cost_volume_confidence.rst

Cost volume confidence

Theoretical basics

The purpose of this step is to compute confidence measure on the cost volume.

The available methods are :

• Ambiguity. This metric is related to a cost curve property and aims to qualify whether a point is ambiguous or not. From one pixel, the ambiguity is computed by the following formula :

  Amb(x,y,\eta) &= Card(d \in [d_min,d_max] | cv(x,y,d) < \min_{d}(cv(x,y,d)) +\eta \})
  

  , where cv(x,y,d) is the cost value at pixel (x,y) for disparity d in disparity range [d_{min},d_{max}]. From the previous equation, ambiguity integral measure is derived and it is defined as the area under the ambiguity curve. Then, ambiguity integral measure is converted into a confidence measure Confidence Ambiguity(x,y) = 1 - Ambiguity Integral.

  The ambiguity integral is by default normalized. However, the user may choose not to perform this normalization by setting the normalization parameter to false.

Sarrazin, E., Cournet, M., Dumas, L., Defonte, V., Fardet, Q., Steux, Y., Jimenez Diaz, N., Dubois, E., Youssefi, D., Buffe, F., 2021. Ambiguity concept in stereo matching pipeline. ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences.

• Risk. This metric consists in evaluating a risk interval associated with the correlation measure, and ultimately the selected disparity, for each point on the disparity map :

  Risk(x,y,\eta) &= max(d) - min(d) \text{ for d "within" } [c_{min}(x,y) ; c_{min}(x,y)+k\eta[
  

  Risk_{min}(x,y) &= \text{mean}_\eta( (1+Risk(x,y,\eta)) - Amb(x,y,\eta))
  

  Risk_{max}(x,y) &= \text{mean}_\eta( Risk(x,y,\eta))
  

  , where c_{min} is the minimum cost value of cv(x,y) at pixel (x,y). Disparities for every similarity value outside of [c_{min}(x,y) ; c_{min}(x,y)+k\eta[[min;min+eta[ are discarded for the risk computation.

  From the previous equations, risk_{min}(x,y) measure is defined as the mean of (1+Risk(x,y,\eta)) - Amb(x,y,\eta) values over \eta, whilst risk_{max}(x,y) measure is defined as the mean of Risk(x,y,k) over \eta.

• Std images intensity : this metric computes the standard deviation of the intensity.

• Confidence intervals : This metric computes upper and lower bounds for each point in the disparity map, using possibility distributions \pi :

  I(i,j) = [\min(D_{i,j}), max(D_{i,j})]
  

  D = \{d~|~\pi_{i,j}(d)\geq threshold\}
  

  \pi_{i,j}(d) = 1 - \frac{cv(i,j,d) - \min_\delta cv(i,j,\delta)}{\max_{i,j,\delta}cv(i,j,\delta) - \min_{i,j,\delta}cv(i,j,\delta)}
  

  The threshold used on \pi is 0.9 by default, but can be changed by the users.

  The intervals sould be regularized in low confidence areas. This can be done directly after computing the intervals, but it is more efficient if done after filtering. To do so, another filtering step using median_for_intervals should be added to the pipeline (see :ref:`filter` for more details).

  More info can be found in (To be published)

  I(i,j) = [\min(D_{i,j}), max(D_{i,j})]
  

  D = \{d~|~\pi_{i,j}(d)\geq threshold\}
  

  \pi_{i,j}(d) = 1 - \frac{cv(i,j,d) - \min_\delta cv(i,j,\delta)}{\max_{i,j,\delta}cv(i,j,\delta) - \min_{i,j,\delta}cv(i,j,\delta)}
  

  The threshold used on \pi is 0.9 by default, but can be changed by the users.

  The intervals sould be regularized in low confidence areas. This can be done directly after computing the intervals, but it is more efficient if done after filtering. To do so, another filtering step using median_for_intervals should be added to the pipeline (see :ref:`filter` for more details).

  More info can be found in (To be published)

Configuration and parameters

Name	Description	Type	Default value	Available value	Required
confidence_method	Cost volume confidence method	str		"std_intensity", "ambiguity", "risk", "interval_bounds"	Yes
eta_max	Maximum \eta	float	0.7	>0	No. Only available if "ambiguity" or "risk" method
eta_step	\eta step	float	0.01	>0	No. Only available if "ambiguity" or "risk" method
normalization	Ambiguity normalization	bool	false	true, false	No. Only available if "ambiguity" method
possibility_threshold	Threshold on possibility distribution	float	0.9	>=0 and <=1	No. Only available if "interval_bounds" method
regularization	Activate regularization	bool	false	true, false	No. Only available if "interval_bounds" method
ambiguity_indicator	Indicator for which ambiguity to use during regularization. Ex: If cfg contains a step "confidence_from_ambiguity.amb" then ambiguity_indicator should be "amb"	str	""		No. Only available if "interval_bounds" method
ambiguity_threshold	A pixel is regularized if threshold>ambiguity	float	0.6	>0 and <1	No. Only available if "interval_bounds" method
ambiguity_kernel_size	Ambiguity kernel size for regularization. See publication for details.	int	5	>=0	No. Only available if "interval_bounds" method
vertical_depth	Depth for graph regularization. See publication for details.	int	2	>=0	No. Only available if "interval_bounds" method
quantile_regularization	Quantile used for regularization	float	0.9	>=0 and <=1	No. Only available if "interval_bounds" method

Example

{
    "input" :
    {
        // ...
    },
    "pipeline" :
    {
        // ...
        "cost_volume_confidence":
        {
            "confidence_method": "ambiguity",
            "eta_max": 0.7,
            "eta_step": 0.01
        }
        // ...
    }
}