the-art MCMC methods and, in addition, support highly distributed and parallelised algorithmic structures. For the first time, our MAP-based techniques provide a means of quantifying uncertainties for radio interferometric imaging for realistic data volumes and practical use, and scale to the emerging big-data era of radio astronomy.Comment: 13 pages, 10 figures, see companion article in this arXiv listin

A Two-stage Classification Method for High-dimensional Data and Point Clouds

High-dimensional data classification is a fundamental task in machine learning and imaging science. In this paper, we propose a two-stage multiphase semi-supervised classification method for classifying high-dimensional data and unstructured point clouds. To begin with, a fuzzy classification method such as the standard support vector machine is used to generate a warm initialization. We then apply a two-stage approach named SaT (smoothing and thresholding) to improve the classification. In the first stage, an unconstraint convex variational model is implemented to purify and smooth the initialization, followed by the second stage which is to project the smoothed partition obtained at stage one to a binary partition. These two stages can be repeated, with the latest result as a new initialization, to keep improving the classification quality. We show that the convex model of the smoothing stage has a unique solution and can be solved by a specifically designed primal-dual algorithm whose convergence is guaranteed. We test our method and compare it with the state-of-the-art methods on several benchmark data sets. The experimental results demonstrate clearly that our method is superior in both the classification accuracy and computation speed for high-dimensional data and point clouds.Comment: 21 pages, 4 figure

Can We Measure Individual Risk Attitudes in a Survey?

We combine a survey and an experiment with real pay-out among Peking University students to measure and validate individual risk attitudes. The experiment involves choosing between a cash payment and playing a lottery. The survey questions ask for the reservation price of a hypothetical lottery and self-assessment of risk attitude on a 0-10 scale. We confirm familiar findings: risk aversion dominates, women are more risk averse than men, risk aversion decreases with increasing parental income, risk attitudes are domain-specific. Correlations between survey measures and experimental measures, are in the right direction, but not very high. The survey measures are valid indicators of experimentally measured risk attitude, but with substantial noise remaining. Heterogeneity in levels and structures of risk attitude is large.risk attitude, survey question, experimental validation

Is Earnings Uncertainty Relevant for Educational Choice? An Empirical Analysis for China

We use the method of Dominitz and Manski (1996) to solicit anticipated wage distributions for continuing to a Master degree or going to work after completing the Bachelor degree. The means of the distributions have an effect on intention to continue as predicted by theory. The dispersions in these individual distributions have no effect on intention to continue, suggesting that anticipated earnings risk does not play a role in the decision.educational choice, wage expectations