The reflectance modeling in shape from shading 
L. Hashemi“”, A. Azizi", M. Rezaeian? 
Dept. of Geomatics Engineering, University of Tehran, Tehran, Iran 
(Ihashemi, aazizi, mrezacian)(Qut.ac.ir 
Commission V, WG V/6 
KEY WORDS: Photogrammetry, Radiometry, Modeling, Visualization, DEM/DTM, Radiation 
ABSTRACT: 
Shape from Shading is one of the methods used for shape recovery which exploits the fact that surface patches, having different 
inclination relative to a light source are imaged with different brightness. 
In order to solve the DTM reconstruction problem by SFS the image formation process has to be modeled and eventually inverted with 
respect to the parameters describing the object surface. Surface reflectance can be exactly described by its bi-directional distribution 
function (BDRF). 
In this paper we show that there exist images that could not have arisen from shading on the smooth surface with uniform reflecting 
properties. This means that the gray shade values are also significantly influenced by the other factors, which have not been included into 
SFS functional model. 
1.INTRODUCTION 
1.1. Introduction 
Shape recovery in computer vision is an inverse problem, 
which transforms single or stereo 2D images to a 3D scene. 
Shape from shading (SFS) is one of the methods used for shape 
recovery which exploits the fact that surface patches, having 
different inclination relative to a light source are imaged with <q > 
different brightness. The surface is generally assumed to have B^ 
constant and known reflectance properties. Therefore SFS only V 
performs well in area with poor image texture where digital Sun 2’ 
image matching fails to produce correct results. uf 
  
sensor 
1.2. Image formation Hn 
La 
| 
In order to solve the DTM reconstruction problem by SFS the 
image formation process has to be modeled and eventually i 
inverted with respect to the parameters describing the object 
surface. The image gray values are influenced by the radiance 
and wavelength of incident illumination, atmospheric effects, 
surface reflectance properties and sensor characteristics. 
  
Surface element 
  
  
. > ? . . . . 7ieure inci P1 re fc ation 
Light fall onto the surface enclosing the incidence angle 7 Figure 1. Principle of image formatior 
between the direction to the light source S and the local 
surfac N. i ing irradiance fis ÿ 
surface normal The incoming irradiance Æ, is partly 2. REFLECTANCE MODELS 
absorbed and partly scattered back into upper hemisphere. A 
sensor lying in direction V , which encloses the emittance angle 
dese Surface reflectance can be exactly described by its bi 
€ between V,N registers the radiance L scattered toward the directional distribution function (BRDF). This function 
describes how light from a given direction is reflected from a 
surface at a given orientation. In its full generality different 
spectra of light may be reflected in an orientation dependent 
way; thus, the BRDF may be, at least theoretically, very 
complex indeed. 
Sensor.