Multiresolution Structure Research Articles

Acoustic simulation using singular boundary method based on loop subdivision surfaces: A seamless integration of CAD and CAE

This paper firstly combines the Burton-Miller-type singular boundary method (BMSBM) with the Loop subdivision surfaces (LSS) for the acoustic simulation of 3D complicated structures. As a modern modeling technique, the LSS provides a flexible and simple means to represent model surfaces by controlling meshes and subdivision rules. Thus, it can achieve arbitrary topology and multi-resolution structures. As a semi-analytical and boundary-type meshless technique, the BMSBM using the fundamental solutions is simple, accurate, and straightforward for solving acoustic radiation and scattering problems. The new approach constructs a geometry model using a subdivision scheme, and therefore can create a multi-resolution hierarchical model meeting various accuracy requirements without a repetitive meshing procedure. The proposed method effectively breaks through the technical bottleneck that the BMSBM makes it difficult to collate boundary nodes of complex structures and achieves a seamless integration between CAD and CAE. The numerical results of three examples demonstrated the effectiveness and accuracy of the proposed method for acoustic simulation. The present study provides an innovative idea for the subsequent optimization of materials and shapes of acoustic structures, which has the potential to enhance precision and efficiency significantly.

Multiresolution categorical regression for interpretable cell-type annotation.

In many categorical response regression applications, the response categories admit a multiresolution structure. That is, subsets of the response categories may naturally be combined into coarser response categories. In such applications, practitioners are often interested in estimating the resolution at which a predictor affects the response category probabilities. In this paper, we propose a method for fitting the multinomial logistic regression model in high dimensions that addresses this problem in a unified and data-driven way. Our method allows practitioners to identify which predictors distinguish between coarse categories but not fine categories, which predictors distinguish between fine categories, and which predictors are irrelevant. For model fitting, we propose a scalable algorithm that can be applied when the coarse categories are defined by either overlapping or nonoverlapping sets of fine categories. Statistical properties of our method reveal that it can take advantage of this multiresolution structure in a way existing estimators cannot. We use our method to model cell-type probabilities as a function of a cell's gene expression profile (i.e., cell-type annotation). Our fitted model provides novel biological insights which may be useful for future automated and manual cell-type annotationmethodology.

Multi-Resolution 3D Rendering for High-Performance Web AR.

In the context of web augmented reality (AR), 3D rendering that maintains visual quality and frame rate requirements remains a challenge. The lack of a dedicated and efficient 3D format often results in the degraded visual quality of the original data and compromises the user experience. This paper examines the integration of web-streamable view-dependent representations of large-sized and high-resolution 3D models in web AR applications. The developed cross-platform prototype exploits the batched multi-resolution structures of the Nexus.js library as a dedicated lightweight web AR format and tests it against common formats and compression techniques. Built with AR.js and Three.js open-source libraries, it allows the overlay of the multi-resolution models by interactively adjusting the position, rotation and scale parameters. The proposed method includes real-time view-dependent rendering, geometric instancing and 3D pose regression for two types of AR: natural feature tracking (NFT) and location-based positioning for large and textured 3D overlays. The prototype achieves up to a 46% speedup in rendering time compared to optimized glTF models, while a 34 M vertices 3D model is visible in less than 4 s without degraded visual quality in slow 3D networks. The evaluation under various scenes and devices offers insights into how a multi-resolution scheme can be adopted in web AR for high-quality visualization and real-time performance.

Hierarchical clustering: Visualization, feature importance and model selection

We propose methods for the analysis of hierarchical clustering that fully use the multi-resolution structure provided by a dendrogram. Specifically, we propose a loss for choosing between clustering methods, a feature importance score and a graphical tool for visualizing the segmentation of features in a dendrogram. Current approaches to these tasks lead to loss of information since they require the user to generate a single partition of the instances by cutting the dendrogram at a specified level. Our proposed methods, instead, use the full structure of the dendrogram. The key insight behind the proposed methods is to view a dendrogram as a phylogeny. This analogy permits the assignment of a feature value to each internal node of a tree through an evolutionary model. Real and simulated datasets provide evidence that our proposed framework has desirable outcomes and gives more insights than state-of-art approaches. We provide an R package that implements our methods.

GMCNet: A Generative Multi-Resolution Framework for Cardiac Registration

Deformable image registration plays a crucial role in estimating cardiac deformation from a sequence of images. However, existing registration methods primarily process images as pairs instead of processing all images in a sequence together. This study proposes a novel end-to-end learning-free generative multi-resolution convolutional neural network (GMCNet) with the primary focus of registering images in a sequence. Even though learning-based methods have yielded high performance for image registration, their performance depends on their ability to learn information from a large number of samples which are difficult to obtain and might bias the framework to the specific domain of data. The proposed learning-free method eliminates the need for a dedicated training set while exploiting the capabilities of neural networks to achieve accurate deformation fields. Due to its capability of parameter sharing through the architecture, the GMCNet can be used as a groupwise registration as well as pairwise registration. The proposed method was evaluated on three different clinical cardiac magnetic resonance imaging datasets and compared quantitatively against nine other state-of-the-art learning and optimization-based algorithms. The proposed method outperformed other methods in all comparisons and yielded average Dice metric values ranging from 0.85 to 0.88 for the datasets. Different aspects of the GMCNet are also explored by assessing 1) the robustness; 2) performance on pairwise registration; 3) the influence of spatial transformation in a controlled environment; and 4) the impact of different multi-resolution structures. The results demonstrate that using temporal information to estimate the deformation fields leads to more accurate registration results and improved robustness under different noise levels. Moreover, the proposed method does not need images for training, and therefore, its prediction is not domain-specific and can be applied to any sequence of images.

Interactive Visualization of Large Point Clouds Using an Autotuning Multiresolution Out-Of-Core Strategy

Abstract Due to the increasingly large amount of data acquired into point clouds, from LiDAR (Light Detection and Ranging) sensors and 2D/3D sensors, massive point clouds processing has become a topic with high interest for several fields. Current client-server applications usually use multiresolution out-of-core proposals; nevertheless, the construction of the data structures required is very time-consuming. Furthermore, these multiresolution approaches present problems regarding point density changes between different levels of detail and artifacts due to the rendering of elements entering and leaving the field of view. We present an autotuning multiresolution out-of-core strategy to avoid these problems. Other objectives are reducing loading times while maintaining low memory requirements, high visualization quality and achieving interactive visualization of massive point clouds. This strategy identifies certain parameters, called performance parameters, and defines a set of premises to obtain the goals mentioned above. The optimal parameter values depend on the number of points per cell in the multiresolution structure. We test our proposal in our web-based visualization software designed to work with the structures and storage format used and display massive point clouds achieving interactive visualization of point clouds with more than 27 billion points.

3D mesh transformer: A hierarchical neural network with local shape tokens

Self-attention networks have revolutionized Natural Language Processing (NLP) and are making impressive strides in image analysis tasks such as image classification and object detection. Inspired by this success, we specifically design a novel self-attention mechanism between local shapes and build a shape Transformer. We split the 3D mesh model into shape patches, which we call shape tokens, and provide polynomial fitting representations of these patches as input to the shape Transformer. The shape token encodes local geometric information and resembles the token (word) status in NLP. The simplification of the mesh model provides a hierarchical multiresolution structure, which allows us to realize the feature learning of a multilayer Transformer. We set high-level features formed by the shape Transformer as visual tokens and propose a vector-type self-attention mechanism to construct a 3D visual Transformer. Finally, we realized a hierarchical network structure based on local shape tokens and high-level visual tokens. Experiments show that our fusion network of 3D shape Transformer with explicit local shape context augmentation and 3D visual Transformer with multi-level structural feature learning achieves excellent performance on shape classification and part segmentation tasks.

Generalized Multiresolution Structures in Reducing Subspaces of Local Fields

Generalized Multiresolution Structures in Reducing Subspaces of Local Fields

Instant neural graphics primitives with a multiresolution hash encoding

Neural graphics primitives, parameterized by fully connected neural networks, can be costly to train and evaluate. We reduce this cost with a versatile new input encoding that permits the use of a smaller network without sacrificing quality, thus significantly reducing the number of floating point and memory access operations: a small neural network is augmented by a multiresolution hash table of trainable feature vectors whose values are optimized through stochastic gradient descent. The multiresolution structure allows the network to disambiguate hash collisions, making for a simple architecture that is trivial to parallelize on modern GPUs. We leverage this parallelism by implementing the whole system using fully-fused CUDA kernels with a focus on minimizing wasted bandwidth and compute operations. We achieve a combined speedup of several orders of magnitude, enabling training of high-quality neural graphics primitives in a matter of seconds, and rendering in tens of milliseconds at a resolution of 1920×1080.

Subdivision-based Mesh Convolution Networks

Convolutionalneural networks (CNNs) have made great breakthroughs in two-dimensional (2D) computer vision. However, their irregular structure makes it hard to harness the potential of CNNs directly on meshes. A subdivision surface provides a hierarchical multi-resolution structure in which each face in a closed 2-manifold triangle mesh is exactly adjacent to three faces. Motivated by these two observations, this article presents SubdivNet , an innovative and versatile CNN framework for three-dimensional (3D) triangle meshes with Loop subdivision sequence connectivity. Making an analogy between mesh faces and pixels in a 2D image allows us to present a mesh convolution operator to aggregate local features from nearby faces. By exploiting face neighborhoods, this convolution can support standard 2D convolutional network concepts, e.g., variable kernel size, stride, and dilation. Based on the multi-resolution hierarchy, we make use of pooling layers that uniformly merge four faces into one and an upsampling method that splits one face into four. Thereby, many popular 2D CNN architectures can be easily adapted to process 3D meshes. Meshes with arbitrary connectivity can be remeshed to have Loop subdivision sequence connectivity via self-parameterization, making SubdivNet a general approach. Extensive evaluation and various applications demonstrate SubdivNet’s effectiveness and efficiency.

Towards point cloud completion: Point Rank Sampling and Cross-Cascade Graph CNN

The Point Fractal Network (PF-Net) is a seminal work with capability of completing the missing regions of point clouds. However, the multi-resolution structure of PF-Net neglects effective feature fusion between each resolution, which makes the resulting shape lack local geometric details. To tackle this problem, we design a novel shape completion network named PRSCN. We first present Point Rank Sampling to rate and sample feature points more objectively through local outline form. In this way, the sampled points can facilitate the downstream tasks. Subsequently, considering the correlation between features from different scales, we design a Cross-Cascade Module to combine features hierarchically. Moreover, we propose Leap-type EdgeConv to enlarge the receptive field while maintain the kernel size unchanged. These improvements together make our CD error 3% lower than that of state-of-the-art method on ShapeNet-part dataset.

Pancreatic cancer tumor analysis in CT images using patch-based multi-resolution convolutional neural network

In this paper we proposed a cascaded structure for extraction of the volumetric shape of the pancreas and tumor in adenocarcinoma patients. This process is a combination of an elastic atlas which is capable of fitting on 3D volumetric shape extracted from CT slices, a convolutional neural network with three forward paths to label the patches of images with coarse to fine resolutions using a multi-resolution structure, a region growing edge detection and finally a wavelet based multi-resolution rendering to extract the volumetric shape of the pancreas and tumor from planar CT slices. The atlas organs were weighted by geometrical parameters which were adjusted at global and organ levels. The classification of image patches was performed using a multiresolution convolutional neural network. The final segmentation of the pancreas and tumor was obtained by applying an edge detection method. A multiresolution wavelet is used for extraction of the volumetric shapes from segmented images. The subjects were 53–86 years of age with a mean and SD of 66 ± 10.24 years. K-fold cross validation is used for all the experiments. The results were compared with those of previously reported methods including Residual Network. The performance of the proposed algorithm was evaluated by Dice Similarity Coefficient (DSC), Jaccard index (JI), precision and recall yielded 89.67, 80.12, 91.37 and 93.63 for pancreas and 81.42, 68.66, 84.97 and 88.24 for tumor, respectively. The results of the proposed fully cascaded method overperformed all the other methods being compared.

Multi-Resolution Filters for Massive Spatio-Temporal Data

Spatio-temporal datasets are rapidly growing in size. For example, environmental variables are measured with increasing resolution by increasing numbers of automated sensors mounted on satellites and aircraft. Using such data, which are typically noisy and incomplete, the goal is to obtain complete maps of the spatio-temporal process, together with uncertainty quantification. We focus here on real-time filtering inference in linear Gaussian state-space models. At each time point, the state is a spatial field evaluated on a very large spatial grid, making exact inference using the Kalman filter computationally infeasible. Instead, we propose a multi-resolution filter (MRF), a highly scalable and fully probabilistic filtering method that resolves spatial features at all scales. We prove that the MRF matrices exhibit a particular block-sparse multi-resolution structure that is preserved under filtering operations through time. We describe connections to existing methods, including hierarchical matrices from numerical mathematics. We also discuss inference on time-varying parameters using an approximate Rao-Blackwellized particle filter, in which the integrated likelihood is computed using the MRF. Using a simulation study and a real satellite-data application, we show that the MRF strongly outperforms competing approaches. Supplementary materials include Python code for reproducing the simulations, some detailed properties of the MRF and auxiliary theoretical results.

A wavelet denoising approach based on unsupervised learning model

Image denoising plays an important role in image processing, which aims to separate clean images from noisy images. A number of methods have been presented to deal with this practical problem over the past several years. The best currently available wavelet-based denoising methods take advantage of the merits of the wavelet transform. Most of these methods, however, still have difficulties in defining the threshold parameter which can limit their capability. In this paper, we propose a novel wavelet denoising approach based on unsupervised learning model. The approach taken aims at exploiting the merits of the wavelet transform: sparsity, multi-resolution structure, and similarity with the human visual system, to adapt an unsupervised dictionary learning algorithm for creating a dictionary devoted to noise reduction. Using the K-Singular Value Decomposition (K-SVD) algorithm, we obtain an adaptive dictionary by learning over the wavelet decomposition of the noisy image. Experimental results on benchmark test images show that our proposed method achieves very competitive denoising performance and outperforms state-of-the-art denoising methods, especially in the peak signal to noise ratio (PSNR), the structural similarity (SSIM) index, and visual effects with different noise levels.

Single image super-resolution via low-rank tensor representation and hierarchical dictionary learning

Super-resolution (SR) has been widely studied due to its importance in real applications and scenarios. In this paper, we focus on generating an SR image from a single low-resolution (LR) input image by employing the multi-resolution structures of an input image. By taking the LR image and its downsampled resolution (DR) and upsampled resolution (UR) versions as inputs, we propose a hierarchical dictionary learning approach to learn the latent UR-LR dictionary pair by preserving the internal structure coherence with the LR-DR dictionary pair. Note that an imposed restriction involved in this process is that the pairwise resolution images are jointly trained to obtain more compact patterns of image patches. In particular, to better explore the underlying structures of tensor data spanned by image patches, we propose a low-rank tensor approximation (LRTA) algorithm based on nuclear-norm regularization to embed input image patches into a low-dimensional space. Experimental results from publicly used images show that our proposed method achieves performance comparable with that of other state-of-the-art SR algorithms, even without using any external training databases.

Toward Optimum Quantification of Pathology-Induced Noises: An Investigation of Information Missed by Human Auditory System

Clinical diagnosis of voice disorder and evaluation of therapy outcome heavily rely on accurate quantification of voice quality, which is closely tied to the physiology and function of the laryngeal mechanism. Considering the evaluation methodology of the voice, two main categories of auditory-perceptual assessment and acoustic analysis can be identified. This article presents a new approach for acoustic analysis of voice quality, which brings several advantages to the field. The proposed approach is non-parametric in the sense that it does not require the estimation of the fundamental frequency or spectral response of the vocal tract. This reduces the computational complexity of the measurement and reduces the possible errors due to inaccurate estimation of those parameters. Additionally, the method does not make any assumption about the phonetic context and hence has the potential to be applied to connected speech. The proposed method benefits from the multiresolution structure of the wavelet analysis for estimating the noisy component of a voice in the spectro-temporal domain. The informativeness of the estimated noise for voice quality distinction is examined based on different noise-quantification approaches. It is shown that deviation from the model of the human auditory system (HAS) leads to performance improvement. Through several analyses, it is argued that using models of HAS for quantification of the noise leads to significant loss of information relevant to voice quality. Findings from this article suggest that perception-based measures of voice quality are highly restricted in capturing important aspects of acoustic that could assist with voice quality distinctions. This characteristic is inherent to HAS and cannot be alleviated, highlighting a significant limitation of perception-based measures.

Few-Shot Breast Cancer Metastases Classification via Unsupervised Cell Ranking.

Tumor metastases detection is of great importance for the treatment of breast cancer patients. Various CNN (convolutional neural network) based methods get excellent performance in object detection/segmentation. However, the detection of metastases in hematoxylin and eosin (H&E) stained whole-slide images (WSI) is still challenging mainly due to two aspects. (1) The resolution of the image is too large. (2) lacking labeled training data. Whole-slide images generally stored in a multi-resolution structure with multiple downsampled tiles. It is difficult to feed the whole image into memory without compression. Moreover, labeling images for the pathologists are time-consuming and expensive. In this paper, we study the problem of detecting breast cancer metastases in the pathological image on patch level. To address the abovementioned challenges, we propose a few-shot learning method to classify whether an image patch contains tumor cells. Specifically, we propose a patch-level unsupervised cell ranking approach, which only relies on images with limited labels. The main idea of the proposed method is that when cropping a patch A from the WSI and further cropping a sub-patch B from A, the cell number of A is always larger than that of B. Based on this observation, we make use of the unlabeled images to learn the ranking information of cell counting to extract the abstract features. Experimental results show that our method is effective to improve the patch-level classification accuracy, compared to the traditional supervised method. The source code is publicly available at https://github.com/fewshot-camelyon.

Multi-fractal multi-resolution structures from DLA – Strange Attractors Hybrids

In this paper we propose and simulate novel multi-fractal multi-resolution structures, which arise when hybrid schemes formed by Diffusion Limited Aggregation (DLA) and Strange Attractors (SA) are considered. First, DLA aggregates formed with a given attachment radio (Ra) are generated so that a particle is attached to the aggregate as soon as it is at a distance Ra from any other particle in it. Second, a randomly chosen SA substitutes each particle of the aggregate, by means of a translation and a homothety with uniform scaling 1/Ra, which preserves the SA shape and circumscribes it to the circle of radius Ra. In this process, each SA is adjusted (re-normalized) to the Ra size. The resulting object mimics a cluster of SA, and exhibits a multi-fractal, multi-resolution structure, with a low-resolution profile similar to that of the DLA aggregate, but composed by SA fractals when a higher resolution is considered. We also describe an iteration of this process in order to generate hybrid superclusters, formed by clusters of DLA-SA hybrids.

Noncommutative Boundaries Arising in Dynamics and Representations of the Cuntz Relations

In a number of recent papers, the idea of generalized boundaries has found use in fractal and in multiresolution analysis; many of the papers having a focus on specific examples. Parallel with this new insight, and motivated by quantum probability, there has also been much research which seeks to study fractal and multiresolution structures with the use of certain systems of noncommutative operators; noncommutative harmonic/stochastic analysis. This in turn entails combinatorial, graph operations, and branching laws. The most versatile, of these noncommutative algebras are the Cuntz algebras; denoted N for the number of isometry generators. N is at least 2. Our focus is on the representations of We aim to develop new noncommutative tools, involving both representation theory and stochastic processes. They serve to connect these parallel developments.In outline, boundaries, Poisson, or Martin, are certain measure spaces (often associated to random walk models), designed to encode the asymptotic behavior, e.g., how trajectories diverge when the number of steps goes to infinity. We stress that our present boundaries (commutative or noncommutative) are purely measure-theoretical objects. Although, as we show, in some cases our boundaries may be compared with more familiar topological boundaries.

Optimal fusion of industrial data streams with different granularities

In the Industry 4.0 era, it is a common situation that measurements are available with different resolutions (or granularities). Multiresolution (or multi-granularity) data can arise, for instance, from aggregation rules applied over measurements collected in batches during non-overlapping periods of time, or in composite sampling schemes (e.g., using industrial auto-sampler devices). Current solutions for optimal data fusion, such as Kalman filters (KF) and Moving Horizon Estimation (MHE) approaches, assume that all variables are measured at the same resolution, even if their acquisition rates are different. Therefore, they are unable to account for the multiresolution structure of data. In this article we introduce a multiresolution framework for the optimal fusion of multiple signals at distinct resolutions. This approach is compared against the benchmark alternative using simulated case studies, where the superior signal processing capability of the novel methodology is demonstrated.