5 research outputs found
Introducing anisotropic tensor to high order variational model for image restoration
Second order total variation (SOTV) models have advantages for image restoration over their first order counterparts including their ability to remove the staircase artefact in the restored image. However, such models tend to blur the reconstructed image when discretised for numerical solution [1–5]. To overcome this drawback, we introduce a new tensor weighted second order (TWSO) model for image restoration. Specifically, we develop a novel regulariser for the SOTV model that uses the Frobenius norm of the product of the isotropic SOTV Hessian matrix and an anisotropic tensor. We then adapt the alternating direction method of multipliers (ADMM) to solve the proposed model by breaking down the original problem into several subproblems. All the subproblems have closed-forms and can be solved efficiently. The proposed method is compared with state-of-the-art approaches such as tensor-based anisotropic diffusion, total generalised variation, and Euler's elastica. We validate the proposed TWSO model using extensive experimental results on a large number of images from the Berkeley BSDS500. We also demonstrate that our method effectively reduces both the staircase and blurring effects and outperforms existing approaches for image inpainting and denoising applications
Spherical harmonics for surface parametrisation and remeshing
This paper proposes a novel method for parametrisation and remeshing incomplete and irregular polygonal meshes. Spherical harmonics basis functions are used for parametrisation. This involves least squares fitting of spherical harmonics basis functions to the surface mesh. Tikhonov regularisation is then used to improve the parametrisation before remeshing the surface. Experiments show that the proposed techniques are effective for parametrising and remeshing polygonal meshes
Novel Methods for Microglia Segmentation, Feature Extraction, and Classification
© 2017 IEEE. Segmentation and analysis of histological images provides a valuable tool to gain insight into the biology and function of microglial cells in health and disease. Common image segmentation methods are not suitable for inhomogeneous histology image analysis and accurate classification of microglial activation states has remained a challenge. In this paper, we introduce an automated image analysis framework capable of efficiently segmenting microglial cells from histology images and analyzing their morphology. The framework makes use of variational methods and the fast-split Bregman algorithm for image denoising and segmentation, and of multifractal analysis for feature extraction to classify microglia by their activation states. Experiments show that the proposed framework is accurate and scalable to large datasets and provides a useful tool for the study of microglial biology
Non-linear process convolutions for multi-output Gaussian processes
The paper introduces a non-linear version of the process convolution
formalism for building covariance functions for multi-output Gaussian
processes. The non-linearity is introduced via Volterra series, one series per
each output. We provide closed-form expressions for the mean function and the
covariance function of the approximated Gaussian process at the output of the
Volterra series. The mean function and covariance function for the joint
Gaussian process are derived using formulae for the product moments of Gaussian
variables. We compare the performance of the non-linear model against the
classical process convolution approach in one synthetic dataset and two real
datasets.Comment: 16 pages plus 2 page supplementary. Accepted to AISTATS 201
Tracking tracer motion in a 4-D electrical resistivity tomography experiment
A new framework for automatically tracking subsurface tracers in electrical resistivity tomography (ERT) monitoring images is presented. Using computer vision and Bayesian inference techniques, in the form of a Kalman filter, the trajectory of a subsurface tracer is monitored by predicting and updating a state model representing its movements. Observations for the Kalman filter are gathered using the maximally stable volumes algorithm, which is used to dynamically threshold local regions of an ERT image sequence to detect the tracer at each time step. The application of the framework to the results of 2-D and 3-D tracer monitoring experiments show that the proposed method is effective for detecting and tracking tracer plumes in ERT images in the presence of noise, without intermediate manual intervention