20,635 research outputs found
A Phase Field Model for Continuous Clustering on Vector Fields
A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns-the actual clustering-during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution shear layer type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. Here, we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.
On Using Physical Analogies for Feature and Shape Extraction in Computer Vision
There is a rich literature of approaches to image feature extraction in computer vision. Many sophisticated approaches exist for low- and high-level feature extraction but can be complex to implement with parameter choice guided by experimentation, but impeded by speed of computation. We have developed new ways to extract features based on notional use of physical paradigms, with parameterisation that is more familiar to a scientifically-trained user, aiming to make best use of computational resource. We describe how analogies based on gravitational force can be used for low-level analysis, whilst analogies of water flow and heat can be deployed to achieve high-level smooth shape detection. These new approaches to arbitrary shape extraction are compared with standard state-of-art approaches by curve evolution. There is no comparator operator to our use of gravitational force. We also aim to show that the implementation is consistent with the original motivations for these techniques and so contend that the exploration of physical paradigms offers a promising new avenue for new approaches to feature extraction in computer vision
Highly corrupted image inpainting through hypoelliptic diffusion
We present a new image inpainting algorithm, the Averaging and Hypoelliptic
Evolution (AHE) algorithm, inspired by the one presented in [SIAM J. Imaging
Sci., vol. 7, no. 2, pp. 669--695, 2014] and based upon a semi-discrete
variation of the Citti-Petitot-Sarti model of the primary visual cortex V1. The
AHE algorithm is based on a suitable combination of sub-Riemannian hypoelliptic
diffusion and ad-hoc local averaging techniques. In particular, we focus on
reconstructing highly corrupted images (i.e. where more than the 80% of the
image is missing), for which we obtain reconstructions comparable with the
state-of-the-art.Comment: 15 pages, 10 figure
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
Sobolev gradients and image interpolation
We present here a new image inpainting algorithm based on the Sobolev
gradient method in conjunction with the Navier-Stokes model. The original model
of Bertalmio et al is reformulated as a variational principle based on the
minimization of a well chosen functional by a steepest descent method. This
provides an alternative of the direct solving of a high-order partial
differential equation and, consequently, allows to avoid complicated numerical
schemes (min-mod limiters or anisotropic diffusion). We theoretically analyze
our algorithm in an infinite dimensional setting using an evolution equation
and obtain global existence and uniqueness results as well as the existence of
an -limit. Using a finite difference implementation, we demonstrate
using various examples that the Sobolev gradient flow, due to its smoothing and
preconditioning properties, is an effective tool for use in the image
inpainting problem
Bridge Simulation and Metric Estimation on Landmark Manifolds
We present an inference algorithm and connected Monte Carlo based estimation
procedures for metric estimation from landmark configurations distributed
according to the transition distribution of a Riemannian Brownian motion
arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric.
The distribution possesses properties similar to the regular Euclidean normal
distribution but its transition density is governed by a high-dimensional PDE
with no closed-form solution in the nonlinear case. We show how the density can
be numerically approximated by Monte Carlo sampling of conditioned Brownian
bridges, and we use this to estimate parameters of the LDDMM kernel and thus
the metric structure by maximum likelihood
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