PSM Surface Reconstruction & Gradient Map Generation

COMPSCI 775ST Assignment 4

From:18/09/2002
Due: 04/10/2002 2:00pm (Friday)

• Aim

• Resource

• Goal

• Details

• Hints

• Questions to be answered

• Example of results

• Understand Photometric stereo
• Understand how to generate a Normal map and how to reconstruct surfaces using the normal map

Sets of three images are available in the following table. Some images are synthetic, some are real images. The illumination directions, ps and qs, for the images are also given.

Name	ps	qs	Name	ps	qs
beet_v1.bmp beet_v2.bmp     (Real) beet_v3.bmp	-0.387930 0.031802 0.389363	0.059682 0.556538 0.104828	Images/ht_1.bmp Images/ht_2.bmp Images/ht_3.bmp	0.5 0.0 0.0	0.0 0.0 1.0
kugeln_1.bmp kugeln_2.bmp kugeln_3.bmp	-0.25 0.0 0.0	0.0 -0.25 0.0	mozart1.bmp mozart2.bmp mozart3.bmp	0.0 -0.315 0.315	0.364 -0.182 -0.182
porsche1.bmp porsche2.bmp porsche3.bmp	0.0 0.5 0.0	0.0 0.0 0.5	sphere_0_0.bmp sphere_05_-05.bmp sphere_-05_-05.ima	0.0 0.5 -0.5	0.0 -0.5 -0.5
stucco1.bmp stucco2.bmp     (Real) stucco3.bmp	-0.387930 0.031802 0.389363	0.059682 0.556538 0.104828	torus1_1.bmp torus1_2.bmp torus1_3.bmp	0.0 0.0 1.0	0.0 1.0 0.0
triangle_0_0_.bmp triangle_0_1_.bmp triangle_1_0_.bmp	0.0 0.0 1.0	0.0 1.0 0.0

• Computation of surface normals from three Photometric Stereo images
• Visualisation of the determined normals in a needle map representation
• Rendering the reconstructed object with a simple reflection model

• Choose appropriate image triplets.  It might be easier to start with synthetic images and move on to the real images later on.
• Explain the concept of photometric stereo and all the related assumptions.
• You may assume that the surface is diffused and modelled by the Lambertian reflection model
• Calculate the surface normals and describe the procedures.
• Visualize the recovered surface normals (p,q) as a needle map.
• Render the object by the result found above, but with many other different illumination directions.
• Discuss possible sources of error and the results in detail.

Calculation of the surface normals

The Photometric Stereo Method (PSM) calculates local surface orientations (normals) according to the surface reflectance properties of the object.  To simplify the task, we assume that our objects have diffuse surfaces and reflect light according to the Lambertian model (see p.122)

The light directions and strengths are known and remain constant over the surface of the object.

Calculate the surface normals using irradiance ratios: Eliminate the denominators of the equation E1/E2 = ... and E1/E3 = ... . Afterwards, you have two linear equations with two unknowns (p and q). Solve for p and q. Implement this formula and apply it to each reliable image point.

The formulas on Page 133 of the lecture notes may be helpful.

Visualising the surface normals

Visualize the recovered surface normal (p,q) as a needle map. A needle is the projection of a normalised surface normal (p,q,-1)/||(p,q,-1)|| on the image plane.

The orientation of a needle and the orientation of the normal are equal.  The length of a needle is proportional to sin(angle((p,q,-1), v)). The vector v=(0,0,-1) represents the line of sight.

Render the recovered object

Once the surface normals are recovered they can be used to render the object using the Lambertian reflection model with an arbitrary illumination direction.  Generate at least two images of the reconstructed object.  The object should be illuminated from directions different to the light directions given in the input images.

You may also be aware of visualisation tools such as VRML, ivview  or plyview.  They can also be used to visualise your results.
Have a look at http://www.cs.auckland.ac.nz/references/#vrml for information about visualisations packages.

• Why do we use 3 input images?
• What are the advantages of albedo-independent approach?
• Under what conditions will photometric stereo fail to produce the correct normal map?

Here are some example results to provide an idea of what to expect in the result.