Image segmentation and edge enhancement with stabilized inverse diffusion equations

Caption title.Includes bibliographical references (p. 24-25).Supported by AFSOR. F49620-95-1-0083 Supported by ONR. N00014-91-J-1004 Supported in part by Boston University under the AFOSR Multidisciplinary Research Program on Reduced Signature Target Recognition. GC123919NGDIlya Pollak, Alan S. Willsky, Hamid Krim

Scale space analysis by stabilized inverse diffusion equations

Caption title.Includes bibliographical references (p. 11).Supported by AFSOR. F49620-95-1-0083 Supported by ONR. N00014-91-J-1004 Supported in part by Boston University under the AFOSR Multidisciplinary Research Program on Reduced Signature Target Recognition. GC123919NGDIlya Pollak, Alan S. Willsky, Hamid Krim

A Framework For TV Logos Learning Using Linear Inverse Diffusion Filters For Noise Removal

Different logotypes represent significant cues for video annotations. A combination of temporal and spatial segmentation methods can be used for logo extraction from various video contents. To achieve this segmentation, pixels with low variation of intensity over time are detected. Static backgrounds can become spurious parts of these logos. This paper offers a new way to use several segmentations of logos to learn new logo models from which noise has been removed. First, we group segmented logos of similar appearances into different clusters. Then, a model is learned for each cluster that has a minimum number of members. This is done by applying a linear inverse diffusion filter to all logos in each cluster. Our experiments demonstrate that this filter removes most of the noise that was added to the logo during segmentation and it successfully copes with misclassified logos that have been wrongly added to a cluster

Automatic solar feature detection using image processing and pattern recognition techniques

The objective of the research in this dissertation is to develop a software system to automatically detect and characterize solar flares, filaments and Corona Mass Ejections (CMEs), the core of so-called solar activity. These tools will assist us to predict space weather caused by violent solar activity. Image processing and pattern recognition techniques are applied to this system. For automatic flare detection, the advanced pattern recognition techniques such as Multi-Layer Perceptron (MLP), Radial Basis Function (RBF), and Support Vector Machine (SVM) are used. By tracking the entire process of flares, the motion properties of two-ribbon flares are derived automatically. In the applications of the solar filament detection, the Stabilized Inverse Diffusion Equation (SIDE) is used to enhance and sharpen filaments; a new method for automatic threshold selection is proposed to extract filaments from background; an SVM classifier with nine input features is used to differentiate between sunspots and filaments. Once a filament is identified, morphological thinning, pruning, and adaptive edge linking methods are applied to determine filament properties. Furthermore, a filament matching method is proposed to detect filament disappearance. The automatic detection and characterization of flares and filaments have been successfully applied on Hα full-disk images that are continuously obtained at Big Bear Solar Observatory (BBSO). For automatically detecting and classifying CMEs, the image enhancement, segmentation, and pattern recognition techniques are applied to Large Angle Spectrometric Coronagraph (LASCO) C2 and C3 images. The processed LASCO and BBSO images are saved to file archive, and the physical properties of detected solar features such as intensity and speed are recorded in our database. Researchers are able to access the solar feature database and analyze the solar data efficiently and effectively. The detection and characterization system greatly improves the ability to monitor the evolution of solar events and has potential to be used to predict the space weather

Image restoration using geometrically stabilized reverse heat equation

Blind restoration of blurred images is a classical ill-posed problem. There has been considerable interest in the use of partial differential equations to solve this problem. The blurring of an image has traditionally been modeled by Witkin [10] and Koenderink [4] by the heat equation. This has been the basis of the Gaussian scale space. However, a similar theoretical formulation has not been possible for deblurring of images due to the ill-posed nature of the reverse heat equation. Here we consider the stabilization of the reverse heat equation. We do this by damping the distortion along the edges by adding a normal component of the heat equation in the forward direction. We use a stopping criterion based on the divergence of the curvature in the resulting reverse heat flow. The resulting stabilized reverse heat flow makes it possible to solve the challenging problem of blind space varying deconvolution. The method is justified by a varied set of experimental results

A new anisotropic diffusion method, application to partial volume effect reduction

The partial volume effect is a significant limitation in medical imaging that results in blurring when the boundary between two structures of interest falls in the middle of a voxel. A new anisotropic diffusion method allows one to create interpolated 3D images corrected for partial volume, without enhancement of noise. After a zero-order interpolation, we apply a modified version of the anisotropic diffusion approach, wherein the diffusion coefficient becomes negative for high gradient values. As a result, the new scheme restores edges between regions that have been blurred by partial voluming, but it acts as normal anisotropic diffusion in flat regions, where it reduces noise. We add constraints to stabilize the method and model partial volume; i.e., the sum of neighboring voxels must equal the signal in the original low resolution voxel and the signal in a voxel is kept within its neighbor's limits. The method performed well on a variety of synthetic images and MRI scans. No noticeable artifact was induced by interpolation with partial volume correction, and noise was much reduced in homogeneous regions. We validated the method using the BrainWeb project database. Partial volume effect was simulated and restored brain volumes compared to the original ones. Errors due to partial volume effect were reduced by 28% and 35% for the 5% and 0% noise cases, respectively. The method was applied to in vivo "thick" MRI carotid artery images for atherosclerosis detection. There was a remarkable increase in the delineation of the lumen of the carotid artery

Stable Backward Diffusion Models that Minimise Convex Energies

The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a backward diffusion model which implements a smart stabilisation approach that can be used in combination with an easy to handle numerical scheme. So far, existing stabilisation strategies in literature require sophisticated numerics to solve the underlying initial value problem. We derive a class of space-discrete one-dimensional backward diffusion as gradient descent of energies where we gain stability by imposing range constraints. Interestingly, these energies are even convex. Furthermore, we establish a comprehensive theory for the time-continuous evolution and we show that stability carries over to a simple explicit time discretisation of our model. Finally, we confirm the stability and usefulness of our technique in experiments in which we enhance the contrast of digital greyscale and colour images

Stable Backward Diffusion Models that Minimise Convex Energies

The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a backward diffusion model which implements a smart stabilisation approach that can be used in combination with an easy-to-handle numerical scheme. So far, existing stabilisation strategies in the literature require sophisticated numerics to solve the underlying initial value problem. We derive a class of space-discrete one-dimensional backward diffusion as gradient descent of energies where we gain stability by imposing range constraints. Interestingly, these energies are even convex. Furthermore, we establish a comprehensive theory for the time-continuous evolution and we show that stability carries over to a simple explicit time discretisation of our model. Finally, we confirm the stability and usefulness of our technique in experiments in which we enhance the contrast of digital greyscale and colour images

On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and SIDEs

Soft wavelet shrinkage, total variation (TV) diffusion, total variation regularization, and a dynamical system called SIDEs are four useful techniques for discontinuity preserving denoising of signals and images. In this paper we investigate under which circumstances these methods are equivalent in the 1-D case. First we prove that Haar wavelet shrinkage on a single scale is equivalent to a single step of space-discrete TV diffusion or regularization of two-pixel pairs. In the translationally invariant case we show that applying cycle spinning to Haar wavelet shrinkage on a single scale can be regarded as an absolutely stable explicit discretization of TV diffusion. We prove that space-discrete TV difusion and TV regularization are identical, and that they are also equivalent to the SIDEs system when a specific force function is chosen. Afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularization of the Laplacian pyramid of the signal. We analyse possibilities to avoid Gibbs-like artifacts for multiscale Haar wavelet shrinkage by scaling the thesholds. Finally we present experiments where hybrid methods are designed that combine the advantages of wavelets and PDE / variational approaches. These methods are based on iterated shift-invariant wavelet shrinkage at multiple scales with scaled thresholds