Combining Contrast Invariant L1 Data Fidelities with Nonlinear Spectral Image Decomposition

This paper focuses on multi-scale approaches for variational methods and corresponding gradient flows. Recently, for convex regularization functionals such as total variation, new theory and algorithms for nonlinear eigenvalue problems via nonlinear spectral decompositions have been developed. Those methods open new directions for advanced image filtering. However, for an effective use in image segmentation and shape decomposition, a clear interpretation of the spectral response regarding size and intensity scales is needed but lacking in current approaches. In this context, $L^1$ data fidelities are particularly helpful due to their interesting multi-scale properties such as contrast invariance. Hence, the novelty of this work is the combination of $L^1$-based multi-scale methods with nonlinear spectral decompositions. We compare $L^1$ with $L^2$ scale-space methods in view of spectral image representation and decomposition. We show that the contrast invariant multi-scale behavior of $L^1-TV$ promotes sparsity in the spectral response providing more informative decompositions. We provide a numerical method and analyze synthetic and biomedical images at which decomposition leads to improved segmentation.Comment: 13 pages, 7 figures, conference SSVM 201

Technical Note: Enhancing Soft Tissue Contrast And Radiation‐Induced Image Changes With Dual‐Energy CT For Radiation Therapy

Purpose The purpose of this work is to investigate the use of low‐energy monoenergetic decompositions obtained from dual‐energy CT (DECT) to enhance image contrast and the detection of radiation‐induced changes of CT textures in pancreatic cancer. Methods The DECT data acquired for 10 consecutive pancreatic cancer patients during routine nongated CT‐guided radiation therapy (RT) using an in‐room CT (Definition AS Open, Siemens Healthcare, Malvern, PA) were analyzed. With a sequential DE protocol, the scanner rapidly performs two helical acquisitions, the first at a tube voltage of 80 kVp and the second at a tube voltage of 140 kVp. Virtual monoenergetic images across a range of energies from 40 to 140 keV were reconstructed using an image‐based material decomposition. Intravenous (IV) bolus‐free contrast enhancement in pancreas patient tumors was measured across a spectrum of monoenergies. For treatment response assessment, the changes in CT histogram features (including mean CT number (MCTN), entropy, kurtosis) in pancreas tumors were measured during treatment. The results from the monoenergetic decompositions were compared to those obtained from the standard 120 kVp CT protocol for the same subjects. Results Data of monoenergetic decompositions of the 10 patients confirmed the expected enhancement of soft tissue contrast as the energy is decreased. The changes in the selected CT histogram features in the pancreas during RT delivery were amplified with the low‐energy monoenergetic decompositions, as compared to the changes measured from the 120 kVp CTs. For the patients studied, the average reduction in the MCTN in pancreas from the first to the last (the 28th) treatment fraction was 4.09 HU for the standard 120 kVp and 11.15 HU for the 40 keV monoenergetic decomposition. Conclusions Low‐energy monoenergetic decompositions from DECT substantially increase soft tissue contrast and increase the magnitude of radiation‐induced changes in CT histogram textures during RT delivery for pancreatic cancer. Therefore, quantitative DECT may assist the detection of early RT response

CGIntrinsics: Better Intrinsic Image Decomposition through Physically-Based Rendering

Intrinsic image decomposition is a challenging, long-standing computer vision problem for which ground truth data is very difficult to acquire. We explore the use of synthetic data for training CNN-based intrinsic image decomposition models, then applying these learned models to real-world images. To that end, we present \ICG, a new, large-scale dataset of physically-based rendered images of scenes with full ground truth decompositions. The rendering process we use is carefully designed to yield high-quality, realistic images, which we find to be crucial for this problem domain. We also propose a new end-to-end training method that learns better decompositions by leveraging \ICG, and optionally IIW and SAW, two recent datasets of sparse annotations on real-world images. Surprisingly, we find that a decomposition network trained solely on our synthetic data outperforms the state-of-the-art on both IIW and SAW, and performance improves even further when IIW and SAW data is added during training. Our work demonstrates the suprising effectiveness of carefully-rendered synthetic data for the intrinsic images task.Comment: Paper for 'CGIntrinsics: Better Intrinsic Image Decomposition through Physically-Based Rendering' published in ECCV, 201

Truncated decompositions and filtering methods with Reflective/Anti-Reflective boundary conditions: a comparison

The paper analyzes and compares some spectral filtering methods as truncated singular/eigen-value decompositions and Tikhonov/Re-blurring regularizations in the case of the recently proposed Reflective [M.K. Ng, R.H. Chan, and W.C. Tang, A fast algorithm for deblurring models with Neumann boundary conditions, SIAM J. Sci. Comput., 21 (1999), no. 3, pp.851-866] and Anti-Reflective [S. Serra Capizzano, A note on anti-reflective boundary conditions and fast deblurring models, SIAM J. Sci. Comput., 25-3 (2003), pp. 1307-1325] boundary conditions. We give numerical evidence to the fact that spectral decompositions (SDs) provide a good image restoration quality and this is true in particular for the Anti-Reflective SD, despite the loss of orthogonality in the associated transform. The related computational cost is comparable with previously known spectral decompositions, and results substantially lower than the singular value decomposition. The model extension to the cross-channel blurring phenomenon of color images is also considered and the related spectral filtering methods are suitably adapted.Comment: 22 pages, 10 figure

Efficient Decomposition of Image and Mesh Graphs by Lifted Multicuts

Formulations of the Image Decomposition Problem as a Multicut Problem (MP) w.r.t. a superpixel graph have received considerable attention. In contrast, instances of the MP w.r.t. a pixel grid graph have received little attention, firstly, because the MP is NP-hard and instances w.r.t. a pixel grid graph are hard to solve in practice, and, secondly, due to the lack of long-range terms in the objective function of the MP. We propose a generalization of the MP with long-range terms (LMP). We design and implement two efficient algorithms (primal feasible heuristics) for the MP and LMP which allow us to study instances of both problems w.r.t. the pixel grid graphs of the images in the BSDS-500 benchmark. The decompositions we obtain do not differ significantly from the state of the art, suggesting that the LMP is a competitive formulation of the Image Decomposition Problem. To demonstrate the generality of the LMP, we apply it also to the Mesh Decomposition Problem posed by the Princeton benchmark, obtaining state-of-the-art decompositions

Modal decomposition of astronomical images with application to shapelets

The decomposition of an image into a linear combination of digitised basis functions is an everyday task in astronomy. A general method is presented for performing such a decomposition optimally into an arbitrary set of digitised basis functions, which may be linearly dependent, non-orthogonal and incomplete. It is shown that such circumstances may result even from the digitisation of continuous basis functions that are orthogonal and complete. In particular, digitised shapelet basis functions are investigated and are shown to suffer from such difficulties. As a result the standard method of performing shapelet analysis produces unnecessarily inaccurate decompositions. The optimal method presented here is shown to yield more accurate decompositions in all cases.Comment: 12 pages, 17 figures, submitted to MNRA