Form From Flow Presented by Megan Wachs

1. Form From FlowPresented by Megan Wachs Region-Based Segmentation on Evolving Surfaces with Application to 3D Reconstruction of Shape and Piecewise Constant Radiance Hailin Jin, Anthony J. Yezzi, & Stefano Soatto

2. What is the problem? • Given a set of images of an object… • We should be able to do 3D reconstruction. • We should be able to estimate the radiance of the object

3. What are the assumptions? • The object is Lambertian • The scene is a collection of smooth surfaces and a background. • The foreground radiance is piecewise constant • The discontinuities in radiance can be modeled as smooth closed curves

4. What are the assumptions?

5. What is the Goal? • Determine the surface S • Determine the curve C that separates regions of different radiance • Determine the radiance values p1 and p2 of the different regions.

6. Previous Approaches • Two main approaches: • Stereo Correspondence • Image Carving

7. Previous ApproachesStereo Correspondence • From multiple images/cameras, find corresponding points and triangulate.

8. Previous ApproachesStereo Correspondence • Problems: • Need to be able to find points, which is hard on objects with low texture and few features. • Need to be able to correspond points • Cameras have to be close to avoid problems with occlusion, which causes greater error.

9. Previous ApproachesImage Carving • Take silhouettes of an object from multiple views • “Carve away” the part that isn’t object • Results in largest object that is in agreement with all scenes

10. The New Approach • Match images to the underlying model, not just to themselves • This has been done before! • The new part: • Allow objects to have discontinuities in radiance • Model the discontinuities as well as the shape

11. The New Approach • Start with a set of images • Give a starting estimate to S, C, and p1 and p2. • Compute the cost function for the surface and the curves • Iterate by updating the unknowns along their gradients until the solution converges to a local minimum

12. An Example Run • Start with a set of images of a Lambertian object captured with a calibrated camera:

13. An Example Run • Give Starting estimate to S, C, p1, p2 :

14. An Example Run • Compute the cost function for the surface and the curves • E(S,C,p1,p2,h) = Edata+Esurf+Ecurv • Edata comes from error in pixel coloration based on the model • Esurf comes from the surface area • Ecurv comes from the length of the curve

15. An Example Run • Determine the gradient descent flow, and update the unknowns in that direction.

16. An Example Run • Results:

17. My Plan : Before Break • Gather data • Calibrate camera • Calibrated image set • Represent the surface S and curve C • Represent the cost and gradient descent flow equations

18. My Plan : After Break • Implement iterative algorithm • Apply the method to a simple surface with 2 radiance regions and one discontinuity.