This article proposes the Mediterranean matrix multiplication, a new, simple and practical randomized algorithm that samples angles between the rows and columns of two matrices with sizes m, n, and p to approximate matrix multiplication in O(k(mn+np+mp)) steps, where k is a constant only related to the precision desired. The number of instructions carried out is mainly bounded by bitwise operators, amenable to a simplified processing architecture and compressed matrix weights. Results show that the method is superior in size and number of operations to the standard approximation with signed matrices. Equally important, this article demonstrates a first application to machine learning inference by showing that weights of fully connected layers can be compressed between 30 × and 100 × with little to no loss in inference accuracy. The requirements for pure floating-point operations are also down as our algorithm relies mainly on simpler bitwise operators.

Local Interpretable Model-Agnostic Explanations (LIME) and SHapley Additive exPlanations (SHAP) algorithms have been widely discussed by the Explainable AI (XAI) community but their application to wider domains are rare, potentially due to the lack of easy-to-use tools built around these methods. In this paper, we present ExMed, a tool that enables XAI data analytics for domain experts without requiring explicit programming skills. It supports data analytics with multiple feature attribution algorithms for explaining machine learning classifications and regressions. We illustrate its domain of applications on two real world medical case studies, with the first one analysing COVID-19 control measure effectiveness and the second one estimating lung cancer patient life expectancy from the artificial Simulacrum health dataset. We conclude that ExMed can provide researchers and domain experts with a tool that both concatenates flexibility and transferability of medical sub-domains and reveal deep insights from data.

Data compression forms a central role in handling the bottleneck of data storage, transmission and processing. Lossless compression requires reducing the file size whilst maintaining bit-perfect decompression, which is the main target in medical applications. This paper presents a novel lossless compression method for 16-bit medical imaging volumes. The aim is to train a neural network (NN) as a 3D data predictor, which minimizes the differences with the original data values and to compress those residuals using arithmetic coding. We evaluate the compression performance of our proposed models to state-of-the-art lossless compression methods, which shows that our approach accomplishes a higher compression ratio in comparison to JPEG-LS, JPEG2000, JP3D, and HEVC and generalizes well.

As scanners produce higher-resolution and more densely sampled images, this raises the challenge of data storage, transmission and communication within healthcare systems. Since the quality of medical images plays a crucial role in diagnosis accuracy, medical imaging compression techniques are desired to reduce scan bitrate while guaranteeing lossless reconstruction. This paper presents a lossless compression method that integrates a Recurrent Neural Network (RNN) as a 3D sequence prediction model. The aim is to learn the long dependencies of the voxel's neighbourhood in 3D using Long Short-Term Memory (LSTM) network then compress the residual error using arithmetic coding. Experiential results reveal that our method obtains a higher compression ratio achieving 15% saving compared to the state-of-the-art lossless compression standards, including JPEG-LS, JPEG2000, JP3D, HEVC, and PPMd. Our evaluation demonstrates that the proposed method generalizes well to unseen modalities CT and MRI for the lossless compression scheme. To the best of our knowledge, this is the first lossless compression method that uses LSTM neural network for 16-bit volumetric medical image compression.

The Expectation Maximization (EM) algorithm is an alternative reconstruction method to the Filtered Back Projection method, providing many advantages including decreased sensitivity to noise. However the algorithm requires a large number of iterations to reach adequate convergence. Due to this, research has been carried out into accelerating the convergence rate of the EM algorithm. In this paper we present an analysis of an EM implementation which uses both OSEM and MGEM, comparing results on a per time basis with both acceleration techniques alone as well as a combination of the two methods. We provide an alternative stopping criterion based on the RMS error of the projections of the current reconstruction and compare the result with an existing variance based approach.

We present an efficient ray-tracing algorithm which, for the first time, does not store any data structures when performing spatial subdivisions, and directly computes intersections inside the scene. This new algorithm is often faster than comparable ray-tracing methods at rendering dynamic scenes, and has a similar level of performance when compared to static ray-tracers. Memory management is made minimal and deterministic, which simplifies ray-tracing engineering, as spatial subdivision data structures are no longer considered in the graphics pipeline. This is possible with a modification of Whitted's naive ray-tracing algorithm by using a divide-and-conquer approach, and by having a sufficient collection of rays in order to reduce the complexity of naive ray-tracing. In particular, the algorithm excels at spontaneously solving large Ray/Primitive intersection problems.

Caricatures are a form of humorous visual art, usually created by skilled artists for the intention of amusement and entertainment. In this paper, we present a novel approach for automatic generation of digital caricatures from facial photographs, which capture artistic deformation styles from hand-drawn caricatures. We introduced a pseudo stress-strain model to encode the parameters of an artistic deformation style using "virtual" physical and material properties. We have also developed a software system for performing the caricaturistic deformation in 3D which eliminates the undesirable artifacts in 2D caricaturization. We employed a Multilevel Free-Form Deformation (MFFD) technique to optimize a 3D head model reconstructed from an input facial photograph, and for controlling the caricaturistic deformation. Our results demonstrated the effectiveness and usability of the proposed approach, which allows ordinary users to apply the captured and stored deformation styles to a variety of facial photographs.

The availability of commodity volumetric displays provides ordinary users with a new means of visualizing 3D data. Many of these displays are in the class of isotropically emissive light devices, which are designed to directly illuminate voxels in a 3D frame buffer, producing X-ray-like visualizations. While this technology can offer intuitive insight into a 3D object, the visualizations are perceptually different from what a computer graphics or visualization system would render on a 2D screen. This paper formalizes rendering on isotropically emissive displays and introduces a novel technique that emulates traditional rendering effects on isotropically emissive volumetric displays, delivering results that are much closer to what is traditionally rendered on regular 2D screens. Such a technique can significantly broaden the capability and usage of isotropically emissive volumetric displays. Our method takes a 3D dataset or object as the input, creates an intermediate light field, and outputs a special 3D volume dataset called a lumi-volume. This lumi-volume encodes approximated rendering effects in a form suitable for display with accumulative integrals along unobtrusive rays. When a lumi-volume is fed directly into an isotropically emissive volumetric display, it creates a 3D visualization with surface shading effects that are familiar to the users. The key to this technique is an algorithm for creating a 3D lumi-volume from a 4D light field. In this paper, we discuss a number of technical issues, including transparency effects due to the dimension reduction and sampling rates for light fields and lumi-volumes. We show the effectiveness and usability of this technique with a selection of experimental results captured from an isotropically emissive volumetric display, and we demonstrate its potential capability and scalability with computer-simulated high-resolution results.

To create a new, flexible system for volume illustration, we have explored the use of Wang Cubes, the 3D extension of 2D Wang Tiles. We use small sets of Wang Cubes to generate a large variety of nonperiodic illustrative 3D patterns and texture, which otherwise would be too large to use in real applications. We also develop a direct volume rendering framework with the generated patterns and textures. Our framework can be used to render volume datasets effectively and a variety of rendering styles can be achieved with less storage. Specifically, we extend the nonperiodic tiling process of Wang Tiles to Wang Cubes and modify it for multipurpose tiling. We automatically generate isotropic Wang Cubes consisting of 3D patterns or textures to simulate various illustrative effects. Anisotropic Wang Cubes are generated to yield patterns by using the volume data, curvature, and gradient information. We also extend the definition of Wang Cubes into a set of different sized cubes to provide multiresolution volume rendering. Finally, we provide both coherent 3D geometry-based and texture-based rendering frameworks that can be integrated with arbitrary feature exploration methods.

Many techniques have already been proposed to improve the efficiency of maximum intensity projection (MIP) volume rendering, but none of them considered the possible hypothesis of a better complexity than either O( n ) for finding the maximum value of n samples along a ray or O( n 3 ) for an object-order algorithm. Here, we fully model and analyze the use of octrees for MIP, and we mathematically show that the average MIP complexity can be reduced to O( n 2 ) for an object-order algorithm, or to O(log( n )) per ray when using the image-order variant of our algorithm. Therefore, this improvement establishes a major advance for interactive MIP visualization of large-volume data.In parallel, we also present an object-order implementation of our algorithm, satisfying the theoretical O( n 2 ) result. It is based on hierarchical occlusion maps that perform on-the-fly visibility of the data, and our results show that it is the most efficient solution for MIP available to date.

Abstract Rapid, visual understanding of volumetric datasets is a crucial outcome of a good volume rendering application, but few current volume rendering systems deliver this result. Our goal is to reduce the volumetric surfing that is required to understand volumetric features by conveying more information in fewer images. In order to achieve this goal, and in contrast with most current methods which still use optical models and alpha blending, our approach reintroduces the order‐independent contribution of every sample along the ray in order to have an equiprobable visualization of all the volume samples. Therefore, we demonstrate how order independent sampling can be suitable for fast volume understanding, show useful extensions to MIP and X‐ray like renderings, and, finally, point out the special advantage of using stereo visualization in these models to circumvent the lack of depth cues. Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/Image, Generation, I.3.7 [Computer Graphics]: Three‐Dimensional graphics and realism.

We present a data structure for three-dimensional fields C/sup 1/ continuous in the modelling space. Regular grids storing the field values discretely are combined with a triquadratic approximation filter to define volume objects. This association of a grid and an approximation/interpolation filter allows the field to be defined by a C/sup 1/ continuous real function and the surface to be directly visualised from its own equation. We show how accurate and high quality interactive visualisation is obtained during the modelling process, and we explain why the visualisation is faithful to the object definition. We also describe, as an example of application of our data structure, how advanced Boolean operators realised with soft or "functionally controlled" transitions are performed under the influence of an interactive modelling tool.

Many direct volume rendering algorithms have been proposed during the last decade to render 256/sup 3/ voxels interactively. However a lot of limitations are inherent to all of them, like low-quality images, a small viewport size or a fixed classification. In contrast, interactive high quality algorithms are still a challenge nowadays. We introduce here an efficient and accurate technique called object-order ray-casting that can achieve up to 10 fps on current workstations. Like usual ray-casting, colors and opacities are evenly sampled along the ray, but now within a new object-order algorithm. Thus, it allows to combine the main advantages of both worlds in term of speed and quality. We also describe an efficient hidden volume removal technique to compensate for the loss of early ray termination.

To render images from volume datasets, an interpolation method also called reconstruction is needed. The level of details of the resultant image closely depends on the filter used for reconstruction. We propose here a new filter producing C1 continue surfaces. The provided image quality is better than current high-quality algorithms, like splatting or trilinear raycasting, where tiny details are often eliminated. In contrast with other studied high quality filters that are practically unusable, our algorithm has been implemented interactively on a modest platform thanks to an efficient implementation using parametric cubes. We also demonstrate the interest of a min-max octree in the visualization of isosurfaces interactively thresholded.