Curve-like Structures Research Articles

Radiation-Hardened and Flexible Pb(Zr0.53Ti0.47)O3 Piezoelectric Sensor for Structural Health Monitoring.

Piezoelectric sensors are excellent damage detectors that can be applied to structural health monitoring (SHM). SHM for complex structures of aerospace vehicles working in harsh conditions is frequently required, posing challenging requirements for a sensor's flexibility, radiation hardness, and high-temperature tolerance. Here, we fabricate a flexible and lightweight Pb(Zr0.53Ti0.47)O3 piezoelectric film on flexible KMg3(AlSi3O10)F2 substrate via van der Waals (vdW) heteroepitaxy, endowing it with robust ferroelectric and piezoelectric properties under low energy-high flux protons (LE-HFPs) radiation (1015 p/cm2). More importantly, the Pb(Zr0.53Ti0.47)O3 film sensor maintains highly stable damage monitoring sensitivity on an aluminum plate under harsh conditions of LE-HFPs radiation (1015 p/cm2, flat structure), high temperature (175 °C, flat structure), and mechanical fatigue (bending 105 cycles under a radius of 5 mm, curved structure). All these superior qualities are suggested to result from the outstanding film crystal quality due to vdW epitaxy. The flexible and lightweight Pb(Zr0.53Ti0.47)O3 film sensor demonstrated in this work provides an ideal candidate for real-time SHM of aerospace vehicles with flat and complex curve-like structures working in harsh aerospace environments.

Vessel Structure Extraction using Constrained Minimal Path Propagation.

Minimal path method has been widely recognized as an efficient tool for extracting vascular structures in medical imaging. In a previous paper, a method termed minimal path propagation with backtracking (MPP-BT) was derived to deal with curve-like structures such as vessel centerlines. A robust approach termed CMPP (constrained minimal path propagation) is here proposed to extend this work. The proposed method utilizes another minimal path propagation procedure to extract the complete vessel lumen after the centerlines have been found. Moreover, a process named local MPP-BT is applied to handle structure missing caused by the so-called close loop problems. This approach is fast and unsupervised with only one roughly set start point required in the whole process to get the entire vascular structure. A variety of datasets, including 2D cardiac angiography, 2D retinal images and 3D kidney CT angiography, are used for validation. A quantitative evaluation, together with a comparison to recently reported methods, is performed on retinal images for which a ground truth is available. The proposed method leads to specificity (Sp) and sensitivity (Se) values equal to 0.9750 and 0.6591. This evaluation is also extended to 3D synthetic vascular datasets and shows that the specificity (Sp) and sensitivity (Se) values are higher than 0.99. Parameter setting and computation cost are analyzed in this paper.

Curve-Like Structure Extraction Using Minimal Path Propagation With Backtracking.

Minimal path techniques can efficiently extract geometrically curve-like structures by finding the path with minimal accumulated cost between two given endpoints. Though having found wide practical applications (e.g., line identification, crack detection, and vascular centerline extraction), minimal path techniques suffer from some notable problems. The first one is that they require setting two endpoints for each line to be extracted (endpoint problem). The second one is that the connection might fail when the geodesic distance between the two points is much shorter than the desirable minimal path (shortcut problem). In addition, when connecting two distant points, the minimal path connection might become inefficient as the accumulated cost increases over the propagation and results in leakage into some non-feature regions near the starting point (accumulation problem). To address these problems, this paper proposes an approach termed minimal path propagation with backtracking. We found that the information in the process of backtracking from reached points can be well utilized to overcome the above problems and improve the extraction performance. The whole algorithm is robust to parameter setting and allows a coarse setting of the starting point. Extensive experiments with both simulated and realistic data are performed to validate the performance of the proposed method.

A DICTIONARY-BASED IMAGE FUSION FOR INTEGRATION OF SAR AND OPTICAL IMAGES

In this letter, a new image fusion methodology for integration of SAR and optical images using combined dictionary is proposed. The approach taken is based on sparse and redundant representations by employing a combined dictionary consisting of wavelets, shearlets and discrete cosine transform (DCT). Wavelets and shearlets provide pointlike and curvelike structures for the optical image, and DCT are taken as obtaining the best performance on SAR image. The experimental results demonstrate feasibility and effectiveness of the method.

Microlocal Analysis of the Geometric Separation Problem

AbstractImage data are often composed of two or more geometrically distinct constituents; in galaxy catalogs, for instance, one sees a mixture of pointlike structures (galaxy superclusters) and curvelike structures (filaments). It would be ideal to process a single image and extract two geometrically “pure” images, each one containing features from only one of the two geometric constituents. This seems to be a seriously underdetermined problem but recent empirical work achieved highly persuasive separations.We present a theoretical analysis showing that accurate geometric separation of point and curve singularities can be achieved by minimizing the ℓ1norm of the representing coefficients in two geometrically complementary frames: wavelets and curvelets. Driving our analysis is a specific property of the ideal (but unachievable) representation where each content type is expanded in the frame best adapted to it. This ideal representation has the property that important coefficients areclustered geometricallyin phase space, and that at fine scales, there is very little coherence between a cluster of elements in one frame expansion and individual elements in the complementary frame. We formally introduce notions ofcluster coherenceandclustered sparsityand use this machinery to show that the underdetermined systems of linear equations can be stably solved by ℓ1minimization; microlocal phase space helps organize the calculations that cluster coherence requires. © 2012 Wiley Periodicals, Inc.

SAR image despeckling using over-complete dictionary

A new methodology for speckle suppression of SAR images using an over-complete dictionary is presented. The approach taken is based on sparse and redundant representations by employing a combined dictionary consisting of wavelets, shearlets and learned dictionaries. Wavelets provide sparse expansions for point-like structures, shearlets provide sparse expansions for curve-like structures, and learning dictionaries are taken as obtaining the best performance on a training set. The experimental results demonstrate that the proposed algorithm provides more effective speckle reduction as well as detail preservation.

Quantifying curvelike structures of measures by using L2 Jones quantities

AbstractWe study the curvelike structure of special measures on ℝn in a multiscale fashion. More precisely, we consider the existence and construction of a sufficiently short curve with a sufficiently large measure. Our main tool is an L2 variant of Jones' β numbers, which measure the scaled deviations of the given measure from a best approximating line at different scales and locations. The Jones function is formed by adding the squares of the L2 Jones numbers at different scales and the same location. Using a special L2 Jones function, we construct a sufficiently short curve with a sufficiently large measure. The length and measure estimates of the underlying curve are expressed in terms of the size of this Jones function. © 2003 Wiley Periodicals, Inc.