We propose a coherent mathematical model for human fingerprint images. Fingerprint structure is represented simply as a hologram - namely a phase modulated fringe pattern. The holographic form unifies analysis, classification, matching, compression, and synthesis of fingerprints in a self-consistent formalism. Hologram phase is at the heart of the method; a phase that uniquely decomposes into two parts via the Helmholtz decomposition theorem. Phase also circumvents the infinite frequency singularities that always occur at minutiae. Reliable analysis is possible using a recently discovered two-dimensional demodulator. The parsimony of this model is demonstrated by the reconstruction of a fingerprint image with an extreme compression factor of 239.

The development of the quaternion wavelet transform, Signal Processing, http://dx.doi.org/10. 1016/j.sigpro.2016.12.025 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. we then go on to detail published approaches to QWTs and to analyse them. We conclude with our own analysis of what it is that should define a QWT as being truly quaternionic and why all but a few of the "QWTs" we have described do not fit our definition.

This work presents the implementation of data-parallel perspective volume rendering on a massively parallel SIMD computer, the MasPar MP-1, and shows the benefits of e$icient indirect addressing (an MP-1 feature) which allows individual processing elements to address their local memory independently. Emphasis is put on the geometric transformations required for volume rendering algorithms. TJte data-parallel algorithm separates multi-dimensional spatial transformations into a series of one-dimensional operations that can be performed in parallel on regular data domains, providing performance linear with data size. The rotation andperspective transformation is reduced to four shearlscale passes. The separable approach allows for predictable and regular data handling, independent of data values, allowing optimization of communication between processing elements. The communications required are data axis transpositions, wJtich can be peflormed using the MP-1 's global router, which delivers scalable peflormance. Wrtualization allows graceful scaling in both problem size and architecture size, and a hierarchical design provides a flexible and portable fiamework suitable for different data-parallel SIMD architectures.1 IMAGE-BASED VISUALIZATION Massively data-parallel architectures can realise close to peak performance on regularly structured image processing and viewing operations, allowing in some cases for real-time (or near real-time) interaction with modelling and viewing parameters [17]. A number of special architectures have been used for volume rendering [ 111.Polygon-based graphic algorithms pose problems of scalability, discretization independent of problem domain, and dependence on special purpose hardware for high performance [9]. Image-or pixel-based algorithms can be scalable with problem size, need not introduce geometrical artifacts and can be implemented on general purpose data-parallel computers. As a result, increases in model complexity (e.g. molecular modelling), empirical data generated from sensors (e.g. remote sensing and medical imaging) and inter-* action impose requirements that polygon-based systems often cannot satisfy. Image-based approaches are particularly well-suited to handling large multidimensional empirical data and the integration of computer vision, computer graphics and image processing 131.2 DATA-PARALLEL VOLUME RENDERING The data-parallel algorithm achieves data access regularization by following the approach taken by Drebin&al.[4], which is a source for better efficiency in data access. Data-parallel geometrical transformations, including rotation and perspective, are applied to the data to localize projection rays within individual processing element memories. Once localization is completed, iso-surface rendering is computed using Levoy's technique [12]. This consists of computing voxel opacities for iso-surface classification, computing Phong shading, and compositing along the viewing rays for the final view (See also [21] for an extensive discussion on volume rendering iss...

X-ray Talbot moiré interferometers can now simultaneously generate two differential phase images of a specimen. The conventional approach to integrating differential phase is unstable and often leads to images with loss of visible detail. We propose a new reconstruction method based on the inverse Riesz transform. The Riesz approach is stable and the final image retains visibility of high resolution detail without directional bias. The outline Riesz theory is developed and an experimentally acquired X-ray differential phase data set is presented for qualitative visual appraisal. The inverse Riesz phase image is compared with two alternatives: the integrated (quantitative) phase and the modulus of the gradient of the phase. The inverse Riesz transform has the computational advantages of a unitary linear operator, and is implemented directly as a complex multiplication in the Fourier domain also known as the spiral phase transform.

We present a method for measuring the optical transfer function (OTF) of a camera lens using a tartan test pattern containing sinusoidal functions with multiple frequencies and orientations. The method is designed to optimize measurement accuracy for an adjustable set of sparse spatial frequencies and be reliable and fast in a wide range of measurement conditions. We describe the pattern design and the algorithm for estimating the OTF accurately from a captured image. Simulations show the tartan method is significantly more accurate than the International Organization for Standardization 12233 standard slanted-edge method. Experimental results from the tartan method were reproducible to 0.01 root mean square and in reasonable agreement with the slanted-edge method.