Publication list

Supervised Bachelor's theses of Ruben Garcia Hernandez

1. Evert Buzon. Theoretical study of stratified photon mapping with kernel. 10 2022.
   BibTeX Entry

   @misc{buzo22, author = {Evert Buzon}, title = {{Theoretical} study of stratified photon mapping with kernel}, year = {2022}, key = {buzo22}, month = {10}, school = {Ludwig-Maximilians-Universität München}, supervisors = {Ruben Garcia Hernandez}, type = {Bachelorthesis}, }
2. Stephan Schaller. Variance of Photon Mapping with Stratification. 11 2021. PDF
   Abstract

   This thesis studies the theoretical aspect of the photon mapping algorithm based on the framework laid out in the paper from Rubén Jesús García-Hernández "Description and Solution of an Unreported Intrinsic Bias in Photon Mapping Density Estimation with Constant Kernel" by applying order statistics to the algorithm to derive theoretical results. We start by recapping the previous results while deriving a first-order approximation to the results. We explain how to reduce the over bias while keeping the variance the same. Furthermore, to reduce variance, we apply stratification to our model and look at the results. We are building upon the previous works: Kathrin Hartmann, in her bachelor thesis - "Theoretical study of photon mapping with stratification" - calculates the expectation values of the irradiance. Zhiming Gan, in his bachelor thesis - "Variance of photon mapping density estimation" - calculates the variances for different filtering kernels. We extend this work by calculating the variance and derive an approximation to expectation values and variance. In the last part of the work, we provide a proof of concept. We show that our theoretical results are in good agreement with experimental values from our simulation.
   BibTeX Entry

   @misc{scha21, author = {Stephan Schaller}, title = {{Variance} of {Photon} {Mapping} with {Stratification}}, year = {2021}, pdf = {https://bib.nm.ifi.lmu.de/pdf/scha21.pdf}, abstract = {This thesis studies the theoretical aspect of the photon mapping algorithm based on the framework laid out in the paper from Rubén Jesús García-Hernández ``Description and Solution of an Unreported Intrinsic Bias in Photon Mapping Density Estimation with Constant Kernel'' by applying order statistics to the algorithm to derive theoretical results. We start by recapping the previous results while deriving a first-order approximation to the results. We explain how to reduce the over bias while keeping the variance the same. Furthermore, to reduce variance, we apply stratification to our model and look at the results. We are building upon the previous works: Kathrin Hartmann, in her bachelor thesis -- ``Theoretical study of photon mapping with stratification'' -- calculates the expectation values of the irradiance. Zhiming Gan, in his bachelor thesis -- "Variance of photon mapping density estimation" -- calculates the variances for different filtering kernels. We extend this work by calculating the variance and derive an approximation to expectation values and variance. In the last part of the work, we provide a proof of concept. We show that our theoretical results are in good agreement with experimental values from our simulation.}, key = {scha21}, month = {11}, school = {Ludwig-Maximilians-Universität München}, supervisors = {Ruben Garcia Hernandez}, type = {Bachelorthesis}, }
3. Kathrin Hartmann. Theoretical study of photon mapping with stratification. 7 2020. PDF
   Abstract

   In the last decades computer-generated images have become indispensable. From product design over the game and film industry until medical analysis - computer graphics plays a significant role in all of these sectors. The photon mapping algorithm is a relevant method used for generating especially photo realistic images. In this work the bias of photon mapping in combination with stratified sampling is examined. For this purpose three types of scenes are considered: a one dimensional setup, surface illumination and volumetric effects. The theoretical study of all three setups detects an overestimation bias similar to the bias described in "Describing and Solution of an Unreported Intrinsic Bias in Photon Mapping Density Estimation with Constant Kernel" by Garcìa et al. This overestimation bias is verified afterwards with an experimental study of stratified photon mapping. With different estimates for calculating the irradiance that were used in other theoretical studies of photon mapping it is investigated how the detected overestimation bias for stratified photon mapping behaves. The estimate proposed by Garcìa et al. leads to a small underestimation bias while the another estimate presented in "A Practical Guide to Global Illumination using Photon Mapping" by Jensen et al. reduces the absolute value of the bias, showing a mixture between over- and underestimation. In the end it is presented scientific research that applies the theoretical concept behind photon mapping and it is proposed a study of variance in combination with stratified photon mapping for a future research area.
   BibTeX Entry

   @misc{hart20, author = {Kathrin Hartmann}, title = {{Theoretical} study of photon mapping with stratification}, year = {2020}, pdf = {https://bib.nm.ifi.lmu.de/pdf/hart20.pdf}, abstract = {In the last decades computer-generated images have become indispensable. From product design over the game and film industry until medical analysis - computer graphics plays a significant role in all of these sectors. The photon mapping algorithm is a relevant method used for generating especially photo realistic images. In this work the bias of photon mapping in combination with stratified sampling is examined. For this purpose three types of scenes are considered: a one dimensional setup, surface illumination and volumetric effects. The theoretical study of all three setups detects an overestimation bias similar to the bias described in "Describing and Solution of an Unreported Intrinsic Bias in Photon Mapping Density Estimation with Constant Kernel" by Garcìa et al. This overestimation bias is verified afterwards with an experimental study of stratified photon mapping. With different estimates for calculating the irradiance that were used in other theoretical studies of photon mapping it is investigated how the detected overestimation bias for stratified photon mapping behaves. The estimate proposed by Garcìa et al. leads to a small underestimation bias while the another estimate presented in "A Practical Guide to Global Illumination using Photon Mapping" by Jensen et al. reduces the absolute value of the bias, showing a mixture between over- and underestimation. In the end it is presented scientific research that applies the theoretical concept behind photon mapping and it is proposed a study of variance in combination with stratified photon mapping for a future research area.}, key = {hart20}, month = {7}, school = {Ludwig-Maximilians-Universität München}, supervisors = {Ruben Garcia Hernandez}, type = {Bachelorthesis}, }
4. Zhiming Gan. Variance of photon mapping density estimation. 11 2018.
   BibTeX Entry

   @misc{gan18, author = {Zhiming Gan}, title = {{Variance} of photon mapping density estimation}, year = {2018}, key = {gan18}, month = {11}, school = {Ludwig-Maximilians-Universität München}, supervisors = {Ruben Garcia Hernandez}, type = {Bachelorthesis}, }
5. Matthias Albert. Visualizing Big Data in Virtual Reality - Interactive Analysis of Large Scale Turbulence Simulations. 9 2018. PDF
   BibTeX Entry

   @misc{albe18, author = {Matthias Albert}, title = {{Visualizing} {Big} {Data} in {Virtual} {Reality} - {Interactive} {Analysis} of {Large} {Scale} {Turbulence} {Simulations}}, year = {2018}, pdf = {http://www.nm.ifi.lmu.de/pub/Fopras/albe18/}, key = {albe18}, month = {9}, school = {Ludwig-Maximilians-Universität München}, supervisors = {Ruben Garcia Hernandez}, type = {Bachelorthesis}, }