Efficient Relaxations for Dense CRFs with Sparse Higher Order Potentials

Dense conditional random fields (CRFs) have become a popular framework for modelling several problems in computer vision such as stereo correspondence and multi-class semantic segmentation. By modelling long-range interactions, dense CRFs provide a labelling that captures finer detail than their sparse counterparts. Currently, the state-of-the-art algorithm performs mean-field inference using a filter-based method but fails to provide a strong theoretical guarantee on the quality of the solution. A question naturally arises as to whether it is possible to obtain a maximum a posteriori (MAP) estimate of a dense CRF using a principled method. Within this paper, we show that this is indeed possible. We will show that, by using a filter-based method, continuous relaxations of the MAP problem can be optimised efficiently using state-of-the-art algorithms. Specifically, we will solve a quadratic programming (QP) relaxation using the Frank-Wolfe algorithm and a linear programming (LP) relaxation by developing a proximal minimisation framework. By exploiting labelling consistency in the higher-order potentials and utilising the filter-based method, we are able to formulate the above algorithms such that each iteration has a complexity linear in the number of classes and random variables. The presented algorithms can be applied to any labelling problem using a dense CRF with sparse higher-order potentials. In this paper, we use semantic segmentation as an example application as it demonstrates the ability of the algorithm to scale to dense CRFs with large dimensions. We perform experiments on the Pascal dataset to indicate that the presented algorithms are able to attain lower energies than the mean-field inference method

Enhancement of Image Resolution by Binarization

Image segmentation is one of the principal approaches of image processing. The choice of the most appropriate Binarization algorithm for each case proved to be a very interesting procedure itself. In this paper, we have done the comparison study between the various algorithms based on Binarization algorithms and propose a methodologies for the validation of Binarization algorithms. In this work we have developed two novel algorithms to determine threshold values for the pixels value of the gray scale image. The performance estimation of the algorithm utilizes test images with, the evaluation metrics for Binarization of textual and synthetic images. We have achieved better resolution of the image by using the Binarization method of optimum thresholding techniques.Comment: 5 pages, 8 figure

Multi-Modal Mean-Fields via Cardinality-Based Clamping

Mean Field inference is central to statistical physics. It has attracted much interest in the Computer Vision community to efficiently solve problems expressible in terms of large Conditional Random Fields. However, since it models the posterior probability distribution as a product of marginal probabilities, it may fail to properly account for important dependencies between variables. We therefore replace the fully factorized distribution of Mean Field by a weighted mixture of such distributions, that similarly minimizes the KL-Divergence to the true posterior. By introducing two new ideas, namely, conditioning on groups of variables instead of single ones and using a parameter of the conditional random field potentials, that we identify to the temperature in the sense of statistical physics to select such groups, we can perform this minimization efficiently. Our extension of the clamping method proposed in previous works allows us to both produce a more descriptive approximation of the true posterior and, inspired by the diverse MAP paradigms, fit a mixture of Mean Field approximations. We demonstrate that this positively impacts real-world algorithms that initially relied on mean fields.Comment: Submitted for review to CVPR 201

Visual Object Tracking: The Initialisation Problem

Model initialisation is an important component of object tracking. Tracking algorithms are generally provided with the first frame of a sequence and a bounding box (BB) indicating the location of the object. This BB may contain a large number of background pixels in addition to the object and can lead to parts-based tracking algorithms initialising their object models in background regions of the BB. In this paper, we tackle this as a missing labels problem, marking pixels sufficiently away from the BB as belonging to the background and learning the labels of the unknown pixels. Three techniques, One-Class SVM (OC-SVM), Sampled-Based Background Model (SBBM) (a novel background model based on pixel samples), and Learning Based Digital Matting (LBDM), are adapted to the problem. These are evaluated with leave-one-video-out cross-validation on the VOT2016 tracking benchmark. Our evaluation shows both OC-SVMs and SBBM are capable of providing a good level of segmentation accuracy but are too parameter-dependent to be used in real-world scenarios. We show that LBDM achieves significantly increased performance with parameters selected by cross validation and we show that it is robust to parameter variation.Comment: 15th Conference on Computer and Robot Vision (CRV 2018). Source code available at https://github.com/georgedeath/initialisation-proble

Manifold Learning in MR spectroscopy using nonlinear dimensionality reduction and unsupervised clustering

Purpose To investigate whether nonlinear dimensionality reduction improves unsupervised classification of 1H MRS brain tumor data compared with a linear method. Methods In vivo single-voxel 1H magnetic resonance spectroscopy (55 patients) and 1H magnetic resonance spectroscopy imaging (MRSI) (29 patients) data were acquired from histopathologically diagnosed gliomas. Data reduction using Laplacian eigenmaps (LE) or independent component analysis (ICA) was followed by k-means clustering or agglomerative hierarchical clustering (AHC) for unsupervised learning to assess tumor grade and for tissue type segmentation of MRSI data. Results An accuracy of 93% in classification of glioma grade II and grade IV, with 100% accuracy in distinguishing tumor and normal spectra, was obtained by LE with unsupervised clustering, but not with the combination of k-means and ICA. With 1H MRSI data, LE provided a more linear distribution of data for cluster analysis and better cluster stability than ICA. LE combined with k-means or AHC provided 91% accuracy for classifying tumor grade and 100% accuracy for identifying normal tissue voxels. Color-coded visualization of normal brain, tumor core, and infiltration regions was achieved with LE combined with AHC. Conclusion Purpose To investigate whether nonlinear dimensionality reduction improves unsupervised classification of 1H MRS brain tumor data compared with a linear method. Methods In vivo single-voxel 1H magnetic resonance spectroscopy (55 patients) and 1H magnetic resonance spectroscopy imaging (MRSI) (29 patients) data were acquired from histopathologically diagnosed gliomas. Data reduction using Laplacian eigenmaps (LE) or independent component analysis (ICA) was followed by k-means clustering or agglomerative hierarchical clustering (AHC) for unsupervised learning to assess tumor grade and for tissue type segmentation of MRSI data. Results An accuracy of 93% in classification of glioma grade II and grade IV, with 100% accuracy in distinguishing tumor and normal spectra, was obtained by LE with unsupervised clustering, but not with the combination of k-means and ICA. With 1H MRSI data, LE provided a more linear distribution of data for cluster analysis and better cluster stability than ICA. LE combined with k-means or AHC provided 91% accuracy for classifying tumor grade and 100% accuracy for identifying normal tissue voxels. Color-coded visualization of normal brain, tumor core, and infiltration regions was achieved with LE combined with AHC. Conclusion The LE method is promising for unsupervised clustering to separate brain and tumor tissue with automated color-coding for visualization of 1H MRSI data after cluster analysis

MRI Super-Resolution using Multi-Channel Total Variation

This paper presents a generative model for super-resolution in routine clinical magnetic resonance images (MRI), of arbitrary orientation and contrast. The model recasts the recovery of high resolution images as an inverse problem, in which a forward model simulates the slice-select profile of the MR scanner. The paper introduces a prior based on multi-channel total variation for MRI super-resolution. Bias-variance trade-off is handled by estimating hyper-parameters from the low resolution input scans. The model was validated on a large database of brain images. The validation showed that the model can improve brain segmentation, that it can recover anatomical information between images of different MR contrasts, and that it generalises well to the large variability present in MR images of different subjects. The implementation is freely available at https://github.com/brudfors/spm_superre

Model Selection Criteria for Segmented Time Series from a Bayesian Approach to Information Compression

The principle that the simplest model capable of describing observed phenomena should also correspond to the best description has long been a guiding rule of inference. In this paper a Bayesian approach to formally implementing this principle is employed to develop model selection criteria for detecting structural change in financial and economic time series. Model selection criteria which allow for multiple structural breaks and which seek the optimal model order and parameter choices within regimes are derived. Comparative simulations against other popular information based model selection criteria are performed. Application of the derived criteria are also made to example financial and economic time series.Complexity theory; segmentation; break points; change points; model selection; model choice.