# VF Log CLP

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## General Information

- Type: CLP
- Category: VectorField
- Author: Nicolas Duchateau
- Contributor: Xavi Planes
- Contact: xavier.planes at upf.edu
- Description: Compute the logarithm of a vector field. The logarithm is approximated by an inverse scaling and squaring method as described in Arsigny et al. [1]. It uses gradient descent for both inverting the vector field and for computing its square root. Hence it has two sets of gradient descent parameters.

## Usage

### Parameters

Label | Type | Flag / Index | Default value / Channel | Description |
---|---|---|---|---|

Parameters | ||||

N composition | integer | N_compose | 10 | 2^N steps decomposition for log-exp |

Log file | file | logAcc | Output filename for the log gradient descent | |

Downsample/Resample | boolean | DSRS | false | DownSample / Resample VF |

Inverse computation | ||||

Delta | float | delta_inv | 0.01 | Gradient descent tolerance for inverse computation |

Max iterations | integer | Nmax_it_inv | 10 | Maximum number of iterations for gradient descent for inverse computation |

Rho | float | rho_inv | 1 | Weight factor for gradient descent for inverse computation |

Square root computation | ||||

Delta | float | delta_sqrt | 0.01 | Gradient descent tolerance for sqrt computation |

Max iterations | integer | Nmax_it_sqrt | 10 | Maximum number of iterations for gradient descent for sqrt computation |

Rho | float | rho_sqrt | 1 | Weight factor for gradient descent for sqrt computation |

Log extension | ||||

Expanding Iterations | integer | N_it | 0 | Number of expanding iterations |

Sigma | float | sig_decrease | 0 | Sigma for the exponential decrease |

Smoothing radius | integer | V_radius | 3 | Smoothing radius |

IO | ||||

Input Vector Field | image (fileExtensions=".mhd" type="vector") | index 0 | input | Input Vector Field |

Output Vector Field | image (fileExtensions=".mhd" type="vector") | index 1 | output | Output Vector Field |

Output recomposed Vector Field | image (fileExtensions=".mhd" type="vector") | --recomposed | output | Perform 2^N compositions of LogVectorField |

### Examples

None

## Development

Source code: C++ Source code and XML description