Spatially Adaptive Research Articles

GENETIC SYNTHESIS OF HYBRID ELECTRO-MECHANICAL SYSTEMS FOR MOTOR-SPINDLE UNITS WITH ADAPTIVE SPATIAL STRUCTURE

The results of fundamental research carried out at the Department of Electromechanics of KPI named after Igor Sikorsky, it was established that the structural organization and evolution of arbitrary classes of technical systems that function on the principles of electromechanical energy conversion is determined by the principles and laws of genetically organized systems. Motor-spindles (M-Ш) also belong to the category of such systems. The energy and genetic core of technical systems with electromechanical energy converters is the active zone of the energy converter, which is a physical and information carrier of genetic information and the corresponding genetic code. The trend of creating multi-coordinate motor-spindle units with a spatially adaptive structure, designed to function as part of metalworking centers and machines with digital control systems, is analyzed. In genetically organized systems, the processes of structuring objects of any level of complexity are implemented on the basis of the elemental information base of genetic programs using genetic synthesis operators. From the point of view of the theory of genetic structure formation, spatial adaptation is the result of chromosomal transformations using the principles of hybridization, mutation, replication, and isomerism. The problem of synthesizing a hybrid multifunctional EM structure for motor-spindle units with a spatially adaptive modular structure was formulated and solved. A generalized genetic model of chromosomal synthesis of hybrid electromechanical modules of motor-spindle units according to a given function has been developed. The structural formulas of hybrid electromagnetic chromosomes, which determine the population structure of original technical solutions, have been determined. Based on the simulation results, the structures of spatially adaptive motor-spindle units with two-, three-, and four-coordinate movement of the working body were synthesized. Based on the results of the research, a genetic catalog was created, which serves as a system basis for the development of original technical solutions for motor-spindle units.

IMDE-UGAN: Improved Memetic Direction Exploitation Optimized U-Net Generative Adversarial Network for Classification of Diabetic Retinopathy

The most important human organ is the eye which is essential for the processing and absorbing of external visual information. Diabetic retinopathy (DR) is the primary factor contributing to the global increase in blindness. To maintain eye health, people have been paying lots of attention to the problem. However, there are still lots of people who have eye problems all around the world. Thus, we proposed the Improved Memetic Direction Exploitation Optimized U-Net Generative Adversarial Network (IMDE-optimized U-Net GAN) model for DR grading. Also, for Multimodal Optimization Problems (MMOPs), a Niching Competition-based Memetic Direction Exploitation (NC-MDE) method is proposed with adaptive local search operations. Additionally, SPatially-ADaptivE (SPADE)-based conditional GANs are used to segment DR. The U-Net GAN model is used to categorize DR images. In the discriminator design, the standard classification network is modified to create the decoder-encoder network known as U-Net. The complete network error of the U-Net GAN architecture is modeled using the IMDE archives. The various performance metrics are used in the method for testing the proposed including accuracy, specificity, sensitivity, and ROC curve. As a result, the proposed method achieves 98.89% of accuracy, 98.54% for sensitivity, and specificity, it achieves 98.67%.

Extension of the spatially adaptive phase-field model to various forms of fracture

The phase field approach has proved to be efficient and has received ample attention amongst the available techniques to model fracture. However, high computational cost still imposes substantial difficulties in the phase-field simulation of fractures. This contribution is based on a recently proposed variational approach for spatial adaptivity in a phase-field model of fracture. The main idea is to consider the regularisation length ϵ as a space-dependent variable in the argument of the energy functional. We extend this now by implementing a strain energy split to ensure that only the tensile energy drives the crack propagation. The displacement, phase field, and optimal regularisation length are then determined locally by minimisation of the modified energy functional. Subsequently, the computed optimal regularisation length is used to refine the mesh size locally. The resultant solution procedure is implemented in the finite element library FEniCS. Numerical investigations on selected examples of different fracture modes demonstrate that the spatially adaptive phase field model has a comparable convergence rate, but a subjacent energy convergence curve resulting in significant computational savings. Moreover, it also computes the peak force more accurately illustrating its potential for usage in practical applications.

A spatially adaptive phase-field model of fracture

Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter ε and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying spatial resolution where needed while simultaneously keeping the computational size of the model as small as possible. Here, a variational-based spatial adaptivity is proposed for a phase-field model of fracture.An extension of the conventional phase-field model is achieved by allowing spatial variation of the regularisation length ε in the energy functional. Similar to the displacement and phase fields, the optimal regularisation length is obtained by minimising the energy functional. This extended phase-field model serves as the foundation for an adaptive mesh refinement strategy, in which the mesh size is determined locally by the optimal regularisation length. The resulting solution procedure is implemented in the framework of the finite element library FEniCS. According to the selected numerical experiment, the spatially adaptive phase-field model converges marginally faster than the conventional phase-field model but with a vastly superior constant, resulting in significant computational savings.

Design Practices for Flood Resilience in Istanbul: Case of Kadiköy Waterfront

Extreme weather events, sea level rise and intensified tsunamis as causes of climate change are becoming major threats for coastal cities. Istanbul, one of the most populated built-up coastal cities in the world, is prone to urban, coastal, and riverine flooding according to studies. Spatial design measurements preparing the urban waterfronts for the consequences of hazardous flooding are adopted in several cities as part of their urban resilience strategies. This paper focuses on physical measurements to adapt Istanbul to the effects of coastal flooding that is neglected so far in urban agenda. In this regard, the paper aims to develop site specific spatial design proposals as possible measurements to increase Istanbul’s waterfronts capacity for an effective flood resilience approach in case of storm events and tsunami intensified through climate change. To achieve this, status analysis and spatial configuration of possible design measures for Istanbul waterfront in a representative study area at neighborhood scale are introduced. To answer how much the waterfronts are at risk and how spatially adaptive strategies can be implemented in the current situation following flood resilience approach, site specific spatial analysis and a strategic design framework are developed. Since a comprehensive district-based guideline for spatial adaptation is currently not embedded in the urban agenda of flood management in Istanbul, this study promotes preparation of multiple guidelines adopting contemporary design measures in flood management for the entire city’s waterfronts by proposing one for Kadiköy.

Multi-resolution lattice Green's function method for incompressible flows

We propose a multi-resolution strategy that is compatible with the lattice Green's function (LGF) technique for solving viscous, incompressible flows on unbounded domains. The LGF method exploits the regularity of a finite-volume scheme on a formally unbounded Cartesian mesh to yield robust and computationally efficient solutions. The original method is spatially adaptive, but challenging to integrate with embedded mesh refinement as the underlying LGF is only defined for a fixed resolution. We present an ansatz for adaptive mesh refinement, where the solutions to the pressure Poisson equation are approximated using the LGF technique on a composite mesh constructed from a series of infinite lattices of differing resolution. To solve the incompressible Navier-Stokes equations, this is further combined with an integrating factor for the viscous terms and an appropriate Runge-Kutta scheme for the resulting differential-algebraic equations. The parallelized algorithm is verified through with numerical simulations of vortex rings, and the collision of vortex rings at high Reynolds number is simulated to demonstrate the reduction in computational cells achievable with both spatial and refinement adaptivity.

Uncertainty quantification for the Hokkaido Nansei-Oki tsunami using B-splines on adaptive sparse grids

Modeling uncertainties in the input parameters of computer simulations is an established way to account for inevitably limited knowledge. To overcome long run-times and high demand for computational resources, a surrogate model can replace the original simulation. We use spatially adaptive sparse grids for the creation of this surrogate model. Sparse grids are a discretization scheme designed to mitigate the curse of dimensionality, and spatial adaptivity further decreases the necessary number of expensive simulations. We combine this with B-spline basis functions which provide gradients and are exactly integrable. We demonstrate the capability of this uncertainty quantification approach for a simulation of the Hokkaido Nansei–Oki Tsunami with anuga. We develop a better understanding of the tsunami behavior by calculating key quantities such as mean, percentiles and maximum run-up. We compare our approach to the popular Dakota toolbox and reach slightly better results for all quantities of interest. References B. M. Adams, M. S. Ebeida, et al. Dakota. Sandia Technical Report, SAND2014-4633, Version 6.11 User’s Manual, July 2014. 2019. https://dakota.sandia.gov/content/manuals. J. H. S. de Baar and S. G. Roberts. Multifidelity sparse-grid-based uncertainty quantification for the Hokkaido Nansei–Oki tsunami. Pure Appl. Geophys. 174 (2017), pp. 3107–3121. doi: 10.1007/s00024-017-1606-y. H.-J. Bungartz and M. Griebel. Sparse grids. Acta Numer. 13 (2004), pp. 147–269. doi: 10.1017/S0962492904000182. M. Eldred and J. Burkardt. Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. 47th AIAA. 2009. doi: 10.2514/6.2009-976. K. Höllig and J. Hörner. Approximation and modeling with B-splines. Philadelphia: SIAM, 2013. doi: 10.1137/1.9781611972955. M. Matsuyama and H. Tanaka. An experimental study of the highest run-up height in the 1993 Hokkaido Nansei–Oki earthquake tsunami. National Tsunami Hazard Mitigation Program Review and International Tsunami Symposium (ITS). 2001. O. Nielsen, S. Roberts, D. Gray, A. McPherson, and A. Hitchman. Hydrodymamic modelling of coastal inundation. MODSIM 2005. 2005, pp. 518–523. https://www.mssanz.org.au/modsim05/papers/nielsen.pdf. J. Nocedal and S. J. Wright. Numerical optimization. Springer, 2006. doi: 10.1007/978-0-387-40065-5. D. Pflüger. Spatially Adaptive Sparse Grids for High-Dimensional Problems. Dr. rer. nat., Technische Universität München, Aug. 2010. https://www5.in.tum.de/pub/pflueger10spatially.pdf. M. F. Rehme, F. Franzelin, and D. Pflüger. B-splines on sparse grids for surrogates in uncertainty quantification. Reliab. Eng. Sys. Saf. 209 (2021), p. 107430. doi: 10.1016/j.ress.2021.107430. M. F. Rehme and D. Pflüger. Stochastic collocation with hierarchical extended B-splines on Sparse Grids. Approximation Theory XVI, AT 2019. Springer Proc. Math. Stats. Vol. 336. Springer, 2020. doi: 10.1007/978-3-030-57464-2_12. S Roberts, O. Nielsen, D. Gray, J. Sexton, and G. Davies. ANUGA. Geoscience Australia. 2015. doi: 10.13140/RG.2.2.12401.99686. I. J. Schoenberg and A. Whitney. On Pólya frequence functions. III. The positivity of translation determinants with an application to the interpolation problem by spline curves. Trans. Am. Math. Soc. 74.2 (1953), pp. 246–259. doi: 10.2307/1990881. W. Sickel and T. Ullrich. Spline interpolation on sparse grids. Appl. Anal. 90.3–4 (2011), pp. 337–383. doi: 10.1080/00036811.2010.495336. C. E. Synolakis, E. N. Bernard, V. V. Titov, U. Kânoğlu, and F. I. González. Standards, criteria, and procedures for NOAA evaluation of tsunami numerical models. NOAA/Pacific Marine Environmental Laboratory. 2007. https://nctr.pmel.noaa.gov/benchmark/. J. Valentin and D. Pflüger. Hierarchical gradient-based optimization with B-splines on sparse grids. Sparse Grids and Applications—Stuttgart 2014. Lecture Notes in Computational Science and Engineering. Vol. 109. Springer, 2016, pp. 315–336. doi: 10.1007/978-3-319-28262-6_13. D. Xiu and G. E. Karniadakis. The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24.2 (2002), pp. 619–644. doi: 10.1137/S1064827501387826.

A Spatially Adaptive Antenna Array for Mm-Wave Wireless Channel Control With Microfluidics Based Reconfiguration

Spatially adaptive antenna array (SAA) is an electronically scanned antenna array with capability of changing its physical location. This new capability allows SAA to control the wireless channel environment to increase link capacity without employing an increased number of antenna elements. Compact and cost-effective implementation of SAA requires a strategically designed RF feed network that can allow the radiating antenna elements to be repositioned while other RF and digital electronics remain stationary. This manuscript introduces a novel RF feed network and demonstrates the first experimental verification of SAA by using microfluidic based reconfiguration. The presented microfluidically reconfigurable SAA (MRSA) exhibits the best possible compact form - a total footprint that is approximately equal to the spatial adaptation range. MRSA operates at 28 GHz with 45 mm ( $4.2~\lambda _{0}$ ) spatial adaptation capability. Evaluating MRSA in communication systems using its measured realized gain patterns show that link level performance of the wireless channel is improved by 24% from 8.5 bps/Hz to 10.5 bps/Hz. Additionally, spectral efficiency is improved by 100% with 5 dB improvement in average signal to interference ratio.

Research on Deep Web POI Acquisition based on Retrieving Word Optimization and Spatial Adaption

Abstract. POI data is a geographical information resource that is the most closely related to the public life, and has been successfully applied in various fields such as urban planning, urban logistics, and car navigation. With the development of technologies such as mobile networks and Internet of Things, the network contains a large number of high-value POI information resources. How to effectively acquire and utilize data resources has become a research hotspot in the field of spatial information. In this paper, a deep-web POI information search method based on independent coverage ranking and spatial adaptive partition is proposed to solve the problems of difficult construction of retrieval word base and limited data request. By constructing candidate search terms, searching greedily, optimizing dimensionality reduction of search terms, and crawling spatially adaptive partitioning, the maximum coverage optimal solution of POI search is approached step by step, and the full POI information of deep web is obtained. It is of great significance to improve the recall rate and collection efficiency of POI data for enriching geographic information resources and improving the ability of spatial information service and content management.

Nonlocal Filtering Applied to 3-D Reconstruction of Tomographic SAR Data

In this paper, we introduce two spatially adaptive filtering methods to improve the estimation of the covariance matrix (CM), which is required for the processing of tomographic SAR data. We evaluate their effect on scatterer separation and height estimation. We propose several criteria to evaluate such methods and introduce a spatial simulation procedure allowing generating a tomographic image stack from a 3-D building model, assuming a multitrack airborne configuration and a distributed target model incorporating multidimensional speckle. Inversion of such a model requires the estimation of a CM from the data. Consequently, we propose two nonlocal methods to improve the estimation of the CM. The first one was previously introduced for polarimetric data and uses pixel similarities based on Riemannian distances between CMs. The second one is a new method extending the previous one to similarities between patches. We show the importance of spatial adaptivity in covariance estimation by comparing the 3-D reconstructions obtained with our filters and other methods. Further experiments on simulated and L-band experimental data show the ability of the nonlocal filters to improve the height estimation and scatterer separation in layover areas thanks to their smoothing and edge-preserving properties.

Nonintrusive Uncertainty Analysis of Fluid-Structure Interaction with Spatially Adaptive Sparse Grids and Polynomial Chaos Expansion

The propagation of uncertainty in physical parameters of fluid-structure interaction problems is a challenging task---both mathematically and in terms of computational workload. In this paper, we employ nonintrusive polynomial chaos expansion and model the uncertainty in five independent input parameters that characterize both fluid and structure. We propose a novel methodology to compute the expansion's coefficients using spatially adaptive sparse grids and products of one-dimensional integrals, which exploits the tensor structure of both sparse grids and probabilistic space. Furthermore, with spatial adaptivity and modified basis functions, we keep the number of sparse grid points small. We test our approach in two test cases: (i) an elastic vertical flap in a channel flow and (ii) a computationally challenging, well-established benchmark. The outputs of interest are the x-deflection and total force on the structure. In the first test case, we consider six implementations of our methodology and two established methods based on sparse grid quadrature. We evaluate the performance (in terms of number of runs of the numerical solver) and accuracy of all eight methods. The results show that one variant of our approach outperforms all the other implementations. We apply our best variant to the benchmark scenario and address the high computational demands of the resulting problem using three levels of parallelism. Importantly, our approach is not restricted to fluid-structure interaction problems. We can address a broad spectrum of computationally expensive problems, provided that sparse grid approximations can be employed.

Millimeter-Wave Wireless Channel Control Using Spatially Adaptive Antenna Arrays

A wireless channel control concept based on spatially, i.e., position adaptive antenna arrays is introduced. This technique simultaneously utilizes beam-steering and spatial adaptation to enhance the wireless channel gain and system capacity. The concept is inspired by the microfluidically reconfigurable RF devices as they can enable compact systems with spatial adaptation capability. Specifically, a five element linear 28 GHz mm-wave antenna array design that can achieve beam-steering via phase shifters and spatial adaptation via microfluidics is detailed. Simulated realized gain patterns at various array positions and phase shifter states are subsequently utilized in link and system level simulations to demonstrate the advantages of the proposed concept. It is shown that a wireless communications system can achieve 51% improvement in the mean signal-to-interference ratio due to the spatial adaptation capability.

SU‐F‐I‐10: Spatially Local Statistics for Adaptive Image Filtering

Purpose:To facilitate adaptive image filtering operations, addressing spatial variations in both noise and signal. Such issues are prevalent in cone‐beam projections, where physical effects such as X‐ray scattering result in spatially variant noise, violating common assumptions of homogeneous noise and challenging conventional filtering approaches to signal extraction and noise suppression.Methods:We present a computational mechanism for probing into and quantifying the spatial variance of noise throughout an image. The mechanism builds a pyramid of local statistics at multiple spatial scales; local statistical information at each scale includes (weighted) mean, median, standard deviation, median absolute deviation, as well as histogram or dynamic range after local mean/median shifting. Based on inter‐scale differences of local statistics, the spatial scope of distinguishable noise variation is detected in a semi‐ or un‐supervised manner. Additionally, we propose and demonstrate the incorporation of such information in globally parametrized (i.e., non‐adaptive) filters, effectively transforming the latter into spatially adaptive filters. The multi‐scale mechanism is materialized by efficient algorithms and implemented in parallel CPU/GPU architectures.Results:We demonstrate the impact of local statistics for adaptive image processing and analysis using cone‐beam projections of a Catphan phantom, fitted within an annulus to increase X‐ray scattering. The effective spatial scope of local statistics calculations is shown to vary throughout the image domain, necessitating multi‐scale noise and signal structure analysis. Filtering results with and without spatial filter adaptation are compared visually, illustrating improvements in imaging signal extraction and noise suppression, and in preserving information in low‐contrast regions.Conclusion:Local image statistics can be incorporated in filtering operations to equip them with spatial adaptivity to spatial signal/noise variations. An efficient multi‐scale computational mechanism is developed to curtail processing latency. Spatially adaptive filtering may impact subsequent processing tasks such as reconstruction and numerical gradient computations for deformable registration.NIH Grant No. R01‐184173

Representation and Spatially Adaptive Segmentation for PolSAR Images Based on Wedgelet Analysis

It is believed that it is essential to take the spatial adaptivity into the segmentation method for polarimetric synthetic aperture radar (PolSAR) images. The size and shape of each segment and the strength of the relationship of neighboring pixels need to depend on the local spatial complexity of the scene. The wedgelet framework provides a promising analysis tool for spatial information. The major advantage of the wedgelet analysis is that it captures the geometrical structure of images at multiple scales, with the local spatial complexity taken into consideration. Hence, in this paper, we propose a wedgelet approximation and analysis framework specially designed for PolSAR data. Based on this framework, a spatially adaptive representation and segmentation method is constructed and presented. It mainly consists of three parts: first, the multiscale wedgelet decomposition is applied to the PolSAR image, and the local geometrical information is captured in an optimal way; then, the image is segmented in a spatially adaptive manner by the multiscale wedgelet representation in the form of the regularized optimization, which keeps a balance between the approximation and parsimony of the representation; the final part is the spatial-complexity-adaptive segmentation refinement based on the Wishart Markov random field model. The performance of the proposed method is presented and analyzed on two experimental data sets, with visual presentation and numerical evaluation. It is also compared with an existing and theoretically well-founded segmentation method. The experiments and results demonstrate the availability and advantage of the proposed method.

Image Restoration via Simultaneous Sparse Coding: Where Structured Sparsity Meets Gaussian Scale Mixture

In image processing, sparse coding has been known to be relevant to both variational and Bayesian approaches. The regularization parameter in variational image restoration is intrinsically connected with the shape parameter of sparse coefficients’ distribution in Bayesian methods. How to set those parameters in a principled yet spatially adaptive fashion turns out to be a challenging problem especially for the class of nonlocal image models. In this work, we propose a structured sparse coding framework to address this issue—more specifically, a nonlocal extension of Gaussian scale mixture (GSM) model is developed using simultaneous sparse coding (SSC) and its applications into image restoration are explored. It is shown that the variances of sparse coefficients (the field of scalar multipliers of Gaussians)—if treated as a latent variable—can be jointly estimated along with the unknown sparse coefficients via the method of alternating optimization. When applied to image restoration, our experimental results have shown that the proposed SSC–GSM technique can both preserve the sharpness of edges and suppress undesirable artifacts. Thanks to its capability of achieving a better spatial adaptation, SSC–GSM based image restoration often delivers reconstructed images with higher subjective/objective qualities than other competing approaches.

A stochastically and spatially adaptive parallel scheme for uncertain and nonlinear two-phase flow problems

Simulating in flow problems in porous media often requires techniques for uncertainty quantification in order to represent parameter values that are not given exactly. Straightforward Monte-Carlo (MC) methods have a limited efficiency due to slow convergence. Better convergence in low-parametric problems can be achieved with polynomial chaos expansion (PCE) techniques. The PCE approach yields a coupled deterministic system to be solved. The degree of coupling increases with the non-linearity of the considered equations and with the order of polynomial expansion. This fact increases the computational effort of PCE and significantly reduces the scalability in parallelization. We present an application of the hybrid stochastic Galerkin finite volume (HSG-FV) method to a two-phase flow problem in two space dimensions. The method extends the classical polynomial chaos expansion by a multi-element discretization in the probability space of the parameters. It leads to a deterministic system that is coupled to a lesser degree than in element-free PCE versions, respectively, fully decoupled in stochastic elements (SE). Therefore, the HSG-FV method allows for more efficient parallelization. For the further reduction of complexity, we present a new stochastic adaptivity method. We present numerical examples in two spatial dimensions with linear and nonlinear fractional flow functions in the two-phase flow problem. The flow functions might depend in a discontinuous manner on the unknown spatial position of porous-medium heterogeneities. Finally, we discuss the interplay of the new method with spatial adaptivity per SE for these problems.

Highly adaptive liquid simulations on tetrahedral meshes

We introduce a new method for efficiently simulating liquid with extreme amounts of spatial adaptivity. Our method combines several key components to drastically speed up the simulation of large-scale fluid phenomena: We leverage an alternative Eulerian tetrahedral mesh discretization to significantly reduce the complexity of the pressure solve while increasing the robustness with respect to element quality and removing the possibility of locking. Next, we enable subtle free-surface phenomena by deriving novel second-order boundary conditions consistent with our discretization. We couple this discretization with a spatially adaptive Fluid-Implicit Particle (FLIP) method, enabling efficient, robust, minimally-dissipative simulations that can undergo sharp changes in spatial resolution while minimizing artifacts. Along the way, we provide a new method for generating a smooth and detailed surface from a set of particles with variable sizes. Finally, we explore several new sizing functions for determining spatially adaptive simulation resolutions, and we show how to couple them to our simulator. We combine each of these elements to produce a simulation algorithm that is capable of creating animations at high maximum resolutions while avoiding common pitfalls like inaccurate boundary conditions and inefficient computation.

Spatially-adaptive sensing in nonparametric regression

While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an adaptive-sensing algorithm which is applicable to general nonparametric-regression problems. The algorithm is spatially adaptive, and achieves improved rates of convergence over spatially inhomogeneous functions. Over standard function classes, it likewise retains the spatial adaptivity properties of a uniform design.

A two-dimensional numerical wave flume based on SA-MPLS method

A spatially adaptive (SA) two-dimensional (2-D) numerical wave flume is presented based on the quadtree mesh system, in which a new multiple particle level set (MPLS) method is proposed to solve the problem of interface tracking, in which common intersection may be traversed by multiple interfaces. By using the adaptive mesh technique and the MPLS method, mesh resolution is updated automatically with time according to flow characteristics in the modeling process with higher resolution around the free surface and the solid boundary and lower resolution in less important area. The model has good performance in saving computer memory and CPU time and is validated by computational examples of small amplitude wave, second-order Stokes wave and cnoidal wave. Computational results also indicate that standing wave and wave overtopping are also reasonably simulated by the model.

ODVBA: Optimally-Discriminative Voxel-Based Analysis

Gaussian smoothing of images prior to applying voxel-based statistics is an important step in voxel-based analysis and statistical parametric mapping (VBA-SPM) and is used to account for registration errors, to Gaussianize the data and to integrate imaging signals from a region around each voxel. However, it has also become a limitation of VBA-SPM based methods, since it is often chosen empirically and lacks spatial adaptivity to the shape and spatial extent of the region of interest, such as a region of atrophy or functional activity. In this paper, we propose a new framework, named optimally-discriminative voxel-based analysis (ODVBA), for determining the optimal spatially adaptive smoothing of images, followed by applying voxel-based group analysis. In ODVBA, nonnegative discriminative projection is applied regionally to get the direction that best discriminates between two groups, e.g., patients and controls; this direction is equivalent to local filtering by an optimal kernel whose coefficients define the optimally discriminative direction. By considering all the neighborhoods that contain a given voxel, we then compose this information to produce the statistic for each voxel. Finally, permutation tests are used to obtain a statistical parametric map of group differences. ODVBA has been evaluated using simulated data in which the ground truth is known and with data from an Alzheimer's disease (AD) study. The experimental results have shown that the proposed ODVBA can precisely describe the shape and location of structural abnormality.