A Contrast- and Luminance-Driven Multiscale Netowrk Model of Brightness Perception

A neural network model of brightness perception is developed to account for a wide variety of data, including the classical phenomenon of Mach bands, low- and high-contrast missing fundamental, luminance staircases, and non-linear contrast effects associated with sinusoidal waveforms. The model builds upon previous work on filling-in models that produce brightness profiles through the interaction of boundary and feature signals. Boundary computations that are sensitive to luminance steps and to continuous lumi- nance gradients are presented. A new interpretation of feature signals through the explicit representation of contrast-driven and luminance-driven information is provided and directly addresses the issue of brightness "anchoring." Computer simulations illustrate the model's competencies.Air Force Office of Scientific Research (F49620-92-J-0334); Northeast Consortium for Engineering Education (NCEE-A303-21-93); Office of Naval Research (N00014-91-J-4100); German BMFT grant (413-5839-01 1N 101 C/1); CNPq and NUTES/UFRJ, Brazi

Inverse Global Illumination using a Neural Radiometric Prior

Inverse rendering methods that account for global illumination are becoming more popular, but current methods require evaluating and automatically differentiating millions of path integrals by tracing multiple light bounces, which remains expensive and prone to noise. Instead, this paper proposes a radiometric prior as a simple alternative to building complete path integrals in a traditional differentiable path tracer, while still correctly accounting for global illumination. Inspired by the Neural Radiosity technique, we use a neural network as a radiance function, and we introduce a prior consisting of the norm of the residual of the rendering equation in the inverse rendering loss. We train our radiance network and optimize scene parameters simultaneously using a loss consisting of both a photometric term between renderings and the multi-view input images, and our radiometric prior (the residual term). This residual term enforces a physical constraint on the optimization that ensures that the radiance field accounts for global illumination. We compare our method to a vanilla differentiable path tracer, and more advanced techniques such as Path Replay Backpropagation. Despite the simplicity of our approach, we can recover scene parameters with comparable and in some cases better quality, at considerably lower computation times.Comment: Homepage: https://inverse-neural-radiosity.github.i

Generating Kernel Aware Polygons

Problems dealing with the generation of random polygons has important applications for evaluating the performance of algorithms on polygonal domain. We review existing algorithms for generating random polygons. We present an algorithm for generating polygons admitting visibility properties. In particular, we propose an algorithm for generating polygons admitting large size kernels. We also present experimental results on generating such polygons

Problems and applications of Discrete and Computational Geometry concerning graphs, polygons, and points in the plane

Esta tesistratasobreproblemasyaplicacionesdelageometríadiscretay computacional enelplano,relacionadosconpolígonos,conjuntosdepuntos y grafos. Después deunprimercapítulointroductorio,enelcapítulo 2 estudiamos una generalizacióndeunfamosoproblemadevisibilidadenelámbitodela O-convexidad. Dadounconjuntodeorientaciones(ángulos) O, decimosque una curvaes O-convexa si suintersecciónconcualquierrectaparalelaauna orientaciónde O es conexa.Cuando O = {0◦, 90◦}, nosencontramosenel caso delaortoconvexidad,consideradodeespecialrelevancia.El O-núcleo de unpolígonoeselconjuntodepuntosdelmismoquepuedenserconectados con cualquierotropuntodelpolígonomedianteunacurva O-convexa.En este trabajoobtenemos,para O = {0◦} y O = {0◦, 90◦}, unalgoritmopara calcular ymantenerel O-núcleodeunpolígonoconformeelconjuntode orientaciones O rota. Dichoalgoritmoproporciona,además,losángulosde rotación paralosqueel O-núcleotieneáreayperímetromáximos. En elcapítulo 3 consideramos unaversiónbicromáticadeunproblema combinatorioplanteadoporNeumann-LarayUrrutia.Enconcreto,de- mostramos quetodoconjuntode n puntosazulesy n puntosrojosenel plano contieneunparbicromáticodepuntostalquetodocírculoquelos tenga ensufronteracontieneensuinterioralmenos n(1− 1 √2 )−o(n) puntos del conjunto.Esteproblemaestáfuertementeligadoalcálculodelosdiagra- mas deVoronoideordensuperiordelconjuntodepuntos,pueslasaristas de estosdiagramascontienenprecisamentetodosloscentrosdeloscírculos que pasanpordospuntosdelconjunto.Porello,nuestralíneadetrabajo actual enesteproblemaconsisteenexplorarestaconexiónrealizandoun estudio detalladodelaspropiedadesdelosdiagramasdeVoronoideorden superior. En loscapítulos 4 y 5, planteamosdosaplicacionesdelateoríadegrafos 6 7 al análisissensorialyalcontroldeltráficoaéreo,respectivamente.Enel primer caso,presentamosunnuevométodoquecombinatécnicasestadísti- cas ygeométricasparaanalizarlasopinionesdelosconsumidores,recogidas a travésdemapeoproyectivo.Estemétodoesunavariacióndelmétodo SensoGraph ypretendecapturarlaesenciadelmapeoproyectivomediante el cálculodelasdistanciaseuclídeasentrelosparesdemuestrasysunor- malización enelintervalo [0, 1]. Acontinuación,aplicamoselmétodoaun ejemplo prácticoycomparamossusresultadosconlosobtenidosmediante métodosclásicosdeanálisissensorialsobreelmismoconjuntodedatos. En elsegundocaso,utilizamoslatécnicadelespectro-coloreadodegrafos para plantearunmodelodecontroldeltráficoaéreoquepretendeoptimizar el consumodecombustibledelosavionesalmismotiempoqueseevitan colisiones entreellos.This thesisdealswithproblemsandapplicationsofdiscreteandcomputa- tional geometryintheplane,concerningpolygons,pointsets,andgraphs. After afirstintroductorychapter,inChapter 2 westudyageneraliza- tion ofafamousvisibilityproblemintheframeworkof O-convexity. Given a setoforientations(angles) O, wesaythatacurveis O-convex if itsin- tersection withanylineparalleltoanorientationin O is connected.When O = {0◦, 90◦}, wefindourselvesinthecaseoforthoconvexity,consideredof specialrelevance.The O-kernel of apolygonisthesubsetofpointsofthe polygonthatcanbeconnectedtoanyotherpointofthepolygonwithan O-convexcurve.Inthisworkweobtain,for O = {0◦} and O = {0◦, 90◦}, an algorithm tocomputeandmaintainthe O-kernelofapolygonasthesetof orientations O rotates. Thisalgorithmalsoprovidestheanglesofrotation that maximizetheareaandperimeterofthe O-kernel. In Chapter 3, weconsiderabichromaticversionofacombinatorialprob- lem posedbyNeumann-LaraandUrrutia.Specifically,weprovethatevery set of n blue and n red pointsintheplanecontainsabichromaticpairof pointssuchthateverycirclehavingthemonitsboundarycontainsatleast n(1 − 1 √2 ) − o(n) pointsofthesetinitsinterior.Thisproblemisclosely related toobtainingthehigherorderVoronoidiagramsofthepointset.The edges ofthesediagramscontain,precisely,allthecentersofthecirclesthat pass throughtwopointsoftheset.Therefore,ourcurrentlineofresearch on thisproblemconsistsonexploringthisconnectionbystudyingindetail the propertiesofhigherorderVoronoidiagrams. In Chapters 4 and 5, weconsidertwoapplicationsofgraphtheoryto sensory analysisandairtrafficmanagement,respectively.Inthefirstcase, weintroduceanewmethodwhichcombinesgeometricandstatisticaltech- niques toanalyzeconsumeropinions,collectedthroughprojectivemapping. This methodisavariationofthemethodSensoGraph.Itaimstocapture 4 5 the essenceofprojectivemappingbycomputingtheEcuclideandistances betweenpairsofsamplesandnormalizingthemtotheinterval [0, 1]. Weap- ply themethodtoareal-lifescenarioandcompareitsperformancewiththe performanceofclassicmethodsofsensoryanalysisoverthesamedataset. In thesecondcase,weusetheSpectrumGraphColoringtechniquetopro- poseamodelforairtrafficmanagementthataimstooptimizetheamount of fuelusedbytheairplanes,whileavoidingcollisionsbetweenthem

Perceptual Error Optimization for {Monte Carlo} Rendering

Realistic image synthesis involves computing high-dimensional light transport integrals which in practice are numerically estimated using Monte Carlo integration. The error of this estimation manifests itself in the image as visually displeasing aliasing or noise. To ameliorate this, we develop a theoretical framework for optimizing screen-space error distribution. Our model is flexible and works for arbitrary target error power spectra. We focus on perceptual error optimization by leveraging models of the human visual system's (HVS) point spread function (PSF) from halftoning literature. This results in a specific optimization problem whose solution distributes the error as visually pleasing blue noise in image space. We develop a set of algorithms that provide a trade-off between quality and speed, showing substantial improvements over prior state of the art. We perform evaluations using both quantitative and perceptual error metrics to support our analysis, and provide extensive supplemental material to help evaluate the perceptual improvements achieved by our methods

Scalable multi-class sampling via filtered sliced optimal transport

We propose a multi-class point optimization formulation based on continuous Wasserstein barycenters. Our formulation is designed to handle hundreds to thousands of optimization objectives and comes with a practical optimization scheme. We demonstrate the effectiveness of our framework on various sampling applications like stippling, object placement, and Monte-Carlo integration. We a derive multi-class error bound for perceptual rendering error which can be minimized using our optimization. We provide source code at https://github.com/iribis/filtered-sliced-optimal-transport.Comment: 15 pages, 17 figures, ACM Trans. Graph., Vol. 41, No. 6, Article 261. Publication date: December 202