Starting this chapter

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1 Computer Vision 5. Source, Shadow, Shading Department of Computer Engineering Jin-Ho Choi 05, April, /40 Starting this chapter The basic radiometric properties of various light sources Develop models of source geometries discuss the radiosity Shadows that result from these sources. Establish a usable model of the shading on a surface Representation of shape Albedo of object under different lights Describe surfaces reflect light onto one another 2/40

2 3.1 Radiometric Properties of Light Source Light source : emit light Source emit in each direction Emitted radiance is dealt with separately from reflected radiance The geometry of source Sources are modelled with simple geometries 1. Point source or line source 2. Sources with simple geometries get complex effects 3/ Radiometric Properties of Light Source Spectral radiance source emits in each direction Emitting constant radiance in each direction : extiance Coloured source use spectral exitance or spectral radiance Sources can have radiosity and exitance nglish 4/40

3 32Q 3.2 Qualitative ti Radiometry What a source look like from the surface Gives qualitative descriptions of brightness Lambert s wall 5/40 More complex wall 6/40

4 3.3 Sources and their effects Light source Anything that emits light that is internally generated similar to radiosity: a source can have both radiosity, because it reflects exitance, because it emits Exitance The internally generated energy radiated per unit time and per unit area on the radiating surface. Sources Point source Line source Area source 7/ Sources and their effects How bright (or what color) are objects or sources? General idea: B(x) E (x) radiosity due to incoming radiance d But what aspects of the incoming radiance will we model? 8/40

5 3.3.1 Point Sources 9/ Point Sources 10/40

6 3.3.1 Point Sources 11/ Point Sources Choosing a Point Source Model A point source at infinity is good model for the sun Poor model : objects is similar in magnitude to distance to source Consider surface patches Consider light bulb in center of room 12/40

7 3.3.2 Line Sources Line Source of good example is single fluorescent light bulb Main interest is radiometric problem 13/ Line sources radiosity due to line source varies with inverse distance, if the source is long enough 14/40

8 3.3.3 Area sources 15/ Area sources 16/40

9 3.4 Local Shading Models We have studied the physics of light Bright things Extracting object information from these models Fraught with all difficulties involved in choosing model Local shading model 17/ Local shading model by a point source 18/40

10 3.4.1 Local shading model by a point source A point that can t seethe source is in shadow For point sources, the geometry is simple 19/ Local shading model by a point source The Appearance of Shadows Shadows occur when the patch can not see one or more sources Any patch on plane is in shadow if ray from patch to source passes through an object If there are many source, shadows will be less dark 20/40

11 3.4.2 Area Sources and their Shadows Local Shading model become : Area sources do not dark shadows with crisp boundaries It is common to distinguish between points in the umbra Points in the penumbra 21/ Area Sources and their Shadows 22/40

12 3.4.3 Ambient Illumination Local shading models problem They predict that some shadow regions are arbitrarily dark This prediction is inaccurate in almost every case Change the environments : Ambient In such an environment it is sometimes possible to model the effect of other patches by adding an ambient illumination term to each patch s radiosity. 23/ Ambient Illumination 24/40

13 3.5 Application: Photometric Stereo Assume: a local shading model a set of point sources that are infinitely distant a set of pictures of an object, obtained in exactly the same camera/object configuration but using different sources A Lambertian object (or the specular component has been identified and removed) 25/40 Projection model for surface recovery - usually called a Monge patch 26/40

14 3.5 Application: Photometric Stereo 27/ Normal and Aledo from Many Views 28/40

15 3.5.1 Normal and Aledo from Many Views 29/ Normal and Aledo from Many Views 30/40

16 Recovering normal and reflectance Given sufficient sources, we can solve the previous equation (most likely need a least squares solution) for g(x, y) Recall that N(x, y) is the unit normal This means that x,y) is the magnitude of g(x, y) This yields a check And If the magnitude of g(x, y) is greater than 1, there s a problem N(x, y) = g(x, y) / x,y) 31/ Shape from Normals 32/40

17 Surface recovered by integration 33/ Interreflections: Global Shading How to simplify interreflection models without losing essential qualitative properties 34/40

18 3.6.1 An Interreflection Model 35/ Solving for Radiosity 36/40

19 3.6.2 Solving for Radiosity 37/40 Shading models Local shading model Surface has radiosity due only to sources visible at each point Advantages: often easy to manipulate, expressions easy supports quite simple theories of how shape information can be extracted from shading Global shading model surface radiosity is due to radiance reflected from other surfaces as well as from surfaces Advantages: usually very accurate Disadvantage: extremely difficult to infer anything from shading values 38/40

20 Image model For each point source, Out of shadow: we know the source vector (by assumption). I j (x, y) kb(x, ( y) We assume we know the k (x, y) N(x, y) S j scaling constant of the linear camera. Fold the g(x,y) V j normal and the reflectance into one In shadow: vector g, and the scaling constant and source I j (x,y) 0 vector into another V j 39/40 Summary local shading model is a poor description of physical processes that give rise to images because surfaces reflect light onto one another easy to model This is a major nuisance; the distribution of light (in principle) depends on the configuration of every radiator; big distant ones are as important as small nearby ones It appears to be hard to extract information from these models Global shading model : Ambient illumination, interreflections 40/40