## ECS 289H: Computer Graphics Models from Range Data

Reading questions are due in class, in writing, on the day that the reading is due. YOU DO NOT HAVE TO COPY THE QUESTIONS
• 1/9: Handout on stereo, distributed in class. For more on the epipolar lines, you might look at the beginning of Marc Pollefeys' page on two-view geometry from his online tutorial.

• If the two digital cameras are "perfectly aligned" the raster lines are epipolar lines. Give a geometric definition of what it means for the two cameras to be "perfectly aligned".
• Sketch the brightness function at a sharp edge in a grey-level image, its first derivative and its second derivative.

• 1/12: Start reading the Spacetime Stereo paper by Davis, Ramamoothi and Rusinkiewicz; try to finish Section 3.
• In section 3.2 they describe how to get depth information with only one camera, using a projector as a "virtual camera". Could this be done with a single light pattern, or do you need a sequence of lighting images?

• 1/14: Continue discussion of spacetime stereo paper.
• In Figure 9 they show a variety of ways of varying the lighting. Which would you choose? Give one or two sentences of justification for your choice.

• 1/16: Part of the class reads and is prepared to explain Daniel Scharstein and Richard Szeliski's High-accuracy stereo depth maps using structured light

Be prepared to answer the following questions for the rest of the class:

• What problem are they trying to solve?
• What cameras and virtual cameras did they use? How were they it all callibrated?
• What light sources were chosen, and why?
• What were the sources of error?
• How good is the output, and how is it measured?

• 1/21: The other part of the class is prepared to explian Li Zhang, Brian Curless, and Steve Seitz' paper Spacetime Stereo: Shape Recovery for Dynamic Scenes.

Be prepared to answer the same questions as last time.

• 1/23: Time to start on Lab 1. Even if you are not taking the class for credit and don't want to try out the stereo camera, you might want read the brief section of the manual listed on the lab page.

For Wds, 1/28 anwer the question on the lab page in writing, and bring in a picture of a model (any model) you made, both with and without color or texture mapping.

In lecture, we discussed the effect of baseline on depth resolution (wide baseline + better resolution), and stereo callibration. For stereo callibration, see Pollefey's pages on two-view computation.

• 1/26: Introduction to alignment. Overview of ICP, and introduction to the quaternion representation for rotation in preparation for studying Horn's algorithm for the closed-form optimal alignment of a set of corresponding pairs of points.

• 1/28: Lab 1 debriefing. How are your pictures? What were all those buttons anyway?

• 1/30 We will discuss Horn's paper, "Closed-Form Solution of Absolute Orientation using Unit Quaternions"; here it is. You don't have to read it but you can.
• Do the two quaternion arithmetic problems as the end of this cheat sheet.

• 2/2: We'll read Szymon Rusinkiewicz and Marc Levoy's paper Efficient variants of the ICP algorithm.

Parts of this paper make sense only to those who have looked at Besl and McKay's paper, "A method for registration of 3D shapes", Patern Analysis and Machine Intellegence Vol 14, num. 2, 1992, and Yang Chen and Gerard Medioni's "Object modeling by registration of multiple range images", Image and Vision Computing, Vol 10, num 3, 1992 (both journals available from UC computers if you go through the library). I will try to hit on the relevant points from these papers in lecture, so reading them is optional.

The main question we will discuss in class is, what choices would you make if you were optimizing for accuracy rather than speed? You do not have to write anything down about this but keep it in mind while reading.

• What is the projection method of choosing correspondances?
• Fig 13 illustrates rejecting pairs on mesh boundarys. Why is this a good idea?

2/4: Guest lecture: Ravi Kolluri, UC Berkeley, on coarse alignment.

2/6: Read Kari Pulli's paper Multiview Registration for Large Data Sets, from the 1999 3DIm conference. You can just skim section 2.

• What is the "virtual pair" approach in Figure 6?
• Why does he feel adding scans incrementally is better than going for a global solution?

• 2/9 Background on robust fitting. The Maximum Likelihood justification for Least-Squares if the noise is assumed Gaussian, M-estimators, and the RANSAC algorithm.

The standard reference for RANSAC is "M. A. Fischler and R. C. Bolles, Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography, Comm. ACM, 24-6 (1981), 381--395". Paper will be distributed in class at a later date.

• 2/11 Background on using an entire video stream. Kanade-Tomasi factorization algorithm.

• 2/16 Holiday.

• 2/18 We will read Brian Curless and Marc Levoy's paper "A volumetric method for building complex models from range images". Concentrate on Section 3.
• Why do the weight values taper off behind the observed surface? What would be wrong with keeping them constant? How about with setting them to zero right away instead of tapering off?

• 2/20 Part of the class will read Brian Curless and Marc Levoy's "Better optical triangulation through spacetime analysis", and explain it to the rest of us.

We will finish the discussion of the previous paper.

A brief demo of laser speckle, based on a suggestion from the Exploratorium summer institute for science teachers.

• 2/23 Part of the class will read Zhao, Fedkiw and Osher's Fast Surface Reconstruction Using the Level Set Method, and explain the main idea to the rest of us. You can skip section 5 if you want.

• 2/25 Background on the level-set method. A good introduction can be found in Sethian's American Scientist article.

• 2/27 I will talk about my paper with Ravi and Sunghee Choi, The Power Crust.

• 3/1 More on power crust, and (if time permits) an overview of Boissonnat's classic paper "Geometric structures for three-dimensional shape reconstruction. ACM Transactions on Graphics 3(4):266--289, 1984", available online through the library. We'll talk about the "sculpting" algorithm in section 3.

• 3/3 Some class members will read and help expain Extremal Feature Extraction from 3-D Vector and Noisy Scalar Fields, by Chi-Keung Tang and Gerard Medioni. This paper whips through the method and five applications in eight short pages. We are interested in the last application in section 4.5.

• 3/5 The class members who have not read anything lately will read and explain Reconstruction and Representation of 3D Objects with Radial Basis Functions, by J. C. Carr, R. K. Beatson, J.B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum and T. R. Evans

• 3/8 Background on radial basis functions.