Chapter 3
Multi-View Depth Estimation

“Nature is not on the surface, it is in the depths. Colors are an expression of these depths on the surface. They rise from the roots of the world.”

Paul CÚzanne, French Post-Impressionist painter. This chapter describes algorithms for estimating the depth of pixels, based on the projective geometry framework introduced in the previous chapter. In the first part, we focus on the estimation of depth images using two views. The key is a description of the basic geometric model and an elementary method that is employed to triangulate the depth of points from two (rectified) images. Because this elementary method results in an inaccurate depth estimation, we subsequently review two depth-calculation/optimization strategies: a local and a one-dimensional optimization strategy. In the second part of this chapter, we show that, instead of employing only two rectified views, multiple views can be employed simultaneously to estimate the depth. Based on this observation, we propose a multi-view depth estimation technique that (1) increases the smoothness properties of estimated depth images, and (2) enforces consistent depth images across the views.

 3.1 Introduction
 3.2 Two-view depth estimation
  3.2.1 Two-view geometry
  3.2.2 Simple depth estimation algorithm
  3.2.3 Difficulties of the described model
 3.3 Previous work on depth estimation
  3.3.1 Matching criterion
  3.3.2 Support of the function
  3.3.3 Optimization strategy
  3.3.4 Experimental results
  3.3.5 Intermediate conclusions
 3.4 Multiple-view depth estimation
  3.4.1 Depth estimation for multi-view video coding
  3.4.2 Two-pass optimization strategy
  3.4.3 Depth sampling of the 3D space
  3.4.4 Depth image post-processing
  3.4.5 Experimental results
 3.5 Summary and conclusions