N-dimensional Images Research Articles

N-Dimensional Image Encoding on Quantum Computers

Quantum computing is currently one of the fastest emerging branches of information processing due to its theoretical computation powers exceeding conventional computers by far. However, currently well-known quantum-powered algorithms are of theoretical nature and its effect on practical problems has yet to be discovered. This work reviews current approaches in context of the applicability of quantum computing for the domain of image processing with respect to 3D computed tomography. It focuses on the encoding of n-dimensional images on a quantum computer and also the quantum measurement process, i.e., the image read-out. First results show that while the encoding is indeed highly efficient and is well-suited for representing 3D voxel data as obtained from computed tomography, the decoding to a classical representation is rather expensive. The latter part is also very sensitive to quantum hardware noise as was evidenced by both noisy simulator and real quantum hardware experiments.

Quantum pixel representations and compression for N-dimensional images

We introduce a novel and uniform framework for quantum pixel representations that overarches many of the most popular representations proposed in the recent literature, such as (I)FRQI, (I)NEQR, MCRQI, and (I)NCQI. The proposed QPIXL framework results in more efficient circuit implementations and significantly reduces the gate complexity for all considered quantum pixel representations. Our method scales linearly in the number of pixels and does not use ancilla qubits. Furthermore, the circuits only consist of R_y gates and text {CNOT} gates making them practical in the NISQ era. Additionally, we propose a circuit and image compression algorithm that is shown to be highly effective, being able to reduce the necessary gates to prepare an FRQI state for example scientific images by up to 90% without sacrificing image quality. Our algorithms are made publicly available as part of QPIXL++, a Quantum Image Pixel Library.

FOUR-DIMENSIONAL BALL IN A GRAPHIC REPRESENTATION

The paper presents a method for geometric modelling of a four-dimensional ball. For this, the regularities of the change in the shape of the projections of simple geometric images of two-dimensional and three-dimensional spaces during rotation are considered. Rotations of a segment and a circle around an axis are considered; it is shown that during rotation the shape of their projections changes from the maximum value to the degenerate projection.
 It was found that the set of points of the degenerate projection belongs to the axis of rotation, and each n-dimensional geometric image during rotation forms a body of a higher dimension, that is, one that belongs to (n + 1) -dimensional space. Identified regularities are extended to the four-dimensional space in which the ball is placed. It is shown that the axis of rotation of the ball will be a degenerate projection in the form of a circle, and the ball, when rotating, changes its size from a volumetric object to a flat circle, then increases again, but in the other direction (that is, it turns out), and then in reverse order to its original position. This rotation is more like a deformation, and such a ball of four-dimensional space is a hypersphere. For geometric modelling of the hypersphere and the possibility of its projection image, the article uses the vector model proposed by P.V. Filippov. The coordinate system 0xyzt is defined. The algebraic equation of the hypersphere is given by analogy with the three-dimensional space along certain coordinates of the center a, b, c, d. A variant of hypersection at t = 0 is considered, which confirms by equations obtaining a two-dimensional ball of three-dimensional space, a point (a ball of zero radius), which coincides with the center of the ball, or an imaginary ball. For the variant t = d, the equation of a two-dimensional ball is obtained, in which the radius is equal to R and the coordinates of all points along the 0t axis are equal to d. The variant of hypersection t = k turned out to be interesting, in which the equation of a two-dimensional sphere was obtained, in which the coordinates of all points along the 0t axis are equal to k, and the radius is . Horizontal vector projections of hypersection are constructed for different values of k. It is concluded that the set of horizontal vector projections of hypersections at t = k defines an ellipse.

An Image Similarity Invariant Feature Extraction Method Based on Radon Transform

With the advancements of computer technology, image recognition technology has been more and more widely applied and feature extraction is a core problem of image recognition. In study, image recognition classifies the processed image and identifies the category it belongs to. By selecting the feature to be extracted, it measures the necessary parameters and classifies according to the result. For better recognition, it needs to conduct structural analysis and image description of the entire image and enhance image understanding through multi-object structural relationship. The essence of Radon transform is to reconstruct the original N-dimensional image in N-dimensional space according to the N-1 dimensional projection data of N-dimensional image in different directions. The Radon transform of image is to extract the feature in the transform domain and map the image space to the parameter space. This paper study the inverse problem of Radon transform of the upper semicircular curve with compact support and continuous in the support. When the center and radius of a circular curve change in a certain range, the inversion problem is unique when the Radon transform along the upper semicircle curve is known. In order to further improve the robustness and discrimination of the features extracted, given the image translation or proportional scaling and the removal of impact caused by translation and proportion, this paper has proposed an image similarity invariant feature extraction method based on Radon transform, constructed Radon moment invariant and shown the description capacity of shape feature extraction method on shape feature by getting intra-class ratio. The experiment result has shown that the method of this paper has overcome the flaws of cracks, overlapping, fuzziness and fake edges which exist when extracting features alone, it can accurately extract the corners of the digital image and has good robustness to noise. It has effectively improved the accuracy and continuity of complex image feature extraction.

Practically Lossless Affine Image Transformation.

In this contribution we introduce an almost lossless affine 2D image transformation method. To this end we extend the theory of the well-known Chirp-z transform to allow for fully affine transformation of general n-dimensional images. In addition we give a practical spatial and spectral zero-padding approach dramatically reducing losses of our transform, where usual transforms introduce blurring artifacts due to sub-optimal interpolation. The proposed method improves the mean squared error by approx. a factor of 1800 compared to the commonly used linear interpolation, and by a factor of 250 to the best competitor. We derive the transform from basic principles with special attention to implementation details and supplement this paper with python code for 2D images. In demonstration experiments we show the superior image quality compared to usual approaches, when using our method. However runtimes are considerably larger than when using toolbox algorithms.

Computing Bone Morphometric Feature Maps from 3-Dimensional Images

This document describes a new remote module implemented for the Insight Toolkit (ITK), itkBoneMorphometry. This module contains bone analysis filters that compute features from N-dimensional images that represent the internal architecture of bone. The computation of the bone morphometry features in this module is based on well known methods. The two filters contained in this module are itkBoneMorphometryFeaturesFilter. which computes a set of features that describe the whole input image in the form of a feature vector, and itkBoneMorphometryFeaturesImageFilter, which computes an N-D feature map that locally describes the input image (i.e. for every voxel). itkBoneMorphometryFeaturesImageFilter can be configured based in the locality of the desired morphometry features by specifying the neighborhood size. This paper is accompanied by the source code, the input data, the choice of parameters and the output data that we have used for validating the algorithms described. This adheres to the fundamental principle that scientific publications must facilitate reproducibility of the reported results.

Computing Textural Feature Maps for N-Dimensional images

This document describes a new remote module implemented for the Insight Toolkit ITK, itkTextureFeatures. This module contains two texture analysis filters that are used to compute feature maps of N-Dimensional images using two well-known texture analysis methods. The two filters contained in this module are itkScalarImageToTextureFeaturesImageFilter (which computes textural features based on intensity-based co-occurrence matrices in the image) and itkScalarImageToRunLengthFeaturesImageFilter (which computes textural features based on equally valued intensity clusters of different sizes or run lengths in the image). The output of this module is a vector image of the same size than the input that contains a multidimensional vector in each pixel/voxel. Filters can be configured based in the locality of the textural features (neighborhood size), offset directions for co-ocurrence and run length computation, the number of bins for the intensity histograms, the intensity range or the range of run lengths. This paper is accompanied with the source code, input data, parameters and output data that we have used for validating the algorithm described in this paper. This adheres to the fundamental principle that scientific publications must facilitate reproducibility of the reported results.

Express Screening of Biological Objects Using Multisensor Stripping Voltamperometry with Pattern Recognition

Express diagnostics of biological objects is necessary for operational preliminary assessment of the condition of the patient. A method of recognition of differences between the norm and pathology is based on analysis of multidimensional patterns of the voltamperogram electrochemical test systems in Electronic formats “language”, “electronic nose”. The basis of such systems is the use of a set (matrix) sensor with completely different characteristics. A. N. Frumkin Institute of Physical Chemistry and Electrochemistry RAS (IPCE) developed a method for multidimensional stripping voltammetry, which allowed you to provide information on biological matter being investigated not as a number, as a response to a single dimension, and in the form of N-dimensional image. Formats are implemented in the process of electrochemical studies of liquid or gaseous phase. Evaluating the closeness of the resulting image object under test with known samples is collected in a database. Examples of express diagnostics of glaucoma are with accordance of the results of the electrochemical research of blood serum.

Flexible multivariate hemodynamics fMRI data analyses and simulations with PyHRF.

As part of fMRI data analysis, the pyhrf package provides a set of tools for addressing the two main issues involved in intra-subject fMRI data analysis: (1) the localization of cerebral regions that elicit evoked activity and (2) the estimation of activation dynamics also known as Hemodynamic Response Function (HRF) recovery. To tackle these two problems, pyhrf implements the Joint Detection-Estimation framework (JDE) which recovers parcel-level HRFs and embeds an adaptive spatio-temporal regularization scheme of activation maps. With respect to the sole detection issue (1), the classical voxelwise GLM procedure is also available through nipy, whereas Finite Impulse Response (FIR) and temporally regularized FIR models are concerned with HRF estimation (2) and are specifically implemented in pyhrf. Several parcellation tools are also integrated such as spatial and functional clustering. Parcellations may be used for spatial averaging prior to FIR/RFIR analysis or to specify the spatial support of the HRF estimates in the JDE approach. These analysis procedures can be applied either to volume-based data sets or to data projected onto the cortical surface. For validation purpose, this package is shipped with artificial and real fMRI data sets, which are used in this paper to compare the outcome of the different available approaches. The artificial fMRI data generator is also described to illustrate how to simulate different activation configurations, HRF shapes or nuisance components. To cope with the high computational needs for inference, pyhrf handles distributing computing by exploiting cluster units as well as multi-core machines. Finally, a dedicated viewer is presented, which handles n-dimensional images and provides suitable features to explore whole brain hemodynamics (time series, maps, ROI mask overlay).

Fuzzy fractal dimension based on escape time algorithm

Fractal dimension is a mathematical concept used to measure the geometrical complexity of fractal set. It is defined for fractal geometric images, and considered as global features for them. There are many methods to estimate the fractal dimension of an object. The box counting dimension is an easier and a widely used one, while the escape time dimension is another method used to estimate the dimension of fractals generated using escape time algorithm. These methods are used to calculate the dimension for monochrome images (2Dimages). The necessity to generalize these concepts to be applicable for real world application ( e.g. gray scale image, or colored images) has motivating us to introducing the concepts of fuzzy sets. Fuzzy fractal dimension is proposed as the fractal feature for n-dimensional image. In this paper, a new approach to determine fractal dimension is proposed and a new local fuzzy fractal dimension based on this approach is proposed also. It will help to extend this feature to be used in many real world applications that cannot be served based on traditional fractal dimension. By this new approach, the FD is estimated with a reduced number of computational processes. This will helps to improve the complexity of the escape time algorithm that is considered as an NP-Hard problem, and with high precision results.

Linear principal transformation: toward locating features in N-dimensional image space

Projection Functions have been widely used for facial feature extraction and optical/handwritten character recognition due to their simplicity and efficiency. Because these transformations are not one-to-one, they may result in mapping distinct points into one point, and consequently losing detailed information. Here, we solve this problem by defining an N-dimensional space to represent a single image. Then, we propose a one-to-one transformation in this new image space. The proposed method, which we referred to as Linear Principal Transformation (LPT), utilizes Eigen analysis to extract the vector with the highest Eigenvalue. Afterwards, extrema in this vector were analyzed to extract the features of interest. In order to evaluate the proposed method, we performed two sets of experiments on facial feature extraction and optical character recognition in three different data sets. The results show that the proposed algorithm outperforms the observed algorithms in the paper and achieves accuracy from 1.4 % up to 14 %, while it has a comparable time complexity and efficiency.

Locally Orderless Registration

This paper presents a unifying approach for calculating a wide range of popular, but seemingly very different, similarity measures. Our domain is the registration of n-dimensional images sampled on a regular grid, and our approach is well suited for gradient-based optimization algorithms. Our approach is based on local intensity histograms and built upon the technique of Locally Orderless Images. Histograms by Locally Orderless Images are well posed and offer explicit control over the three inherent and unavoidable scales: the spatial resolution, intensity levels, and spatial extent of local histograms. Through Locally Orderless Images, we offer new insight into the relations between these scales. We demonstrate our unification by developing a Locally Orderless Registration algorithm for two quite different similarity measures, namely, Normalized Mutual Information and Sum of Squared Differences, and we compare these variations both theoretically and empirically. Finally, using our algorithm, we explain the empirically observed differences between two popular joint density estimation techniques used in registration: Parzen Windows and Generalized Partial Volume.

Multimodal imaging: modelling and segmentation with biomedical applications

The maximum a posteriori (MAP) technique, combining intensity and spatial interactions, has been a standard statistical approach for image segmentation. Crucial steps for the MAP technique are the model identification, incorporation of priors, and the optimisation approach. This paper describes an unsupervised MAP segmentation framework of N-dimensional multimodal images. The input image and its desired labelling are described by a joint Markov-Gibbs random field (MGRF) model of independent image signals and interdependent region labels. A kernel approach is used to model the joint and marginal probability densities of objects from the gray level histogram, incorporating a generalised linear combination of Gaussians (LCG). A novel maximum likelihood estimate (MLE) for the number of classes in the LCG model is introduced. An approach is devised for MGRF model identification based on region characteristics. The segmentation process employs LCG to provide an initial segmentation, then α-expansion move algorithm iteratively refines the labelled image using MGRF. The resulting MAP algorithm is studied in terms of convergence and sensitivity to initialisation, improper estimation of the number of classes, and discontinuities in the objects. The framework is modular, allowing incorporation of intensity and spatial interactions with varying complexity, and can be extended to incorporate shape priors.

Tensor scale: An analytic approach with efficient computation and applications

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods.

Multilocal Creaseness Measure

This document describes the implementation using the Insight Toolkit of an algorithm for detecting creases (ridges and valleys) in N-dimensional images, based on the Local Structure Tensor of the image. In addition to the filter used to calculate the creaseness image, a filter for the computation of the structure tensor is also included in this submission.

Segmentation of multispectral MR images through an annealed rough neural network

In this paper, multispectral image segmentation using a rough neural network based on an annealed strategy with a cooling schedule is created. The main purpose is to embed an annealed cooling schedule into the rough neural network to construct a segmentation system named annealed rough neural net (ARNN). The classification system is a paradigm for the implementation of annealed reasoning and rough systems in neural network architecture. Instead of all the information in the image are fed into the neural network, the upper- and lower-bound gray level, captured from a training vector in a multispectral image, were fed into a rough neuron in the ARNN. Therefore, only 2-channel images are selected as the training samples if an N-dimensional multispectral image was used. In the simulation results, the proposed network not only reduces the consuming time but also reserves the classification performance.

Geodesic image and video editing

This article presents a new, unified technique to perform general edge-sensitive editing operations on n-dimensional images and videos efficiently. The first contribution of the article is the introduction of a Generalized Geodesic Distance Transform (GGDT), based on soft masks. This provides a unified framework to address several edge-aware editing operations. Diverse tasks such as denoising and nonphotorealistic rendering are all dealt with fundamentally the same, fast algorithm. Second, a new Geodesic Symmetric Filter (GSF) is presented which imposes contrast-sensitive spatial smoothness into segmentation and segmentation-based editing tasks (cutout, object highlighting, colorization, panorama stitching). The effect of the filter is controlled by two intuitive, geometric parameters. In contrast to existing techniques, the GSF filter is applied to real-valued pixel likelihoods (soft masks), thanks to GGDTs and it can be used for both interactive and automatic editing. Complex object topologies are dealt with effortlessly. Finally, the parallelism of GGDTs enables us to exploit modern multicore CPU architectures as well as powerful new GPUs, thus providing great flexibility of implementation and deployment. Our technique operates on both images and videos, and generalizes naturally to n-dimensional data. The proposed algorithm is validated via quantitative and qualitative comparisons with existing, state-of-the-art approaches. Numerous results on a variety of image and video editing tasks further demonstrate the effectiveness of our method.

Shells and Spheres: An n-Dimensional Framework for Medial-Based Image Segmentation.

We have developed a method for extracting anatomical shape models from n-dimensional images using an image analysis framework we call Shells and Spheres. This framework utilizes a set of spherical operators centered at each image pixel, grown to reach, but not cross, the nearest object boundary by incorporating “shells” of pixel intensity values while analyzing intensity mean, variance, and first-order moment. Pairs of spheres on opposite sides of putative boundaries are then analyzed to determine boundary reflectance which is used to further constrain sphere size, establishing a consensus as to boundary location. The centers of a subset of spheres identified as medial (touching at least two boundaries) are connected to identify the interior of a particular anatomical structure. For the automated 3D algorithm, the only manual interaction consists of tracing a single contour on a 2D slice to optimize parameters, and identifying an initial point within the target structure.

Alternative Memory Models for ITK Images

By default ITK images use a contiguous memory model. This means pixel elements are stored in a single 1-D array, where each element is adjacent in memory to the previous element. However in some situations it is not desirable to use this memory model. This document describes three alternative memory models: slice contiguous, sparse, and single-bit binary images. Slice contiguous images are three-dimensional images, in which each slice is stored in a contiguous 1-D array, but the slices are not necessarily adjacent in memory. Slice contiguous images are well suited for interoperability with applications representing images using DICOM. Sparse images are n-dimensional images, in which each pixel is stored in a hash table data structure. This memory model is well suited for images with very large dimensions, but few pixels which are actually relevant. Single-bit binary images internally represent each pixel as a single-bit, in contrast to eight-bits required to represent a boolean. Single-bit binary images allow very compact representations for on-off masks. Source code, tests, and examples are provided to allow easy reproduction and use.

An Optimized N-Dimensional Hough Filter for Detecting Spherical Image Objects

An Insight Toolkit (ITK) algorithm for detection of spherical objects using Hough methods with voting is presented in this paper. Currently, the usage of Hough methods for detecting linear and circular elements exists for 2D images in ITK. The current work extends those filters in several ways. Firstly, the new filters operate on N-dimensional images. Secondly, they work in physical coordinates which is quite essential in medical imaging modalities. Thirdly, they are optimized (multi-threaded execution, stratified sampling etc.) for usage on large datasets and show a significant speedup even in 2D and on small images. Our implementation follows the same underlying mathematics of Hough transforms (as implemented by the 2D filters) but with some minor variations. The main variation lies in the pattern of voting that involves selecting voting regions easily and efficiently accessible to region iterators rather than cones that are difficult to generalize in higher dimensions. We include 2D example code, parameter settings and show the results generated on embryonic images of the zebrafish from optical microscopy.