Moving-edge detection via heat flow analogy

In this paper, a new and automatic moving-edge detection algorithm is proposed, based on using the heat flow analogy. This algorithm starts with anisotropic heat diffusion in the spatial domain, to remove noise and sharpen region boundaries for the purpose of obtaining high quality edge data. Then, isotropic and linear heat diffusion is applied in the temporal domain to calculate the total amount of heat flow. The moving-edges are represented as the total amount of heat flow out from the reference frame. The overall process is completed by non-maxima suppression and hysteresis thresholding to obtain binary moving edges. Evaluation, on a variety of data, indicates that this approach can handle noise in the temporal domain because of the averaging inherent of isotropic heat flow. Results also show that this technique can detect moving-edges in image sequences, without background image subtraction

A multiresolution framework for local similarity based image denoising

In this paper, we present a generic framework for denoising of images corrupted with additive white Gaussian noise based on the idea of regional similarity. The proposed framework employs a similarity function using the distance between pixels in a multidimensional feature space, whereby multiple feature maps describing various local regional characteristics can be utilized, giving higher weight to pixels having similar regional characteristics. An extension of the proposed framework into a multiresolution setting using wavelets and scale space is presented. It is shown that the resulting multiresolution multilateral (MRM) filtering algorithm not only eliminates the coarse-grain noise but can also faithfully reconstruct anisotropic features, particularly in the presence of high levels of noise

Finding faint HI structure in and around galaxies: scraping the barrel

Soon to be operational HI survey instruments such as APERTIF and ASKAP will produce large datasets. These surveys will provide information about the HI in and around hundreds of galaxies with a typical signal-to-noise ratio of $\sim$ 10 in the inner regions and $\sim$ 1 in the outer regions. In addition, such surveys will make it possible to probe faint HI structures, typically located in the vicinity of galaxies, such as extra-planar-gas, tails and filaments. These structures are crucial for understanding galaxy evolution, particularly when they are studied in relation to the local environment. Our aim is to find optimized kernels for the discovery of faint and morphologically complex HI structures. Therefore, using HI data from a variety of galaxies, we explore state-of-the-art filtering algorithms. We show that the intensity-driven gradient filter, due to its adaptive characteristics, is the optimal choice. In fact, this filter requires only minimal tuning of the input parameters to enhance the signal-to-noise ratio of faint components. In addition, it does not degrade the resolution of the high signal-to-noise component of a source. The filtering process must be fast and be embedded in an interactive visualization tool in order to support fast inspection of a large number of sources. To achieve such interactive exploration, we implemented a multi-core CPU (OpenMP) and a GPU (OpenGL) version of this filter in a 3D visualization environment ($\tt{SlicerAstro}$).Comment: 17 pages, 9 figures, 4 tables. Astronomy and Computing, accepte

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods

Segmentation of ultrasound images of thyroid nodule for assisting fine needle aspiration cytology

The incidence of thyroid nodule is very high and generally increases with the age. Thyroid nodule may presage the emergence of thyroid cancer. The thyroid nodule can be completely cured if detected early. Fine needle aspiration cytology is a recognized early diagnosis method of thyroid nodule. There are still some limitations in the fine needle aspiration cytology, and the ultrasound diagnosis of thyroid nodule has become the first choice for auxiliary examination of thyroid nodular disease. If we could combine medical imaging technology and fine needle aspiration cytology, the diagnostic rate of thyroid nodule would be improved significantly. The properties of ultrasound will degrade the image quality, which makes it difficult to recognize the edges for physicians. Image segmentation technique based on graph theory has become a research hotspot at present. Normalized cut (Ncut) is a representative one, which is suitable for segmentation of feature parts of medical image. However, how to solve the normalized cut has become a problem, which needs large memory capacity and heavy calculation of weight matrix. It always generates over segmentation or less segmentation which leads to inaccurate in the segmentation. The speckle noise in B ultrasound image of thyroid tumor makes the quality of the image deteriorate. In the light of this characteristic, we combine the anisotropic diffusion model with the normalized cut in this paper. After the enhancement of anisotropic diffusion model, it removes the noise in the B ultrasound image while preserves the important edges and local details. This reduces the amount of computation in constructing the weight matrix of the improved normalized cut and improves the accuracy of the final segmentation results. The feasibility of the method is proved by the experimental results.Comment: 15pages,13figure