pandora2d.multiscale.model_estimation

This module contains methods associated to the estimation model for the MVP

Attributes

COMPRESSION_FACTOR

Functions

get_invalid_disp_mask(→ numpy.typing.NDArray)	Compute mask for points equal to invalid_disp in row_map or col_map.
add_mesh_validity_band(→ xarray.Dataset)	Add a 'MESH_validity' band to an existing validity dataset.
make_position_vectors(→ Tuple[numpy.typing.NDArray, ...)	Construct initial et final positions vectors using dataset_disp_maps coordinates
make_polynomial_design_matrix(→ numpy.typing.NDArray)	Construct a 2D polynomial design matrix up to a given degree.
check_nb_observations(design_matrix)	Check if we have more parameters than observations, in which case a ValueError is raised.
estimate_model(→ Tuple[numpy.typing.NDArray, ...)	Estimate deformation model from initial positions to final positions
estimate_model_cholesky(→ Tuple[numpy.typing.NDArray, ...)	Estimate deformation model from initial positions to final positions
estimate_init_disparity_grids(...)	Estimate initial disparity grids (rows and columns) according to scale factor
get_next_shape_mesh_list(→ List[int])	Return list of shape for mesh for next resolution.
concatenate_estimated_grids(→ numpy.typing.NDArray)	Concatenate the estimated disparity grids computed by mesh
get_init_disparity_grids(→ Tuple[numpy.typing.NDArray, ...)	Return initial disparity grid after computing least square coefficients
get_init_disparity_grids_with_mesh(...)	Return initial disparity grid after computing least square coefficients

Module Contents

pandora2d.multiscale.model_estimation.COMPRESSION_FACTOR = 0.5

pandora2d.multiscale.model_estimation.get_invalid_disp_mask(row_map: numpy.typing.NDArray, col_map: numpy.typing.NDArray, invalid_disp: int | float) → numpy.typing.NDArray

Compute mask for points equal to invalid_disp in row_map or col_map. This mask is then used to remove invalid points from position vectors.

Parameters:

• row_map – row disparity map

• col_map – col disparity map

• invalid_disp – invalid disparity value

Returns:

invalid mask for position matrix

pandora2d.multiscale.model_estimation.add_mesh_validity_band(dataset_disp_maps: xarray.Dataset) → xarray.Dataset

Add a ‘MESH_validity’ band to an existing validity dataset.

Parameters:

dataset_disp_maps – xarray Dataset containing the validity data and the disparity maps

pandora2d.multiscale.model_estimation.make_position_vectors(dataset_disp_maps: xarray.Dataset) → Tuple[numpy.typing.NDArray, numpy.typing.NDArray, numpy.typing.NDArray, numpy.typing.NDArray]

Construct initial et final positions vectors using dataset_disp_maps coordinates and disparity maps. To reduce numerical instability, a compression factor is used to create the final and initial position grids.

For the least squares problem y=Xb:

• X is constructed using init_row_coords and init_col_coords

• y is either final_row_coords or final_col_coords.

Parameters:

dataset_disp_maps – disparity maps dataset

Returns:

initial position vectors and final position vectors

pandora2d.multiscale.model_estimation.make_polynomial_design_matrix(row_init_coords: numpy.typing.NDArray, col_init_coords: numpy.typing.NDArray, degree: int) → numpy.typing.NDArray

Construct a 2D polynomial design matrix up to a given degree.

It generates all polynomial combination of the input variables col_init_coords and row_init_coords.

For the least squares problem y=Xb, X is the design matrix.

Parameters:

• col_init_coords – initial column positions

• row_init_coords – initial row positions

• degree – polynomial degree

Returns:

polynomial design matrix

pandora2d.multiscale.model_estimation.check_nb_observations(design_matrix: numpy.typing.NDArray)

Check if we have more parameters than observations, in which case a ValueError is raised.

Parameters:

design_matrix – Design matrix

pandora2d.multiscale.model_estimation.estimate_model(dataset_disp_maps: xarray.Dataset, degree: int) → Tuple[numpy.typing.NDArray, numpy.typing.NDArray, numpy.typing.NDArray, numpy.typing.NDArray]

Estimate deformation model from initial positions to final positions by resolving y=Xb.

Parameters:

• degree – polynomial degree

• dataset_disp_maps – disparity maps dataset

Returns:

least square solution and sum of residuals for rows and columns

pandora2d.multiscale.model_estimation.estimate_model_cholesky(dataset_disp_maps: xarray.Dataset, degree: int, lambda_ridge: int | float | None = None) → Tuple[numpy.typing.NDArray, numpy.typing.NDArray, numpy.typing.NDArray, numpy.typing.NDArray]

Estimate deformation model from initial positions to final positions by resolving y=Xb using Cholesky decomposition.

We have X.T*X*b = X.T*y and X.T*X = L*L.T with L a lower triangular matrix. Then, using Cholesky decomposition we can resolve L*z=X.T*y and L.T*b = z.

If a value is specified for lamba_ridge, Ridge regularization is used.

Parameters:

• dataset_disp_maps – disparity maps dataset

• degree – polynomial degree

• lambda_ridge – Ridge regularization factor

Returns:

least square solution and sum of residuals for rows and columns

pandora2d.multiscale.model_estimation.estimate_init_disparity_grids(dataset_disp_maps: xarray.Dataset, coefficients_row: numpy.typing.NDArray, coefficients_col: numpy.typing.NDArray, degree: int, next_resolution_shape: Tuple) → Tuple[numpy.typing.NDArray, numpy.typing.NDArray]

Estimate initial disparity grids (rows and columns) according to scale factor and coefficients of least squares resolution.

Parameters:

• dataset_disp_maps – disparity maps dataset

• coefficients_row – row coefficients computed by least squares resolution

• coefficients_col – col coefficients computed by least squares resolution

• degree – polynomial degree

• next_resolution_shape – shape of image for next resolution

Returns:

initial disparity grids for rows and columns

pandora2d.multiscale.model_estimation.get_next_shape_mesh_list(next_resolution_shape: int, nb_mesh: int) → List[int]

Return list of shape for mesh for next resolution. This list is then used to estimate initial disparity grid at next resolution with the right shape for each mesh.

Parameters:

• next_resolution_shape – next resolution shape (row or column)

• nb_mesh – number of mesh (row or column)

Returns:

List of shape by mesh (row or column)

pandora2d.multiscale.model_estimation.concatenate_estimated_grids(estimated_init_grid_list: List[numpy.typing.NDArray], nb_row_mesh: int, nb_col_mesh: int) → numpy.typing.NDArray

Concatenate the estimated disparity grids computed by mesh and return the full initial disparity grid for next resolution.

Parameters:

• estimated_init_grid_list

• nb_row_mesh – number of mesh for rows

• nb_col_mesh – number of mesh for columns

Returns:

full estimated initial disparity grid for next resolution

pandora2d.multiscale.model_estimation.get_init_disparity_grids(dataset_disp_maps: xarray.Dataset, multiscale_cfg: Dict, next_resolution_shape: Tuple) → Tuple[numpy.typing.NDArray, numpy.typing.NDArray, numpy.typing.NDArray, numpy.typing.NDArray]

Return initial disparity grid after computing least square coefficients

Parameters:

• dataset_disp_maps – disparity maps dataset

• multiscale_cfg – multiscale pipeline configuration

• next_resolution_shape – shape of image for next resolution

Returns:

initial disparity grids for rows and columns and sum of squared residuals

pandora2d.multiscale.model_estimation.get_init_disparity_grids_with_mesh(dataset_disp_maps: xarray.Dataset, multiscale_cfg: Dict, next_resolution_shape: Tuple) → Tuple[numpy.typing.NDArray, numpy.typing.NDArray, numpy.typing.NDArray, numpy.typing.NDArray, xarray.Dataset]

Return initial disparity grid after computing least square coefficients for each mesh

Parameters:

• dataset_disp_maps – disparity maps dataset

• multiscale_cfg – multiscale pipeline configuration

• next_resolution_shape – shape of image for next resolution

Returns:

initial disparity grids for rows and columns and RMSE for row and columns