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 )

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