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A multiscale approach to estimating topographically correlated propagation delays in radar interferograms

When targeting small amplitude surface deformation, using repeat orbit Interferometric Synthetic Aperture Radar (InSAR) observations can be plagued by propagation delays, some of which correlate with topographic variations. These topographically-correlated delays result from temporal variations in vertical stratification of the troposphere. An approximate model assuming a linear relationship between topography and interferometric phase has been used to correct observations with success in a few studies. Here, we present a robust approach to estimating the transfer function, K, between topography and phase that is relatively insensitive to confounding processes (earthquake deformation, phase ramps from orbital errors, tidal loading, etc.). Our approach takes advantage of a multiscale perspective by using a band-pass decomposition of both topography and observed phase. This decomposition into several spatial scales allows us to determine the bands wherein correlation between topography and phase is significant and stable. When possible, our approach also takes advantage of any inherent redundancy provided by multiple interferograms constructed with common scenes. We define a unique set of component time intervals for a given suite of interferometric pairs. We estimate an internally consistent transfer function for each component time interval, which can then be recombined to correct any arbitrary interferometric pair. We demonstrate our approach on a synthetic example and on data from two locations: Long Valley Caldera, California, which experienced prolonged periods of surface deformation from pressurization of a deep magma chamber, and one coseismic interferogram from the 2007 Mw 7.8 Tocapilla earthquake in northern Chile. In both examples, the corrected interferograms show improvements in regions of high relief, independent of whether or not we pre-correct the data for a source model. We believe that most of the remaining signals are predominately due to heterogeneous water vapor distribution that requires more sophisticated correction methods than those described here.

Extracting Meaningful Curves from Images

Since the beginning, Mathematical Morphology has proposed to extract shapesfrom images as connected components of level sets. These methods have proved veryefficient in shape recognition and shape analysis. In this paper, we present an improved method to select the most meaningful level lines (boundaries of level sets) from an image. This extraction can be based on statistical arguments, leading to a parameter free algorithm. It permits to roughly extract all pieces of level lines of an image, that coincide with pieces of edges. By this method, the numberof encoded level lines is reduced by a factor 100, without any loss of shape contents. In contrast to edge detection algorithms or snakes methods, such a level lines selection method delivers accurate shape elements, without user parameter since selection parameters can be computed by the Helmholtz Principle. The paper aims at improving the original method proposed in [10]. We give a mathematicalinterpretation of the model, which explains why some pieces of curve are overdetected. We introduce a multiscale approach that makes the method more robust to noise. A more local algorithm is introduced, taking local contrast variations into account. Finally, we empirically prove that regularity makes detection more robust but does not qualitatively change the results.

Multiscale InSAR Time Series (MInTS) analysis of surface deformation

[1] We present a new approach to extracting spatially and temporally continuous ground deformation fields from interferometric synthetic aperture radar (InSAR) data. We focus on unwrapped interferograms from a single viewing geometry, estimating ground deformation along the line-of-sight. Our approach is based on a wavelet decomposition in space and a general parametrization in time. We refer to this approach as MInTS (Multiscale InSAR Time Series). The wavelet decomposition efficiently deals with commonly seen spatial covariances in repeat-pass InSAR measurements, since the coefficients of the wavelets are essentially spatially uncorrelated. Our time-dependent parametrization is capable of capturing both recognized and unrecognized processes, and is not arbitrarily tied to the times of the SAR acquisitions. We estimate deformation in the wavelet-domain, using a cross-validated, regularized least squares inversion. We include a model-resolution-based regularization, in order to more heavily damp the model during periods of sparse SAR acquisitions, compared to during times of dense acquisitions. To illustrate the application of MInTS, we consider a catalog of 92 ERS and Envisat interferograms, spanning 16 years, in the Long Valley caldera, CA, region. MInTS analysis captures the ground deformation with high spatial density over the Long Valley region.

An A Contrario Decision Method for Shape Element Recognition

Shape recognition is the field of computer vision which addresses the problem of finding out whether a query shape lies or not in a shape database, up to a certain invariance. Most shape recognition methods simply sort shapes from the database along some (dis-)similarity measure to the query shape. Their main weakness is the decision stage, which should aim at giving a clear-cut answer to the question: “do these two shapes look alike?” In this article, the proposed solution consists in bounding the number of false correspondences of the query shape among the database shapes, ensuring that the obtained matches are not likely to occur “by chance”. As an application, one can decide with a parameterless method whether any two digital images share some shapes or not.

Toward a combined tool to assist dermatologists in melanoma detection from dermoscopic images of pigmented skin lesions

Highlights? Classification of melanocytic lesions as malignant or benign from dermoscopic images. ? Border, texture, color and structure features inspired by the clinical practice. ? Method designed and tested on a database of 655 images of melanocytic lesions. ? Automatic lesion segmentation. Classification based on AdaBoost with decision trees. ? Sensitivity/specificity: 90%/77% (90%/85%) for automatic (manual) segmentation. In this paper we propose a machine learning approach to classify melanocytic lesions as malignant or benign, using dermoscopic images. The lesion features used in the classification framework are inspired on border, texture, color and structures used in popular dermoscopy algorithms performed by clinicians by visual inspection. The main weakness of dermoscopy algorithms is the selection of a set of weights and thresholds, that appear not to be robust or independent of population. The use of machine learning techniques allows to overcome this issue. The proposed method is designed and tested on an image database composed of 655 images of melanocytic lesions: 544 benign lesions and 111 malignant melanoma. After an image pre-processing stage that includes hair removal filtering, each image is automatically segmented using well known image segmentation algorithms. Then, each lesion is characterized by a feature vector that contains shape, color and texture information, as well as local and global parameters. The detection of particular dermoscopic patterns associated with melanoma is also addressed, and its inclusion in the classification framework is discussed. The learning and classification stage is performed using AdaBoost with C4.5 decision trees. For the automatically segmented database, classification delivered a specificity of 77% for a sensitivity of 90%. The same classification procedure applied to images manually segmented by an experienced dermatologist yielded a specificity of 85% for a sensitivity of 90%.

A Unified Framework for Detecting Groups and Application to Shape Recognition

A unified a contrario detection method is proposed to solve three classical problems in clustering analysis. The first one is to evaluate the validity of a cluster candidate. The second problem is that meaningful clusters can contain or be contained in other meaningful clusters. A rule is needed to define locally optimal clusters by inclusion. The third problem is the definition of a correct merging rule between meaningful clusters, permitting to decide whether they should stay separate or unite. The motivation of this theory is shape recognition. Matching algorithms usually compute correspondences between more or less local features (called shape elements) between images to be compared. Each pair of matching shape elements leads to a unique transformation (similarity or affine map.) The present theory is used to group these shape elements into shapes by detecting clusters in the transformation space.

Boosting monte carlo rendering by ray histogram fusion

This article proposes a new multiscale filter accelerating Monte Carlo renderer. Each pixel in the image is characterized by the colors of the rays that reach its surface. The proposed filter uses a statistical distance to compare with each other the ray color distributions associated with different pixels, at each scale. Based on this distance, it decides whether two pixels can share their rays or not. This simple and easily reproducible algorithm provides a psnr gain of 10 to 15 decibels, or equivalently accelerates the rendering process by using 10 to 30 times fewer samples without observable bias. The algorithm is consistent, does not assume a particular noise model, and is immediately extendable to synthetic movies. Being based on the ray color values only, it can be combined with all rendering effects.

Changes in Postural Control Parameters after Vestibular Rehabilitation in Patients with Central Vestibular Disorders

Objective—The aim of this study was to determine postural responses before and after a vestibular rehabilitation program (VRP) in 14 patients with central vestibular disorders (CVD). Material and Methods—The confidence ellipse (CE) of the center of pressure distribution area and the sway velocity (SV) were the parameters used for the quantitative assessment of postural control (PC). These two parameters were analyzed before and after a VRP for two visual conditions. Behavioral postural responses were studied by means of the time–frequency scalogram using wavelets and the sway frequency content was measured in arbitrary units of energy density. Results—Ten patients showed a significant decrease in the CE and SV after the rehabilitative treatment, thus improving their PC. Seven of these patients were assessed again after a period of 12±5 months, during which they had not received any physical training. All of them showed increases in the CE and SV, indicating an impairment of PC. Conclusions—Many CVD patients damage the neural mechanisms involved in retaining the plastic changes in the PC parameters after rehabilitative treatment. Continuation of training may be necessary in order to maintain the improvement in PC obtained with a VRP.

The Non-parametric Sub-pixel Local Point Spread Function Estimation Is a Well Posed Problem

Most medium to high quality digital cameras (dslrs) acquire images at a spatial rate which is several times below the ideal Nyquist rate. For this reason only aliased versions of the cameral point-spread function (psf) can be directly observed. Yet, it can be recovered, at a sub-pixel resolution, by a numerical method. Since the acquisition system is only locally stationary, this psf estimation must be local. This paper presents a theoretical study proving that the sub-pixel psf estimation problem is well-posed even with a single well chosen observation. Indeed, theoretical bounds show that a near-optimal accuracy can be achieved with a calibration pattern mimicking a Bernoulli(0.5) random noise. The physical realization of this psf estimation method is demonstrated in many comparative experiments. We use an algorithm to accurately estimate the pattern position and its illumination conditions. Once this accurate registration is obtained, the local psf can be directly computed by inverting a well conditioned linear system. The psf estimates reach stringent accuracy levels with a relative error of the order of 2% to 5%. To the best of our knowledge, such a regularization-free and model-free sub-pixel psf estimation scheme is the first of its kind.

Pigmented Skin Lesions Classification Using Dermatoscopic Images

In this paper we propose a machine learning approach to classify melanocytic lesions in malignant and benign from dermatoscopic images. The image database is composed of 433 benign lesions and 80 malignant melanoma. After an image pre-processing stage that includes hair removal filtering, each image is automatically segmented using well known image segmentation algorithms. Then, each lesion is characterized by a feature vector that contains shape, color and texture information, as well as local and global parameters that try to reflect structures used in medical diagnosis. The learning and classification stage is performed using AdaBoost.M1 with C4.5 decision trees. For the automatically segmented database, classification delivered a false positive rate of 8.75% for a sensitivity of 95%. The same classification procedure applied to manually segmented images by an experienced dermatologist yielded a false positive rate of 4.62% for a sensitivity of 95%.