In this paper, we use the ideas presented in [1] to construct application-targeted convolutional neural network architectures (CNN). Specifically, we design frame filter banks consisting of sparse kernels with custom-selected orientations that can act as finite-difference operators. We then use these filter banks as the building blocks of structured receptive field CNNs [2] to compare baseline models with more application-oriented methods. Our tests are done on Google's Quick, Draw! data set.
Water turbidity is a frequent impediment for achieving satisfactory imaging clarity in underwater video and inhibits the extraction of information concerning the condition of submerged structures. Ports, rivers, lakes and inland waterways are notoriously difficult spots for camera inspections due to poor visibility. This problem motivated us to study methods to extract a cleaner image/video from the one acquired in an almost real-time setting (delay of the order of 6-7 secs). This type of problem arises in image post-processing as an illumination neutralization problem. and, it can also be viewed as a blind deconvolution problem. We present a mathematical method which enables the derivation of a cleaner image from a poor visibility original by means of a combination of linear and non-linear deterministic mathematical transformations for illumination neutralization. Moreover, we propose a new stochastic model for the effects of water turbidity in sub-aquatic video and still images. In the light of this model, illumination neutralization does not offer the full solution to this dehazing problem.
In this paper we demonstrate how the post-processing of gray-scale images with algorithms which have a singularity enhancement effect can assume the role of auxiliary modalities, as in the case where an intelligent system fuses information from multiple physical modalities. We show that as in multimodal AI-fusion, “virtual” multimodal inputs can improve the performance of object detection. We design, implement and test a novel Convolutional Neural Network architecture, based on the Faster R-CNN network for multiclass object detection and classification. Our architecture combines deep feature representations of the input images, generated by networks trained independently on physical and virtual imaging modalities. Using an analog of the ROC curve, the Average Recall over Precision curve, we show that the fusion of certain virtual modality inputs, capable of enhancing singularities and neutralizing illumination, improve recognition accuracy.
Spines are protrusions of neuronal dendritic surfaces. These subcellular compartments are essential in neuronal information processing since electrical signals from other neurons are transmitted to dendrites via synaptic gateways located at dendritic spines. One of the important tasks for assessing synaptic strength is estimating the volume of spines, which is quite challenging because the image resolution for spines in live animal microscopy images is low and the level of noise is high. In order to carry out this task we develop a method for spine surface segmentation using sparse representations based on directional 3D filters with small spatial support.
As advances in imaging technologies make more and more data available for biomedical applications, there is an increasing need to develop efficient quantitative algorithms for the analysis and processing of imaging data. In this paper, we introduce an innovative multiscale approach called Directional Ratio which is especially effective to distingush isotropic from anisotropic structures. This task is especially useful in the analysis of images of neurons, the main units of the nervous systems which consist of a main cell body called the soma and many elongated processes called neurites. We analyze the theoretical properties of our method on idealized models of neurons and develop a numerical implementation of this approach for analysis of fluorescent images of cultured neurons. We show that this algorithm is very effective for the detection of somas and the extraction of neurites in images of small circuits of neurons.
The automated reconstruction of neuronal morphology is a fundamental task for investigating several problems associated with the nervous system. Revealing the mechanisms of synaptic plasticity, signal transmission, network connectivity and circuit dynamics requires accurate quantitative analyses of digital three-dimensional reconstructions. Yet, while many commercial and non-commercial software packages for neuronal reconstruction are available, these packages typically provide limited quantitative information and require a significant manual intervention. Recent advances in applied harmonic analysis, especially in the area of multiscale representations, offer a variery of techniques and ideas which have the potential to dramatically impact this very active field of scientific investigation. In this paper, we apply such ideas for (i) the derivation of a multiscale directional representation from isotropic filters aimed at detecting tubular structures and (ii) the development of a multiscale quantitative measure capable of distingushing isotropic from anisotropic structures. We showcase the application of these methods for the extraction of geometric features used for the detection of somas and dendritic branches of neurons.
In this paper we implement a method for the 3D-rigid motion invariant texture discrimination and binary
classification for discrete 3D-textures that are spatially homogeneous by modelling them as stationary Gaussian
random fields. We use a novel 'distance' between 3D-textures that remains invariant under all 3D-rigid motions
of the texture to develop rules for 3D-rigid motion invariant texture discrimination and binary classification of
textures.
We present steerlets, a new class of wavelets which allow us to define wavelet transforms that are covariant with
respect to rigid motions in d dimensions. The construction of steerlets is derived from an Isotropic Multiresolution
Analysis, a variant of a Multiresolution Analysis whose core subspace is closed under translations by integers
and under all rotations. Steerlets admit a wide variety of design characteristics ranging from isotropy, that is the
full insensitivity to orientations, to directional and orientational selectivity for local oscillations and singularities.
The associated 2D or 3D-steerlet transforms are fast MRA-type of transforms suitable for processing of discrete
data. The subband decompositions obtained with 2D or 3D-steerlets behave covariantly under the action of the
respective rotation group on an image, so that each rotated steerlet is the linear combination of other steerlets
in the same subband.
The main goal of this paper is to introduce formally the concept of texture segmentation/identification in three
dimensional images. A major problem in texture texture segmentation/identification is the lack of robustness to
both translations and rotations. This problem is more difficult to overcome in 3D-images, such as those generated
by modalities such as x-ray CT and MRI. To facilitate 3D-texture segmentation/identification which is robust to
3D rigid motions we formally introduce the concept of steerable feature maps and of appropriate metrics in the
feature space. We also introduce a new multiscale representation giving rise to a steerable feature map used in
our exploratory project in cardiovascular imaging and we propose a
3D-texture segmentation algorithm utilizing
this steerable feature map.
We analyze localized textural consistencies in high-resolution Micro CT scans of coronary arteries to identify the appearance of diagnostically relevant changes in tissue. For the efficient and accurate processing of CT volume data, we use fast algorithms associated with three-dimensional so-called isotropic multiresolution wavelets that implement a redundant, frame-based image encoding without directional preference. Our algorithm identifies textural consistencies by correlating coefficients in the wavelet representation.
KEYWORDS: Denoising, Wavelets, Image denoising, Digital filtering, Sensors, 3D image processing, 3D metrology, Linear filtering, Algorithm development, Electronic filtering
Three dimensional (3D) surfaces can be sampled parametrically in the form of range image data. Smoothing/denoising of such raw data is usually accomplished by adapting techniques developed for intensity image processing, since both range and intensity images comprise parametrically sampled geometry and appearance measurements, respectively. We present a transform-based algorithm for surface denoising, motivated by our previous work on intensity image denoising, which utilizes a non-separable Parseval frame and an ensemble thresholding scheme. The frame is constructed from separable (tensor) products of a piecewise linear spline tight frame and incorporates the weighted average operator and the Sobel operators in directions that are integer multiples of 45°. We compare the performance of this algorithm with other transform-based methods from the recent literature. Our results indicate that such transform methods are suited to the task of smoothing range images.
In this paper we present a non-separable multiresolution structure based on frames which is defined by radial scaling functions of the form of the Shannon scaling function. We also construct the resulting frame multiwavelets, which can be isotropic as well. Our construction can be carried out in any number of dimensions and for a great variety of dilation matrices.
We introduce the concept of frames of translates and we characterize the countable families of vectors generating such frames. In this context we generalize the concept of the Grammian introduced by Ron and Shen. We apply this characterization to study Generalized frame MRAs of L2(R). We also provide the characterization of frame multiwavelet sets associated with GFMRAs of L2(R) and we present examples of GFMRAs.
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 perhaps infinite subset of the core subspace, which we call frame multi scaling vector set. We characterize the associated frame multi wavelet vector sets by generalizing the concept of the low and high pass filters and the Quadrature Mirror filter condition. We include an extensive overview of related work of other and we conclude with some examples.
KEYWORDS: Optical character recognition, Wavelets, Feature extraction, Discrete wavelet transforms, Quantization, Human vision and color perception, Wavelet transforms, Detection and tracking algorithms, Fourier transforms, Information science
We present an approach to off-line optical character recognition for hand-written or printed characters using for feature extraction and classification biorthogonal discrete wavelet transform. Our aim is to optimize character recognition methods independently of printing styles, writing styles and fonts used. Characters are identified with their contours, thus characterized from their curvature function. Curvature function is used for feature extraction while classification is accomplished by LVQ algorithms. This method achieves great recognition accuracy and font insensitivity requiring only a small training set of characters.
KEYWORDS: Wavelets, Linear filtering, Fourier transforms, Radon, Thulium, Information operations, Space operations, Lead, Lutetium, Information technology
This paper examines classes of unitary operators of L2(R) contained in the commutant of the shift operator, such that for any pari of multiresolution analyses of L2(R) there exists a unitary operator in one of these classes, which maps all the scaling functions of the first multiresolution analysis to scaling functions of the other. We use these unitary operators to provide an interesting class of scaling functions. We show that the Dai-Larson unitary parameterization of orthonormal wavelets is not suitable for the study of scaling functions. These operators give an interesting relation between low-pass filters corresponding to scaling functions, which is implemented by a special class of unitary low-pass filters corresponding to scaling functions, which is implemented by a special class of unitary operators acting on L2([ -(pi) , (pi) ]), which we characterize. Using this characterization we recapture Daubechies' orthonormal wavelets by passing the spectral factorization process.
This paper provides classes of unitary operations of L2(R) contained in the commutant of the Shift operator, such that for any pair of multiresolution analyses of L2(R) there exists a unitary operator in one of these classes, which maps all the scaling functions of the first multiresolution analysis to scaling functions of the other. We also develop an equivalence relation between multiresolution analyses of L2(R). This relation called unitary equivalence is created by the action of a group of unitary operators contained in all the classes mentioned previously, in a way that the multiresolution structure and the Decomposition and Reconstruction algorithms remain invariant. A characterization of this relation in terms of the scaling functions is given. Distinct equivalence classes of multiresolution analyses are derived. Finally, we prove that B-splines give rise to non-equivalent examples.
This paper is concerned with the development of an equivalence relation between two multiresolution analyses of L2(R). The relation called unitary equivalence is created by the action of a unitary operator in a way that the multiresolution structure and the decomposition and reconstruction algorithms remain invariant. A characterization in terms of the scaling functions of the multiresolution analyses is given. Distinct equivalence classes of multiresolution analyses are derived. Finally, we prove that B-splines give rise to non- equivalent examples.
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