Manos Papadakis

The geometry and the analytic properties of isotropic multiresolution analysis

In this paper we investigate Isotropic Multiresolution Analysis (IMRA), isotropic refinable functions, and wavelets. The main results are the characterization of IMRAs in terms of the Lax–Wiener Theorem, and the characterization of isotropic refinable functions in terms of the support of their Fourier transform. As an immediate consequence of these results, there are no compactly supported (in the space domain) isotropic refinable functions in many dimensions. Next we study the approximation properties of IMRAs. Finally, we discuss the application of IMRA wavelets to 2D and 3D-texture segmentation in natural and biomedical images.

Perinasal Imaging of Physiological Stress and Its Affective Potential

In this paper, we present a novel framework for quantifying physiological stress at a distance via thermal imaging. The method captures stress-induced neurophysiological responses on the perinasal area that manifest as transient perspiration. We have developed two algorithms to extract the perspiratory signals from the thermophysiological imagery. One is based on morphology and is computationally efficient, while the other is based on spatial isotropic wavelets and is flexible; both require the support of a reliable facial tracker. We validated the two algorithms against the clinical standard in a controlled lab experiment where orienting responses were invoked on n=18 subjects via auditory stimuli. Then, we used the validated algorithms to quantify stress of surgeons (n=24) as they were performing suturing drills during inanimate laparoscopic training. This is a field application where the new methodology shines. It allows nonobtrusive monitoring of individuals who are naturally challenged with a task that is localized in space and requires directional attention. Both algorithms associate high stress levels with novice surgeons, while low stress levels are associated with experienced surgeons, raising the possibility for an affective measure (stress) to assist in efficacy determination. It is a clear indication of the methodologys promise and potential.

The Characterization of Low Pass Filters and Some Basic Properties of Wavelets, Scaling Functions and Related Concepts

AbstractThe “classical” wavelets, those ψ εL2(R) such that {2j/2ψ(2jx−k)}, j,kεZ, is an orthonormal basis for L2 (R), are known to be characterized by two simple equations satisfied by

Automatic Morphological Reconstruction of Neurons from Multiphoton and Confocal Microscopy Images Using 3D Tubular Models

\hat \psi

Facial component-landmark detection

. The “multiresolution analysis” wavelets (briefly, the MRA wavelets) have a simple characterization and so do the scaling functions that produce these wavelets. Only certain smooth classes of the low pass filters that are determined by these scaling functions, however, appear to be characterized in the literature (see Chapter 7 of [3] for an account of these matters). In this paper we present a complete characterization of all these filters. This somewhat technical result does provide a method for simple constructions of low pass filters whose only smoothness assumption is a Holder condition at the origin. We also obtain a characterization of all scaling sets and, in particular, a description of all bounded scaling sets as well as a detailed description of the class of scaling functions.

Nonseparable Radial Frame Multiresolution Analysis in Multidimensions

We present a general mathematical theory for lifting frames that allows us to modify existing filters to construct new ones that form Parseval frames. We apply our theory to design nonseparable Parseval frames from separable (tensor) products of a piecewise linear spline tight frame. These new frame systems incorporate the weighted average operator, the Sobel operator, and the Laplacian operator in directions that are integer multiples of 45/spl deg/. A new image denoising algorithm is then proposed, tailored to the specific properties of these new frame filters. We demonstrate the performance of our algorithm on a diverse set of images with very encouraging results.

Improved automatic centerline tracing for dendritic and axonal structures.

The challenges faced in analyzing optical imaging data from neurons include a low signal-to-noise ratio of the acquired images and the multiscale nature of the tubular structures that range in size from hundreds of microns to hundreds of nanometers. In this paper, we address these challenges and present a computational framework for an automatic, three-dimensional (3D) morphological reconstruction of live nerve cells. The key aspects of this approach are: (i) detection of neuronal dendrites through learning 3D tubular models, and (ii) skeletonization by a new algorithm using a morphology-guided deformable model for extracting the dendritic centerline. To represent the neuron morphology, we introduce a novel representation, the Minimum Shape-Cost (MSC) Tree that approximates the dendrite centerline with sub-voxel accuracy and demonstrate the uniqueness of such a shape representation as well as its computational efficiency. We present extensive quantitative and qualitative results that demonstrate the accuracy and robustness of our method.

Efficient processing of fluorescence images using directional multiscale representations

We define a very generic class of multiresolution analysis of abstract Hilbert spaces. Their core subspaces have a frame produced by the action of an abelian unitary group on a countable frame multiscaling vector set, which may be infinite. We characterize all the associated frame multiwavelet vector sets and we generalize the concept of low and high pass filters. We also prove a generalization of the quadratic (conjugate) mirror filter condition, and we give two algorithms for the construction of the high pass filters associated to a given low pass filter.