On the Subspace of Image Gradient Orientations

We introduce the notion of Principal Component Analysis (PCA) of image gradient orientations. As image data is typically noisy, but noise is substantially different from Gaussian, traditional PCA of pixel intensities very often fails to estimate reliably the low-dimensional subspace of a given data population. We show that replacing intensities with gradient orientations and the $\ell_2$ norm with a cosine-based distance measure offers, to some extend, a remedy to this problem. Our scheme requires the eigen-decomposition of a covariance matrix and is as computationally efficient as standard $\ell_2$ PCA. We demonstrate some of its favorable properties on robust subspace estimation

How to compare noisy patches? Patch similarity beyond Gaussian noise

International audienceMany tasks in computer vision require to match image parts. While higher-level methods consider image features such as edges or robust descriptors, low-level approaches (so-called image-based) compare groups of pixels (patches) and provide dense matching. Patch similarity is a key ingredient to many techniques for image registration, stereo-vision, change detection or denoising. Recent progress in natural image modeling also makes intensive use of patch comparison. A fundamental difficulty when comparing two patches from "real" data is to decide whether the differences should be ascribed to noise or intrinsic dissimilarity. Gaussian noise assumption leads to the classical definition of patch similarity based on the squared differences of intensities. For the case where noise departs from the Gaussian distribution, several similarity criteria have been proposed in the literature of image processing, detection theory and machine learning. By expressing patch (dis)similarity as a detection test under a given noise model, we introduce these criteria with a new one and discuss their properties. We then assess their performance for different tasks: patch discrimination, image denoising, stereo-matching and motion-tracking under gamma and Poisson noises. The proposed criterion based on the generalized likelihood ratio is shown to be both easy to derive and powerful in these diverse applications

PVR: Patch-to-Volume Reconstruction for Large Area Motion Correction of Fetal MRI

In this paper we present a novel method for the correction of motion artifacts that are present in fetal Magnetic Resonance Imaging (MRI) scans of the whole uterus. Contrary to current slice-to-volume registration (SVR) methods, requiring an inflexible anatomical enclosure of a single investigated organ, the proposed patch-to-volume reconstruction (PVR) approach is able to reconstruct a large field of view of non-rigidly deforming structures. It relaxes rigid motion assumptions by introducing a specific amount of redundant information that is exploited with parallelized patch-wise optimization, super-resolution, and automatic outlier rejection. We further describe and provide an efficient parallel implementation of PVR allowing its execution within reasonable time on commercially available graphics processing units (GPU), enabling its use in the clinical practice. We evaluate PVR's computational overhead compared to standard methods and observe improved reconstruction accuracy in presence of affine motion artifacts of approximately 30% compared to conventional SVR in synthetic experiments. Furthermore, we have evaluated our method qualitatively and quantitatively on real fetal MRI data subject to maternal breathing and sudden fetal movements. We evaluate peak-signal-to-noise ratio (PSNR), structural similarity index (SSIM), and cross correlation (CC) with respect to the originally acquired data and provide a method for visual inspection of reconstruction uncertainty. With these experiments we demonstrate successful application of PVR motion compensation to the whole uterus, the human fetus, and the human placenta.Comment: 10 pages, 13 figures, submitted to IEEE Transactions on Medical Imaging. v2: wadded funders acknowledgements to preprin

Ranking and significance of variable-length similarity-based time series motifs

The detection of very similar patterns in a time series, commonly called motifs, has received continuous and increasing attention from diverse scientific communities. In particular, recent approaches for discovering similar motifs of different lengths have been proposed. In this work, we show that such variable-length similarity-based motifs cannot be directly compared, and hence ranked, by their normalized dissimilarities. Specifically, we find that length-normalized motif dissimilarities still have intrinsic dependencies on the motif length, and that lowest dissimilarities are particularly affected by this dependency. Moreover, we find that such dependencies are generally non-linear and change with the considered data set and dissimilarity measure. Based on these findings, we propose a solution to rank those motifs and measure their significance. This solution relies on a compact but accurate model of the dissimilarity space, using a beta distribution with three parameters that depend on the motif length in a non-linear way. We believe the incomparability of variable-length dissimilarities could go beyond the field of time series, and that similar modeling strategies as the one used here could be of help in a more broad context.Comment: 20 pages, 10 figure