Dense Disparity Map Estimation Respecting
Image Discontinuities
by
L.Alvarez, R.Deriche, J.Sánchez and J.Weickert

We propose an energy based method to estimate a dense disparity map between 3 images while preserving its
discontinuities accordingly to the image boundaries that may be present. We first derive a simplified expression
for the disparity that allows us to easily estimate it from a stereo pair of images. Dicsontinuities are preserved using
a regularization constraint term based on the Nagel and Enkelmann operator to better estimate and preserve the
discontinuities. We assume that the epipolar geometry is known, and we include this information in the energy model.
We derive the associated Euler-Lagrange equation and we approach the solution of the underlying partial differential
equation using a gradient descent method. In order to reduce the risk to be trapped within some irrelevant local minima,
we use a focusing strategy based on a linear Gaussian scale space.

For more details see the paper Dense Disparity Map Estimation Respecting Image Discontinuities

Next we present several experiments to illustrate the method Figure 1. We present the a classical synthetic stereo pair and the
disparity computed by our method (on the right) and the exact
disparity (on the left). If you click on the image you will see an
illustration of the focusing strategy used by the algorithm Figure 2. We present a stereo pair from the INRIA, on the left, we present
the disparity computed using a correlation technique, an on the right, the disparity
compute with our algorithm (If you click on the image you will see a movie with the
3D reconstruction. If you click here you will see an illustration of the focusing strategy
used by the algorithm, where we present the evolution of the 2 components of the
disparity map. ) Figure 3. We present a stereo pair from the INRIA. On the left, we present
the disparity computed using a correlation technique, and on the right, the disparity
computed with our algorithm (If you click on the image you will see a movie with the
3D reconstruction ) Figure 4. We present a stereo pair from the INRIA. On the left, we present
the disparity computed using a correlation technique, and on the right, the disparity
computed with our algorithm (If you click on the image you will see a movie with the
3D reconstruction )

lalvarez@dis.ulpgc.es / updated January 15, 2000