From c1a4ad4e77f1c13f154a9da7ab82a83ec87fab8d Mon Sep 17 00:00:00 2001 From: CDaut Date: Wed, 21 Jun 2023 14:14:54 +0200 Subject: [PATCH] started results section --- handout/handout.tex | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/handout/handout.tex b/handout/handout.tex index 1e26b54..9f5850a 100644 --- a/handout/handout.tex +++ b/handout/handout.tex @@ -34,6 +34,7 @@ \usepackage[english]{babel} \usepackage{csquotes} \usepackage{amsmath} +\usepackage{amsfonts} \usepackage{tikz} \usetikzlibrary{calc,patterns,angles,quotes,shapes,arrows, positioning,overlay-beamer-styles} @@ -105,7 +106,7 @@ Thus the problem can be mitigated by not sampling a pixel uniformly, but importa \subfloat[edge sampling]{ \input{diagrams/edge_sampling.tex} } - \caption{The figure depicts the sampling situation in a single pixel. We are interested in the gradient with respect to the gray triangle moving up. Area sampling does not account for this color change whereas edge sampling does. Primary occlusion is handled correctly.}\label{fig:area_vs_edge_sampling} + \caption{The figure depicts the sampling situation in a single pixel. The gradient with respect to the gray triangle moving up is the metric to be calculated. Area sampling does not account for this color change whereas edge sampling does. Primary occlusion is handled correctly.}\label{fig:area_vs_edge_sampling} \end{figure} Consider a situation as depicted in figure~\ref{fig:area_vs_edge_sampling}. When the gray triangle moves up, the white area decreases and the gray area increases. Thus white should contribute less to the pixel color. Area sampling does not account for this change, since all samples land on an area with the same color before and after movement. Edge sampling does account for this change because especially areas of discontinuity i.e.\ the edges are sampled. The samples will have a different colors after the triangle moves up, correctly capturing the gradient. Primary occlusion is handled correctly because the sample that intersected the blocker before, will also intersect the blocker after movement as it is independent of the triangle movement. @@ -124,7 +125,8 @@ As seen in figure~\ref{fig:halfspaces} the edge separates the space into two hal Mathematically this yields that the Integral can be separated into two parts. One part that represents the discontinuous edges and one part that accounts for the original pixel integral over continuous regions. \section{Results} - +The main application of differentiable ray tracing discussed in the paper is inverse rendering. That is: Given images of a scene, synthesize a 3D representation of that scene. To do this an error function $e: \Phi\mapsto\mathbb{R}$ that measures how close an approximate render is to a target image with respect to a set of scene parameters $\Phi$ is required.\\ +Given this function and a set of target images the inverse rendering problem can be solved using differentiable rendering. The first step is to render an approximation of the scene differentiably. The resulting images are then compared to the target images by calculating the error. Since the rendering process is differentiable the gradient of the error function can be calculated, allowing for a minimization of the error function using a process such as stochastic gradient descent. % BIBLIOGRAPHY \nocite{*} % List all entries of the .bib file, even those not cited in the main body