Rotation-Covariant Texture Learning Using Steerable Riesz Wavelets

We propose a texture learning approach that exploits local organizations of scales and directions. First, linear combinations of Riesz wavelets are learned using kernel support vector machines. The resulting texture signatures are modeling optimal class-wise discriminatory properties. The visualization of the obtained signatures allows verifying the visual relevance of the learned concepts. Second, the local orientations of the signatures are optimized to maximize their responses, which is carried out analytically and can still be expressed as a linear combination of the initial steerable Riesz templates. The global process is iteratively repeated to obtain final rotation-covariant texture signatures. Rapid convergence of class-wise signatures is observed, which demonstrates that the instances are projected into a feature space that leverages the local organizations of scales and directions. Experimental evaluation reveals average classification accuracies in the range of 97% to 98% for the Outex_TC_00010, the Outex_TC_00012, and the Contrib_TC_00000 suites for even orders of the Riesz transform, and suggests high robustness to changes in images orientation and illumination. The proposed framework requires no arbitrary choices of scales and directions and is expected to perform well in a large range of computer vision applications

Standardised convolutional filtering for radiomics

The Image Biomarker Standardisation Initiative (IBSI) aims to improve reproducibility of radiomics studies by standardising the computational process of extracting image biomarkers (features) from images. We have previously established reference values for 169 commonly used features, created a standard radiomics image processing scheme, and developed reporting guidelines for radiomic studies. However, several aspects are not standardised. Here we present a preliminary version of a reference manual on the use of convolutional image filters in radiomics. Filters, such as wavelets or Laplacian of Gaussian filters, play an important part in emphasising specific image characteristics such as edges and blobs. Features derived from filter response maps have been found to be poorly reproducible. This reference manual forms the basis of ongoing work on standardising convolutional filters in radiomics, and will be updated as this work progresses.Comment: 62 pages. For additional information see https://theibsi.github.io

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Solid Spherical Energy (SSE) CNNs for Efficient 3D Medical Image Analysis

Invariance to local rotation, to differentiate from the global rotation of images and objects, is required in various texture analysis problems. It has led to several breakthrough methods such as local binary patterns, maximum response and steerable filterbanks. In particular, textures in medical images often exhibit local structures at arbitrary orientations. Locally Rotation Invariant (LRI) Convolutional Neural Networks (CNN) were recently proposed using 3D steerable filters to combine LRI with Directional Sensitivity (DS). The steerability avoids the expensive cost of convolutions with rotated kernels and comes with a parametric representation that results in a drastic reduction of the number of trainable parameters. Yet, the potential bottleneck (memory and computation) of this approach lies in the necessity to recombine responses for a set of predefined discretized orientations. In this paper, we propose to calculate invariants from the responses to the set of spherical harmonics projected onto 3D kernels in the form of a lightweight Solid Spherical Energy (SSE) CNN. It offers a compromise between the high kernel specificity of the LRI-CNN and a low memory/operations requirement. The computational gain is evaluated on 3D synthetic and pulmonary nodule classification experiments. The performance of the proposed approach is compared with steerable LRI-CNNs and standard 3D CNNs, showing competitive results with the state of the art

Local Geometric Transformations in Image Analysis

The characterization of images by geometric features facilitates the precise analysis of the structures found in biological micrographs such as cells, proteins, or tissues. In this thesis, we study image representations that are adapted to local geometric transformations such as rotation, translation, and scaling, with a special emphasis on wavelet representations. In the first part of the thesis, our main interest is in the analysis of directional patterns and the estimation of their location and orientation. We explore steerable representations that correspond to the notion of rotation. Contrarily to classical pattern matching techniques, they have no need for an a priori discretization of the angle and for matching the filter to the image at each discretized direction. Instead, it is sufficient to apply the filtering only once. Then, the rotated filter for any arbitrary angle can be determined by a systematic and linear transformation of the initial filter. We derive the Cramér-Rao bounds for steerable filters. They allow us to select the best harmonics for the design of steerable detectors and to identify their optimal radial profile. We propose several ways to construct optimal representations and to build powerful and effective detector schemes; in particular, junctions of coinciding branches with local orientations. The basic idea of local transformability and the general principles that we utilize to design steerable wavelets can be applied to other geometric transformations. Accordingly, in the second part, we extend our framework to other transformation groups, with a particular interest in scaling. To construct representations in tune with a notion of local scale, we identify the possible solutions for scalable functions and give specific criteria for their applicability to wavelet schemes. Finally, we propose discrete wavelet frames that approximate a continuous wavelet transform. Based on these results, we present a novel wavelet-based image-analysis software that provides a fast and automatic detection of circular patterns, combined with a precise estimation of their size

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

The impact of arterial input function determination variations on prostate dynamic contrast-enhanced magnetic resonance imaging pharmacokinetic modeling: a multicenter data analysis challenge, part II

This multicenter study evaluated the effect of variations in arterial input function (AIF) determination on pharmacokinetic (PK) analysis of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data using the shutter-speed model (SSM). Data acquired from eleven prostate cancer patients were shared among nine centers. Each center used a site-specific method to measure the individual AIF from each data set and submitted the results to the managing center. These AIFs, their reference tissue-adjusted variants, and a literature population-averaged AIF, were used by the managing center to perform SSM PK analysis to estimate Ktrans (volume transfer rate constant), ve (extravascular, extracellular volume fraction), kep (efflux rate constant), and τi (mean intracellular water lifetime). All other variables, including the definition of the tumor region of interest and precontrast T1 values, were kept the same to evaluate parameter variations caused by variations in only the AIF. Considerable PK parameter variations were observed with within-subject coefficient of variation (wCV) values of 0.58, 0.27, 0.42, and 0.24 for Ktrans, ve, kep, and τi, respectively, using the unadjusted AIFs. Use of the reference tissue-adjusted AIFs reduced variations in Ktrans and ve (wCV = 0.50 and 0.10, respectively), but had smaller effects on kep and τi (wCV = 0.39 and 0.22, respectively). kep is less sensitive to AIF variation than Ktrans, suggesting it may be a more robust imaging biomarker of prostate microvasculature. With low sensitivity to AIF uncertainty, the SSM-unique τi parameter may have advantages over the conventional PK parameters in a longitudinal study