THESIS GENERATION OF TERRAIN TEXTURES USING NEURAL NETWORKS Submitted by Santiago Alvarez Department of Computer Science In partial fulllment of the requirements for the degree of Master of Science Colorado State University Fort Collins Colorado Fall COLORADO STATE UNIVERSITY September WE HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER OUR SUPERVISION BY SANTIAGO ALVAREZ ENTITLED GENERATION OF TERRAIN TEXTURES USING NEURAL NETWORKS BE ACCEPTED AS FULFILLING IN PART REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE Committee on Graduate Work Adviser Department Head ii ABSTRACT OF THESIS GENERATION OF TERRAIN TEXTURES USING NEURAL NETWORKS Realistic visualization of terrain can b e achieved by combining color and top ographic information Threedimensional terrain mo dels obtained from Digital Elevation Mo dels DEMs can b e rendered by mapping aerial photographs on top of them However there may b e terrain mo dels for which a texture photograph is not available In those cases it is useful to have some technique which generates articial textures using terrain information of similar regions This pro ject explores the use of neural networks MultiLayer Perceptrons MLPs in particular to generate articial terrain textures from DEMs This type of neural network has b een referred as a universal function approximator In this case the network approximates the mapping b etween elevation samples and pixel colors Three main issues were address in this pro ject rst the quality of the textures pro duce by the MLP second the eect of dierent input representations on the tex ture quality in particular the eect of including slop e information and a neighborho o d of elevation samples in the input vector and third the accuracy of the trained MLP in rendering unseen terrain with similar characteristics as those used during training Santiago Alvarez Department of Computer Science Colorado State University Fort Collins Colorado Fall iii ACKNOWLEDGEMENTS I wish to thank my advisor Dr Mike Goss for his guidance and teachings throughout the completion of this degree I am also grateful to Dr Chuck Anderson who served in my committee and contributed to this work with numerous discussions and reviews Thanks also go to Dr Denis Dean for serving in my committee providing me with useful information and reading and commenting on the initial manuscript I wish to thank Dr Mario MejaNavarro for all the material he shared with me and the time he devoted to help me I am grateful to Alicia C Lizarraga for providing me with imp ortant references I have also b eneted from other friends and colleagues who contributed to this work in many dierent ways I express here my gratitude to my parents and sister whose encouragement has always b een essential to my work Sin su ayuda no hubiera alcanzado esta y muchas otras metas iv DEDICATION A todos los que en veintiseis a nos han hecho de mi lo que soy Inclusive a aquel los que fueron un obstaculo v CONTENTS Introduction Data Description Neural Network Mo del Data Preparation Normalization Training Validation and Test Sets Exp eriment Description Parameter Search and Percentage of Data Sampled Including the Surface Normal Vector Using the HSV Color Mo del Network Generalization Results Parameter Search and Percentage of Data Sampled Including the Surface Normal Vector Using the HSV Color Mo del Network Generalization Discussion REFERENCES vi LIST OF FIGURES Example of a blo ck diagram of a DEM and its aerial photograph A twolayer p erceptron showing the notation for units and weights Two common activation functions used for MLPs Lo calization of cam cam cam and cam Registered aerial photographs Blo ck diagrams of the registered digital elevation mo dels DEM and photograph RGB histograms DEM and photograph HSV histograms Test and training errors for training sets with dierent sizes Results obtained using a element neighborho o d of elevation samples Results obtained using a element neighborho o d of elevation samples and the surface normal vector Slop e discontinuities in the DEMs that aect the elevationtocolor mapping Color distributions of the target and output textures for cam Results obtained using the single elevation sample and the surface normal vector Results obtained using a element neighborho o d of elevation samples and the surface normal vector HSV outputs Network approximation of cam cam and cam from cam data RMSE b etween target and output textures using network trained with cam data vii LIST OF TABLES Lo cation of the data sets in Universal Transverse Mercator UTM co ordinates Distribution parameters of the combined DEMs and the combined aerial pho tographs Elevation ranges of the DEMs used viii Chapter INTRODUCTION Terrain textures are essential for rendering highquality terrain images Realistic vi sualization can b e obtained by combining color and top ographic information Cohen and Gotsman Miller Taylor and Barrett Terrain color can b e obtained from aerial or satellite images These photographs usually cover a small p ortion of ter rain from a vertical view angle Topographic information can b e obtained from Digital Elevation Mo dels DEMs A DEM contains a number of elevation samples that can b e extracted from stereoscopic terrain photographs The rendering of terrain mo dels using computer graphics has multiple applications It is used by the military for ight simulation simulation of the displays of some electro optical weapons and mission planning This technology is also used in the civilian market for urban and rural planning the generation of animations and many other applications The most common metho d to render realistic images of actual terrain is to obtain a D p olygonal mo del of the terrain from a DEM Fowler McCullagh Tarvy das Scarlatos This p olygonalization reduces the complexity of the terrain representation allowing faster access and pro cessing Once the terrain mo del has b een created the terrain texture is mapp ed onto it and pro jected according to the desired view The nal realism of the rendered image dep ends on the resolution and quality of the D mo del generated and the realism of the terrain texture mapp ed onto the mo del However terrain textures are not always available In those cases where a terrain texture cannot b e obtained it would b e useful to have some technique that would generate terrain textures with an acceptable quality using elevation and land cover information In such cases an articially generated mo del can b e rendered Such a mo del could b e the result of a simulation pro cess that tries to predict some terrain parameters or could also b e an arbitrary mo del built for visualization purp oses This pro ject explored the use of neural networks to generate articial terrain textures from terrain mo dels A simplied mo del structure containing only elevation data was used The goal was to b e able to generate terrain textures from elevation data using a neural network trained with available terrain mo dels and photographs Sp ecically it was of most interest to determine the quality of the terrain textures that could b e obtained from elevation data and how the input representation could aect the results Additionally the generality of this approach was addressed The simplied terrain mo del was exp ected to pro duce enough information to address the texture generation problem The app earance of terrain at a given p oint is highly inuenced by its altitude and slop e This relationship should b e similar within a limited geographical area If such a close relationship exists a neural network can b e used to nd an interpolation of the mapping b etween elevation and color Even though elevation is not the only factor that determines the terrain texture it should play an imp ortant role Other factors such as light exp osure type of soil and weather have a ma jor impact on the kind of vegetation and ro cks found on some terrain However their inuence on the app earance of the terrain was assumed constant or closely related to elevation or slop e for this pro ject We can overcome the lack of a general mo del that relates elevation with terrain texture by using neural networks One feature of neural networks is that they can b e trained on a relatively small number of examples of a relationship Once trained the network can induce a complete relationship that interpolates in a sensible way The use of this characteristic should give some insight ab out how close a relationship there is b etween elevation and texture and how realistic the results pro duced by a trained network are Data Description Two basic types of data were considered in this pro ject Digital Elevations Mo dels DEMs and aerial photographs As dened by Burrough any digital representa tion of relief over space is known as a DEM Their uses include Elab oration of top ographic maps by government