Disparity refinement

Theoretical basics

The purpose of this step is to refine the disparity identified in the previous step. It consists in interpolating the coefficients of similarity.

Note

The cost volume disparity dimension is sampled at the input images rate by default. Thus disparities tested are integers. However, to prevent from aliasing effects when refining the disparity map, one can use the subpix parameter. This will add subpixel disparities into the cost volume by oversampling the disparity dimension by an even factor.

The available interpolation methods are :

Vfit [Haller2010], consists in estimating a symmetrical form V from 3 points: the disparity $d$ identified at the previous step as well as $d - 1$ and $d + 1$ with their costs. The following figure represents the function to be estimated :

The interpolation is given by the following formula, where $c$ the matching cost, and $p$ the slope :

$y &= c(d + 1) + (x - 1) * p \\ y &= c(d - 1) + (x - (-1)) * -p \\ x &= (c(d - 1) - c(d + 1)) / (2*p)$
Quadratic, consists in estimating a parabola from 3 points: the disparity $d$ identified at the previous step as well as $d - 1$ and $d + 1$ with their costs. The following figure represents the function to be estimated :

$y &= ax^2 + bx + c \\ a &= (c(d-1) - 2*c(d) + c(d+1) / 2 \\ b &= (c(d+1) - c(d-1)) / 2 \\ c &= c(d) \\ x &= -b / 2a \\$

[Haller2010]

HALLER, István, PANTILIE, C., ONIGA, F., et al. Real-time semi-global dense stereo solution with improved sub-pixel accuracy. In : 2010 IEEE Intelligent Vehicles Symposium. IEEE, 2010. p. 369-376.

Note

If one of the coefficients is invalid, $d$ , $d - 1$ or $d + 1$ , interpolation is not performed.

Configuration and parameters

Name	Description	Type	Default value	Available value	Required
refinement_method	Refinement method	string		“vfit”, “quadratic”	Yes

Example

{
    "input" :
    {
        // ...
    },
    "pipeline" :
    {
        // ...
        "refinement":
        {
           "refinement_method": "vfit"
        }
        // ...
    }
}