Left-invariant evolutions of wavelet transforms on the Similitude Group

Enhancement of multiple-scale elongated structures in noisy image data is relevant for many biomedical applications but commonly used PDE-based enhancement techniques often fail at crossings in an image. To get an overview of how an image is composed of local multiple-scale elongated structures we construct a multiple scale orientation score, which is a continuous wavelet transform on the similitude group, SIM(2). Our unitary transform maps the space of images onto a reproducing kernel space defined on SIM(2), allowing us to robustly relate Euclidean (and scaling) invariant operators on images to left-invariant operators on the corresponding continuous wavelet transform. Rather than often used wavelet (soft-)thresholding techniques, we employ the group structure in the wavelet domain to arrive at left-invariant evolutions and flows (diffusion), for contextual crossing preserving enhancement of multiple scale elongated structures in noisy images. We present experiments that display benefits of our work compared to recent PDE techniques acting directly on the images and to our previous work on left-invariant diffusions on orientation scores defined on Euclidean motion group.Comment: 40 page

Une nouvelle classe d'opérateurs de Teager-Kaiser multidimensionnels basée sur les dérivées directionnelles d'ordre supérieur

This work aims at introducing some energy operators linked to Teager-Kaiser energy operator and its associated higher order versions and expand them to multidimensional signals. These operators are very useful for analyzing oscillatory signals with time-varying amplitude and frequency (AM-FM). We prove that gradient tensors combined with Kronecker powers allow to express these operators by directional derivatives along any n-D vector. In particular, we show that the construction of a large class of non linear operators for AM-FM multidimensional signal demodulation is possible. Also, a new scalar function using the directional derivative along a vector giving the ”sign” of the frequency components is introduced. An application of this model to local n-D AM-FM signal is presented and related demodulation error rates estimates. To show the effectiveness and the robustness of our method in term of envelope and frequency components extraction, results obtained on synthetic and real data are compared to multi-dimensional energy separation algorithm and to our recently introduced n-D operator

Fast and Robust Small Infrared Target Detection Using Absolute Directional Mean Difference Algorithm

Infrared small target detection in an infrared search and track (IRST) system is a challenging task. This situation becomes more complicated when high gray-intensity structural backgrounds appear in the field of view (FoV) of the infrared seeker. While the majority of the infrared small target detection algorithms neglect directional information, in this paper, a directional approach is presented to suppress structural backgrounds and develop a more effective detection algorithm. To this end, a similar concept to the average absolute gray difference (AAGD) is utilized to construct a novel directional small target detection algorithm called absolute directional mean difference (ADMD). Also, an efficient implementation procedure is presented for the proposed algorithm. The proposed algorithm effectively enhances the target area and eliminates background clutter. Simulation results on real infrared images prove the significant effectiveness of the proposed algorithm.Comment: The Final version (Accepted in Signal Processing journal

Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging

Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well-defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations $U:\mathbb{R}^{d} \rtimes S^{d-1} \to \mathbb{R}$ defined on the extended space of positions and orientations, which we relate to data on the roto-translation group $SE(d)$, $d=2,3$. This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in $SE(d)$. These curve fits minimize first or second order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on $SE(d)$. We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation $U$ and we show their advantage compared to the standard left-invariant frame on $SE(d)$. Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores

High-ISO long-exposure image denoising based on quantitative blob characterization

Blob detection and image denoising are fundamental, sometimes related tasks in computer vision. In this paper, we present a computational method to quantitatively measure blob characteristics using normalized unilateral second-order Gaussian kernels. This method suppresses non-blob structures while yielding a quantitative measurement of the position, prominence and scale of blobs, which can facilitate the tasks of blob reconstruction and blob reduction. Subsequently, we propose a denoising scheme to address high-ISO long-exposure noise, which sometimes spatially shows a blob appearance, employing a blob reduction procedure as a cheap preprocessing for conventional denoising methods. We apply the proposed denoising methods to real-world noisy images as well as standard images that are corrupted by real noise. The experimental results demonstrate the superiority of the proposed methods over state-of-the-art denoising methods

Idealized computational models for auditory receptive fields

This paper presents a theory by which idealized models of auditory receptive fields can be derived in a principled axiomatic manner, from a set of structural properties to enable invariance of receptive field responses under natural sound transformations and ensure internal consistency between spectro-temporal receptive fields at different temporal and spectral scales. For defining a time-frequency transformation of a purely temporal sound signal, it is shown that the framework allows for a new way of deriving the Gabor and Gammatone filters as well as a novel family of generalized Gammatone filters, with additional degrees of freedom to obtain different trade-offs between the spectral selectivity and the temporal delay of time-causal temporal window functions. When applied to the definition of a second-layer of receptive fields from a spectrogram, it is shown that the framework leads to two canonical families of spectro-temporal receptive fields, in terms of spectro-temporal derivatives of either spectro-temporal Gaussian kernels for non-causal time or the combination of a time-causal generalized Gammatone filter over the temporal domain and a Gaussian filter over the logspectral domain. For each filter family, the spectro-temporal receptive fields can be either separable over the time-frequency domain or be adapted to local glissando transformations that represent variations in logarithmic frequencies over time. Within each domain of either non-causal or time-causal time, these receptive field families are derived by uniqueness from the assumptions. It is demonstrated how the presented framework allows for computation of basic auditory features for audio processing and that it leads to predictions about auditory receptive fields with good qualitative similarity to biological receptive fields measured in the inferior colliculus (ICC) and primary auditory cortex (A1) of mammals.Comment: 55 pages, 22 figures, 3 table

Level-Set Based Artery-Vein Separation in Blood Pool Agent CE-MR Angiograms

Blood pool agents (BPAs) for contrast-enhanced (CE) magnetic-resonance angiography (MRA) allow prolonged imaging times for higher contrast and resolution. Imaging is performed during the steady state when the contrast agent is distributed through the complete vascular system. However, simultaneous venous and arterial enhancement in this steady state hampers interpretation. In order to improve visualization of the arteries and veins from steady-state BPA data, a semiautomated method for artery-vein separation is presented. In this method, the central arterial axis and central venous axis are used as initializations for two surfaces that simultaneously evolve in order to capture the arterial and venous parts of the vasculature using the level-set framework. Since arteries and veins can be in close proximity of each other, leakage from the evolving arterial (venous) surface into the venous (arterial) part of the vasculature is inevitable. In these situations, voxels are labeled arterial or venous based on the arrival time of the respective surface. The evolution is steered by external forces related to feature images derived from the image data and by internal forces related to the geometry of the level sets. In this paper, the robustness and accuracy of three external forces (based on image intensity, image gradient, and vessel-enhancement filtering) and combinations of them are investigated and tested on seven patient datasets. To this end, results with the level-set-based segmentation are compared to the reference-standard manually obtained segmentations. Best results are achieved by applying a combination of intensity- and gradient-based forces and a smoothness constraint based on the curvature of the surface. By applying this combination to the seven datasets, it is shown that, with minimal user interaction, artery-vein separation for improved arterial and venous visualization in BPA CE-MRA can be achieved