Bidirectional Path Research Articles

Two‐stage Resampling for Bidirectional Path Tracing with Multiple Light Sub‐paths

AbstractRecent advances in bidirectional path tracing (BPT) reveal that the use of multiple light sub‐paths and the resampling of a small number of these can improve the efficiency of BPT. By increasing the number of pre‐sampled light sub‐paths, the possibility of generating light paths that provide large contributions can be better explored and this can alleviate the correlation of light paths due to the reuse of pre‐sampled light sub‐paths by all eye sub‐paths. The increased number of pre‐sampled light subpaths, however, also incurs a high computational cost. In this paper, we propose a two‐stage resampling method for BPT to efficiently handle a large number of pre‐sampled light sub‐paths. We also derive a weighting function that can treat the changes in path probability due to the two‐stage resampling. Our method can handle a two orders of magnitude larger number of presampled light sub‐paths than previous methods in equal‐time rendering, resulting in stable and better noise reduction than state‐of‐the‐art methods.

Three‐port DC–DC converter based on quadratic boost converter for stand‐alone PV/battery systems

In this study, a three-port DC–DC converter is proposed based on quadratic boost converter. The proposed converter contains paths to enable the flow of power from input source to load and battery. Furthermore, it makes a path available to energise the load by the battery. The proposed converter has a bidirectional path using two additional switches and two diodes. Power flows from the input source and the battery to the load in a single-stage resulting in higher efficiency. The proposed converter has three switches and two duty cycles defined. By adjusting the duty cycles, maximum input power and output voltage can be regulated based on the input source power and the battery condition. To control the proposed converter, three operation modes are defined. In order to design the control system, the proposed converter is analysed and the small-signal models are obtained. Using a decoupling network for the integrated small-signal models, separated closed-loop controllers are designed. Finally, a prototype for the proposed converter is prepared to validate feasibility and effectiveness of the proposed converter and the control method by experimental results.

Spectral Mollification for Bidirectional Fluorescence

AbstractFluorescent materials can shift energy between wavelengths, thereby creating bright and saturated colors both in natural and artificial materials. However, rendering fluorescence for continuous wavelengths or combined with wavelength dependent path configurations so far has only been feasible using spectral unidirectional methods. We present a regularization‐based approach for supporting fluorescence in a spectral bidirectional path tracer. Our algorithm samples camera and light sub‐paths with independent wavelengths, and when connecting them mollifies the BSDF at one of the connecting vertices such that it reradiates light across multiple wavelengths. We discuss arising issues such as color bias in early iterations, consistency of the method and MIS weights in the presence of spectral mollification. We demonstrate our method in scenes combining fluorescence and transport phenomena that are difficult to render with unidirectional or spectrally discrete methods.

Resampling-aware Weighting Functions for Bidirectional Path Tracing Using Multiple Light Sub-Paths

Bidirectional path tracing (BPT) with multiple importance sampling (MIS) is a popular technique for rendering realistic images. Recently, it has been shown that BPT can be improved by preparing multiple light sub-paths and by resampling a small number of light sub-paths from them to generate full paths with large contribution. Traditionally, for MIS weights, the balance heuristic has widely been used to minimize the upper bound of variance, where each full path is weighted in proportion to the probability of the path. Although the probability of the path can change due to the resampling process, the weighting functions used in the previous methods remain unaffected by the change in probability, resulting in less efficiency. To address this problem, we propose new weighting functions for BPT with multiple light sub-paths. Our main contribution is a precise formulation of the variance and the derivation of the weighting functions that can appropriately treat the change in probability. We demonstrate that our weighting functions significantly improve the image quality. We will release a simple version of our implementation as open source to ensure reproducibility.

A novel algorithm for TOP-K optimal path on complex multiple attribute graph

In the rapidly-changing information world, the various users and personalised requirements lead to an urgent need for complex multiple attribute decision-making. In addition, the TOP-K path of single attribute decision cannot meet the actual needs. The TOP-K mainly has non-repeatable vertex, repeatable vertex, index and other algorithms. But these techniques are mainly based on the single attribute. There are few documents introducing the complex multiple attribute decision-making problem so for. Therefore, a Tdp algorithm is presented in this paper. Firstly, it uses the technology of interval number and extreme value to solve the uncertain attribute value. Then, TOPSIS technique solves the complex multiple attribute decision-making problems. By this way, the comprehensive score is achieved. Secondly, the paper proposes blocking and bidirectional shortest path algorithm for TOP-K optimal path. Finally, comparison and analysis between Tdp and the Yen were made. Result confirms that Tdp algorithm improves the TOP-K optimal technology.

AKITA: A CAREER COUNSELING CASE FOR PRACTICE AND THEORETICAL REFLECTION

A case in the Hong Kong Chinese context is presented in this paper to illustrate the use of both quantitative (Holland's SDS) and qualitative career assessment (Card Sorts) to help a 16-year-old girl overcome career indecision. Guided by both Holland's Hexagonal Career Types Theory and Socio-Cognitive Career Theory, a career counsellor can promote a client's positive changes after two counseling sessions. This case supports Tracey's (2002) and Nauta et al.'s (2002) postulated bidirectional causal path between self-efficacy and interests. In addition, it highlights that partial match instead of perfect match between Self-directed search (SDS) scores and choice of academic major is more pragmatic or effective while performing quantitative assessment. Finally, it points to the need for establishing local SDS norms, examining the Holland codes for occupations in Hong Kong, and researching the link between congruence and maximal career outcomes in future research.

Calculation of MIS weights for bidirectional path tracing with photon maps in presence of direct illumination

Calculation of MIS weights for bidirectional path tracing with photon maps in presence of direct illumination

Selectively metropolised Monte Carlo light transport simulation

Light transport is a complex problem with many solutions. Practitioners are now faced with the difficult task of choosing which rendering algorithm to use for any given scene. Simple Monte Carlo methods, such as path tracing, work well for the majority of lighting scenarios, but introduce excessive variance when they encounter transport they cannot sample (such as caustics). More sophisticated rendering algorithms, such as bidirectional path tracing, handle a larger class of light transport robustly, but have a high computational overhead that makes them inefficient for scenes that are not dominated by difficult transport. The underlying problem is that rendering algorithms can only be executed indiscriminately on all transport, even though they may only offer improvement for a subset of paths. In this paper, we introduce a new scheme for selectively combining different Monte Carlo rendering algorithms. We use a simple transport method (e.g. path tracing) as the base, and treat high variance "fireflies" as seeds for a Markov chain that locally uses a Metropolised version of a more sophisticated transport method for exploration, removing the firefly in an unbiased manner. We use a weighting scheme inspired by multiple importance sampling to partition the integrand into regions the base method can sample well and those it cannot, and only use Metropolis for the latter. This constrains the Markov chain to paths where it offers improvement, and keeps it away from regions already handled well by the base estimator. Combined with stratified initialization, short chain lengths and careful allocation of samples, this vastly reduces non-uniform noise and temporal flickering artifacts normally encountered with a global application of Metropolis methods. Through careful design choices, we ensure our algorithm never performs much worse than the base estimator alone, and usually performs significantly better, thereby reducing the need to experiment with different algorithms for each scene.

Variance-aware multiple importance sampling

Many existing Monte Carlo methods rely on multiple importance sampling (MIS) to achieve robustness and versatility. Typically, the balance or power heuristics are used, mostly thanks to the seemingly strong guarantees on their variance. We show that these MIS heuristics are oblivious to the effect of certain variance reduction techniques like stratification. This shortcoming is particularly pronounced when unstratified and stratified techniques are combined (e.g., in a bidirectional path tracer). We propose to enhance the balance heuristic by injecting variance estimates of individual techniques, to reduce the variance of the combined estimator in such cases. Our method is simple to implement and introduces little overhead.

The Impact of Classroom Climate on Aggression and Victimization in Early Adolescence

Identifying factors that influence peer aggression and victimization is important because of their high prevalence rates and associated negative outcomes during early adolescence. Limited research has examined the impact of environmental and contextual factors, such as school climate, on peer aggression and victimization. This study longitudinally examined bidirectional relations between school climate and peer aggression and between school climate and victimization over 6 months. Participants were 265 sixth-, seventh-, and eighth-grade students (50% female; 82% African American). Bidirectional path regression analyses showed that students who reported higher levels of positive student-teacher relationships at Time 1 engaged in lower frequencies of aggression and experienced less victimization at Time 2. Students who reported higher levels of awareness and reporting of violence at Time 1 had more positive student-teacher relationships and engaged in lower frequencies of aggression at Time 2.

Hierarchical russian roulette for vertex connections

While bidirectional path tracing is a well-established light transport algorithm, many samples are required to obtain high-quality results for specular-diffuse-glossy or glossy-diffuse-glossy reflections especially when they are highly glossy. To improve the efficiency for such light path configurations, we propose a hierarchical Russian roulette technique for vertex connections. Our technique accelerates a huge number of Russian roulette operations according to an approximate scattering lobe at an eye-subpath vertex for many cached light-subpath vertices. Our method dramatically reduces the number of random number generations needed for Russian roulette by introducing a hierarchical rejection algorithm which assigns random numbers in a top-down fashion. To efficiently reject light vertices in each hierarchy, we also introduce an efficient approximation of anisotropic scattering lobes used for the probability of Russian roulette. Our technique is easy to integrate into some existing bidirectional path tracing-based algorithms which cache light-subpath vertices (e.g., probabilistic connections, and vertex connection and merging). In addition, unlike existing many-light methods, our method does not restrict multiple importance sampling strategies thanks to the simplicity of Russian roulette. Although the proposed technique does not support perfectly specular surfaces, it significantly improves the efficiency for caustics reflected on extremely glossy surfaces in an unbiased fashion.

A Survey on Gradient‐Domain Rendering

AbstractMonte Carlo methods for physically‐based light transport simulation are broadly adopted in the feature film production, animation and visual effects industries. These methods, however, often result in noisy images and have slow convergence. As such, improving the convergence of Monte Carlo rendering remains an important open problem. Gradient‐domain light transport is a recent family of techniques that can accelerate Monte Carlo rendering by up to an order of magnitude, leveraging a gradient‐based estimation and a reformulation of the rendering problem as an image reconstruction. This state of the art report comprehensively frames the fundamentals of gradient‐domain rendering, as well as the pragmatic details behind practical gradient‐domain uniand bidirectional path tracing and photon density estimation algorithms. Moreover, we discuss the various image reconstruction schemes that are crucial to accurate and stable gradient‐domain rendering. Finally, we benchmark various gradient‐domain techniques against the state‐of‐the‐art in denoising methods before discussing open problems.

A bidirectional path analysis model of smoking cessation self-efficacy and concurrent smoking status: impact on abstinence outcomes.

Self-efficacy is routinely associated with abstinence in the addictions literature, and is a major component relapse-prevention models. The magnitude of this relationship has been brought into question following equivocal results in studies controlling for concurrent smoking status. The aim of our study was to clarify the relationship between cessation self-efficacy, smoking status, and cessation outcomes in a cohort of treatment-seeking smokers. Smokers participating in the FLEX trial, a randomized trial investigating the efficacy of three pharmacologic treatments for smoking cessation, completed questionnaires assessing cessation self-efficacy at baseline and at weeks 1, 3, 5 and 10 post-target quit date; smoking status was verified using expired carbon monoxide. Structural models were fit in order to ascertain the relationship between cessation self-efficacy and concurrent smoking at each time-point, and to assess the association between cessation self-efficacy, smoking and seven-day point prevalence smoking status at week 10. A total of 737 treatment-seeking smokers participated. In our path model, self-efficacy and smoking status at all time points were associated with week 10 abstinence (except week 3 self-efficacy), after controlling these values' previous time-points. All direct pathways between cessation self-efficacy and smoking were also significant, supporting a bidirectional relationship. Our results support a bidirectional and reciprocal relationship between cessation self-efficacy and concurrent smoking behavior; participants with higher confidence were more likely to be smoke-free, and concurrent smoking status predicted levels of confidence over the ensuing weeks. Both measures were associated with week 10 abstinence. Our results indicate that while correlated, both cessation self-efficacy and current smoking behavior during a cessation attempt are important independent markers of ultimate cessation success.

RenderMan

Pixar’s RenderMan renderer is used to render all of Pixar’s films and by many film studios to render visual effects for live-action movies. RenderMan started as a scanline renderer based on the Reyes algorithm, and it was extended over the years with ray tracing and several global illumination algorithms. This article describes the modern version of RenderMan, a new architecture for an extensible and programmable path tracer with many features that are essential to handle the fiercely complex scenes in movie production. Users can write their own materials using a bxdf interface and their own light transport algorithms using an integrator interface—or they can use the materials and light transport algorithms provided with RenderMan. Complex geometry and textures are handled with efficient multi-resolution representations, with resolution chosen using path differentials. We trace rays and shade ray hit points in medium-sized groups, which provides the benefits of SIMD execution without excessive memory overhead or data streaming. The path-tracing architecture handles surface, subsurface, and volume scattering. We show examples of the use of path tracing, bidirectional path tracing, VCM, and UPBP light transport algorithms. We also describe our progressive rendering for interactive use and our adaptation of denoising techniques.

Matrix factorization based instrumental variable approach for simultaneous identification of Bi-directional path models

This paper proposes a closed-loop identification approach to integrate matrix factorization algorithms with generalized instrumental variable (GIV) techniques to simultaneously identify the parameters and orders for both forward and backward path models. Aside from the technique of UD factorization, the QR factorization technique, which possesses good numerical property, is utilized for the proposed GIV-based method. The major difficulty and novelty of the proposed approach lies in how to properly construct instruments, number of instruments, and weighting matrices to obtain enhanced identification performance. To the end, the identification accuracy properties, in terms of the covariance matrix of the parameter estimates, are provided. In addition, a sufficient condition of consistent parameter estimates for the GIV-based approach is discussed. The effectiveness of the proposed identification method is demonstrated by simulation results.

Towards the LISA backlink: experiment design for comparing optical phase reference distribution systems

LISA is a proposed space-based laser interferometer detecting gravitational waves by measuring distances between free-floating test masses housed in three satellites in a triangular constellation with laser links in-between. Each satellite contains two optical benches that are articulated by moving optical subassemblies for compensating the breathing angle in the constellation. The phase reference distribution system, also known as backlink, forms an optical bi-directional path between the intra-satellite benches.In this work we discuss phase reference implementations with a target non-reciprocity of at most μrad , equivalent to 1 pm for a wavelength of 1064 nm in the frequency band from 0.1 mHz to 1 Hz. One phase reference uses a steered free beam connection, the other one a fiber together with additional laser frequencies. The noise characteristics of these implementations will be compared in a single interferometric set-up with a previously successfully tested direct fiber connection. We show the design of this interferometer created by optical simulations including ghost beam analysis, component alignment and noise estimation. First experimental results of a free beam laser link between two optical set-ups that are co-rotating by ±1° are presented. This experiment demonstrates sufficient thermal stability during rotation of less than 10−4 K at 1 mHz and operation of the free beam steering mirror control over more than 1 week.

λ-GRASP with bi-directional path relinking for the bi-objective orienteering problem

This paper presents a new approach to solve the bi-objective orienteering problem (BOOP). The BOOP is a multi-objective extension of the well-known orienteering problem (OP). The multi-objective aspect stems from the personalised tourist routes planning problem, in which each point of interest in a city provides different profits associated with different categories. The aim of the BOOP is to find routes satisfying a given travel cost restriction, and visiting some points of interest that maximise the total collected of different profits. To generate a good approximation of Pareto-optimal solutions, we develop a new metaheuristic method based on hybridisation of λ-GRASP and a new variant of the path relinking procedure called bi-directional path relinking (BDPR). The latter is used as an intensification phase, with the goal to obtain new solutions that can eventually be part of the set of the Pareto-optimal solutions. The proposed approach is tested on benchmark instances taken from the literature. It is compared with the Pareto ant colony optimisation algorithm (P-ACO) and the variable neighbourhood search method (VNS). Computational results show that, compared to the P-ACO and the VNS procedures, the proposed method provide a good approximation of the Pareto front for the bi-objective orienteering problem.

λ-GRASP with bi-directional path relinking for the bi-objective orienteering problem

This paper presents a new approach to solve the bi-objective orienteering problem (BOOP). The BOOP is a multi-objective extension of the well-known orienteering problem (OP). The multi-objective aspect stems from the personalised tourist routes planning problem, in which each point of interest in a city provides different profits associated with different categories. The aim of the BOOP is to find routes satisfying a given travel cost restriction, and visiting some points of interest that maximise the total collected of different profits. To generate a good approximation of Pareto-optimal solutions, we develop a new metaheuristic method based on hybridisation of λ-GRASP and a new variant of the path relinking procedure called bi-directional path relinking (BDPR). The latter is used as an intensification phase, with the goal to obtain new solutions that can eventually be part of the set of the Pareto-optimal solutions. The proposed approach is tested on benchmark instances taken from the literature. It is compared with the Pareto ant colony optimisation algorithm (P-ACO) and the variable neighbourhood search method (VNS). Computational results show that, compared to the P-ACO and the VNS procedures, the proposed method provide a good approximation of the Pareto front for the bi-objective orienteering problem.

A path relinking-based scatter search for the resource-constrained project scheduling problem

Project scheduling has received growing attention from researchers in recent decades in order to recommend models and methods to tackle problems for real-size projects. In this paper, we consider the resource-constrained project scheduling problem (RCPSP), which consists of scheduling activities in order to minimise the project duration in presence of precedence and resource constraints. We propose a hybrid metaheuristic based on scatter search that involves forward-backward improvement and reversing the project network at each iteration of the search. A bidirectional path relinking method with a new move is used as a solution combination method and a new improvement procedure is proposed in the reference set update method. The proposed method is applied to the standard benchmark projects from the PSPLIB library. The computational results show that the proposed scatter search produces high-quality solutions in a reasonable computational time and is among the best performing metaheuristics.

Bidirectional Rendering of Vector Light Transport

AbstractOn the foundations of many rendering algorithms it is the symmetry between the path traversed by light and its adjoint path starting from the camera. However, several effects, including polarization or fluorescence, break that symmetry, and are defined only on the direction of light propagation. This reduces the applicability of bidirectional methods that exploit this symmetry for simulating effectively light transport. In this work, we focus on how to include these non‐symmetric effects within a bidirectional rendering algorithm. We generalize the path integral to support the constraints imposed by non‐symmetric light transport. Based on this theoretical framework, we propose modifications on two bidirectional methods, namely bidirectional path tracing and photon mapping, extending them to support polarization and fluorescence, in both steady and transient state.