Questions tagged [monte-carlo]

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1answer
92 views

PDF for sampling emissive meshes for NEE/MIS

I'm writing a Monte Carlo path tracer, and I'm trying to allow any mesh to be an emitter, but I'm not entirely sure about the probabilities to use when I sample them. Right now, my algorithm for light ...
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1answer
57 views

Integrating BRDF using Importance Sampling

I read some articles about BRDF integration with and without importance sampling and I don't understand one thing in equations. If we integrate a BRDF over hemisphere with uniform sample direction ...
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0answers
39 views

Is this way of transforming QMC samples into barycentric tri coordinates agnostic to mesh-topology?

While I'll try my best to give all relevant info in all possible brevity below, please refer to the spoiler and link at the bottom of the post for the (more lengthy) original description if needed. ...
1
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1answer
140 views

Energy redistribution sample re-integration

I'm implementing ERPT-style energy redistribution of primary samples within a pathtracer. Specifically, to improve the sampling of defocused areas. The core algorithm does two things: If sample ...
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0answers
72 views

Implementing monte carlo path traced refractions problem

I am writing a forward monte carlo path tracer with the added feature of specular refractions for transparent materials, I have managed to come this far but something is not quite right and I am ...
3
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0answers
162 views

Understanding BRDF sampling

I'm trying to understand BRDF importance sampling following the exemples of the lambertian/diffuse model and the reciprocal Phong model. I would like to be able to extend the principle to other ...
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0answers
135 views

Visualize the variance of an image

Let $h_j$ denote the image reconstruction filter of pixel $j$. I'm estimating the color value $$I_j=\int h_jf\:{\rm d}\mu$$ of the $j$th pixel (see [Veach, Section 8.2]) by an asymptotically ...
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1answer
96 views

BDPT - How to handle deterministic ray PDF?

I'm trying to implement a simple BDPT without MIS as described in Lafortune's paper. I've used the weighting scheme defined in the paper in which they suggest that the weight be based on the surface ...
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0answers
79 views

Relation between camera sensor responsivity and image reconstruction filter associated with a pixel

Let $W_{\text e}$ denote the camera sensor responsivity (i.e. importance) and $h_j$ and $W_{\text e}^{(j)}$ denote the image reconstruction filter and sensor response associated with the $j$th pixel, ...
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2answers
167 views

Properties of the image reconstruction filter in rendering

Let $f$ denote the measurement contribution function for paths of length $k\in\mathbb N$, i.e. $$f(x)=g(x_0\leftrightarrow x_1)W_{\text e}(x_1\to x_0)t_k(x_0,\ldots,x_k)L_{\text e}(x_k\to x_{k-1}),$$ ...
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0answers
144 views

Scaling of the final image in Metropolis Light Transport

I don't understand why the PBR implementation of Metorpolis Light Transport scales the final image by b / mutationsPerPixel. The authors write: Each Metropolis ...
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0answers
40 views

Quantify the variance of pixel measurements

Say $E_j$ is an estimator of the value $$I_j=\int f_j\:{\rm d}\lambda$$ of the $j$th pixel given by the path space integral of the corresponding measurement contribution function $f_j$. $f_j$ is of ...
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47 views

Distribution of the first vertex on a camera subpath in bidirectional path tracing

Suppose we are sampling camera rays of a perspective camera with a finite aperture. The PBRT implementation of the sampling scheme looks like this: ...
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0answers
48 views

Chart swaps and path inversion in bidirectional path tracing

I've got a hard time to understand how we would implement the following in practice. I'd be great if someone could explain the details for the example below. Assume we're generating a path ${\rm x}=(\...
1
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1answer
67 views

In bidirectional path tracing, is a camera subpath with $n$ vertices determined by a fixed number of random numbers?

In the Multiplexed Metropolis Light Transport implementation of the book Physically Based Rendering, the proposal samples are generated by the Primary Sample Space Sampler ...
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1answer
152 views

How to calculate the PDF of a multi-lobe BSDF

In PBRT, a BSDF is represented as an array of BxDF lobes. Each lobe sets a bitflag representing what kind of lobe it is. (Specular, Diffuse, Reflection, Transmission, etc.) I'm investigating how PBRT ...
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0answers
27 views

Report standard deviation in Rendering results

I noticed that a common metrics for image quality assessment (Monte Carlo path tracing) is MSE between the generated image and a reference one. My question is: why isn't the standard deviation ever ...
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0answers
136 views

Multiple Importance Sampling in Bidirectional Path Tracing

I'm trying to understand the computation of the path density described in the book Physically Based Rendering. They assume that a path $$x=(x_0,\ldots,x_{n-1})=(q_0,\ldots,q_{s-1},p_{t-1},\ldots,p_0)$$...
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1answer
280 views

Rendering equation in terms of paths rather than directions

Path tracing seems to perform Monte Carlo integration where the space being integrated over is the space of paths (e.g. chains of rays) but the rendering equation is stated in terms of outgoing rays. ...
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1answer
375 views

Monte Carlo Importance Sampling

I am following the "Ray Tracing - the Rest of your Life" book by Peter Shirley and I am facing some troubles in the implementation of Monte Carlo importance sampling, and Direct light sampling. Monte ...
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2answers
2k views

Multiple Importance Sampling in Path tracer produces Dark Images

So I recently implemented Multiple Importance Sampling in my path tracer which was based on next event estimation. The problem is without MIS I get images like, This is obtained by setting ...
3
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1answer
152 views

Ask for help on understand an algorithm which combines stratified sampling and importance sampling of Monte Carlo

I cannot understand an algorithm which combines stratified sampling and importance sampling of Monte Carlo. It is introduced in Page 73 of a textbook "Advanced Global Illumination", 2nd edition, ...
2
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1answer
150 views

How do we approximate the integral of the measurement contribution function in Metropolis Light Transport?

In Metropolis Light Transport, we need to approximate the integral of the measurement contribution function. I've read that this can be done using a traditional approach like path tracing. However, ...
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1answer
353 views

How does Primary Sample Space Metropolis Light Transport work?

For simplicity, assume we're only dealing with surfaces which have either a Lambertian or perfectly specular material. Morever, assume that the only type of lights are area lights (i.e. surfaces with ...
1
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1answer
328 views

Path tracer isn't converging

So I just completed a naive path tracer that uses explicit direct light sampling. Problem is the path tracer isn't converging. It's like a raytracer, showing a single image on each pass. More info on ...
3
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1answer
417 views

Is there ongoing research on Markov Chain Monte Carlo algorithms (other than Metropolis-Hastings) for use in ray tracing?

Metropolis Light Transport is an application of the Metropolis-Hastings algorithm. Its variants differ only in the used "mutation strategy". Is there ongoing research on other Markov Chain Monte ...
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0answers
110 views

Tail Recursive Monte Carlo Raytracing

I am writing a raytracer in F# using montecarlo sampling I would like to make my recursive calls tail recursive but I am not sure of this is possible with MC raytracing as one has to evaluate sampled ...
4
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2answers
133 views

Variance of estimator (Monte Carlo Integration)

So I was reading this paper by Lafortune, "Mathematical Models and Monte Carlo algorithms" and in it he writes. We have a function or integrand I we want to estimate given as, $I = \int f(x) dx$ We ...
1
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1answer
811 views

Phong Modified BRDF Implementation

According to: https://www.cs.virginia.edu/~jdl/importance.doc For a specular sample: (page 4 of the document) $$pdf(\theta_{i}) = \frac{n+1}{2\pi} \cos^n(a)$$ And this is how you choose an ...
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1answer
360 views

Direct illumination, specular surfaces, and MIS

Multiple Importance Sampling (MIS) is a technique used by Veach's VCM technique to balance responses of different surfaces to different types of importance sampling for direct illumination. My ...
3
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1answer
155 views

Primary ray directions (MC Path tracer)

Do primary rays conform to the frustum? If they're randomly directed, is the randomness fitted to some distribution (as it would be for a diffuse BRDF? I'm building my existing raymarcher into a monte ...
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0answers
68 views

Sample Correlation and Random Variables -- An Intuitive Explanation?

I'm mainly trying to understand what it means for Monte Carlo samples to be correlated. Can somebody fit this into the theory of what I know about random variables, covariance and correlation? And ...
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0answers
583 views

What's the nature of Monte Carlo noise?

Monte Carlo rendering is just a process of sampling and reconstruction to evaluate the rendering equation. Why is it called noise rather than error?
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1answer
129 views

Monte Carlo Integration

Let $I$ = the value of integration and $p$ = probability distribution. The estimator is denoted as $\left\langle I \right >$ and is $$\left\langle I \right >=\frac{1}{N}\sum_{i=1}^{N}\frac{f(...
5
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1answer
95 views

The variance for the Monte Carlo estimator

I was wondering about the variance for Monte Carlo. The book (Advanced Global Illumination 2ed, p.60) writes the equation as follows: $\sigma^2 = \frac{1}{N} \int(\frac{f(x)}{p(x)} - I)^2p(x)dx$ $\...
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0answers
504 views

Problem with specular BRDF (Monte Carlo & Path Tracing)

Above on the left is my attempt and on the right is what I'm aiming for.As you can see my sphere with the specular brdf has a weird dark ring In my radiance function I am recursing through the ...
2
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1answer
173 views

Troubleshoot half vector sampling from a distribution (cook-torrence, trowbridge-reitz, etc)

I am learning ray tracing and the mathematics behind it. I have a working monte-carlo raytracer I am experimenting on. I have gotten past pure diffuse BRDFS, area lights, acceleration structures, ...
7
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1answer
928 views

Path Tracing With Multiple Lights

I've got my path tracer working great for a single light, but I'm having trouble coming up with a solution for scenes with multiple lights. My first thought was to just send a ray to each light and ...
2
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0answers
159 views

Picking multiple light sources from a mixture densities

According to Peter Shirely paper, one pdf(probability density function) can be defined for the union of the light sources and pick only one using a random number from this density: $$p(x) = \alpha_1 ...
3
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2answers
1k views

Generation of stratified cosine weighted samples on hemisphere

I have had luck with cosine weighted hemisphere samples, and I know how to generate stratified uniform samples, but I wanted to experiment with combining the two. However, how do I correctly stratify ...
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1answer
5k views

Does cosine weighted hemisphere sampling still require NdotL when calculating contribution for indirect light?

When converting from uniform hemisphere sampling to cosine weighted hemisphere sampling I am confused by a statement in an article. My current indirect contribution is calculated as: ...
8
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1answer
431 views

Is this Russian roulette code correct?

I'm using www.scratchapixel.com among other resources to help me learn how to implement a renderer. I am looking at the following code from this page where a packet of photons moving through a ...
8
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2answers
894 views

Why random monte carlo sampling instead of uniform sampling?

Why is it that it's so common to use monte carlo randomized sample locations, instead of uniform sampling? I'm assuming that taking randomized samples gives some benefit but I don't know what they ...
9
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1answer
2k views

Full Monte-Carlo Volumetric Scattering

I would like to add full monte-carlo volumetric scattering to my path tracer, but I'm having a hard time researching how to do it. Let me explain what I would like to do: A ray enters a material, and ...
5
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1answer
1k views

What effects does path tracing capture that recursive ray tracing does not?

So I have been wanting to make a rendering engine as a summer project. I'd like to shoot for photo-realism of static scenes rather than real time dynamic game like graphics. So in my research I came ...
8
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1answer
1k views

How does everyone count "Rays per Second"?

Recently I'm developing a Monte-Carlo path tracer. To measure my tracer's performance, I decided to implement a simple mechanism to count how many rays can it trace in a second. Then here comes the ...
24
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3answers
8k views

Is Russian Roulette really the answer?

I have seen that in some implementations of Path Tracing, an approach called Russian Roulette is used to cull some of the paths and share their contribution among the other paths. I understand that ...
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2answers
2k views

How to build a decent lens/camera objective model for path tracing?

I have written a small path-tracer after learning and experimenting on smallpt. The only thing that I did not write (and understood) myself is how the initial rays are computed and fired from the ...
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2answers
747 views

How do correlated samples influence the behavior of a Monte Carlo renderer?

Most descriptions of Monte Carlo rendering methods, such as path tracing or bidirectional path tracing, assume that samples are generated independently; that is, a standard random number generator is ...
35
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3answers
13k views

Why does monte carlo ray tracing perform better than distributed ray tracing?

I've heard that the quality of a monte carlo ray tracer (based on path tracing algorithms) is much more realistic than a distributed (stochastic) engine. I try to understand why, but I'm just at the ...