**Name**

**amle** Level line image interpolation using the AMLE model

**Command Synopsis**

**amle** [-i *image_init*] [-n *n*] [-w *omega*] [-t *ht*] [-s *mse*] *input* *output*

-iimage_init: Initial condition image

-nn: Number of iterations for the implicit Euler scheme

-womega: Relaxation parameter, must be in ]0,2[

-tht: Time increment

-smse: Stop if the MSE between two iterations is lower than mse

input: Original cimage with missing level lines

output: Output fimage with interpolated level lines

**Function Summary**

void amle (Init , Input , Output , omega , n , ht , mse )

Cimage Init ;

Cimage Input ;

Fimage Output ;

int *n ;

float *omega , *ht ;

float *mse ;

**Description**

This module implements the numerical scheme associated to the AMLE model (absolutely minimizing Lipschitz interpolant, see the main reference [CMS98] and [Aro67][Cao98][Fro99] for related works).

The following evolution problem

= *D*^{2}*u*, with *u*(0, *x*) = *u*_{0}(*x*)

is solved using an implicit Euler scheme.
The input image corresponds to the initial function *u*_{0}, and the output
image to the solution *u*(*t*, *x*) at the time
*t* = *n*×*h*_{t} where
*n* is the number of iterations and *h*_{t} the time increment.

In practice, the input image must have the value 0 at pixel locations where no initial data have to be set (e.g. unknown values) and non 0 values to set initial data. The output image has the same values that the input image for the pixel locations set as initial data. For the other locations (set to 0 in the input image), the diffusion process of AMLE interpolates a new value.

You may use the module `amle_init`

to create the input image
from an original image, this last one being typically a quantized image:
the AMLE model will reconstuct (or ``dequantize'') the image by
interpolating the missing level lines.

It is possible to make the interpolation faster by setting values closed
to the reconstructed values at pixel locations which do not correspond
to the initial data (i.e. at locations set to 0 in the input image).
To do so, include the image of the estimated values using the `-i`

option.
In practice, the estimated image is the quantized image put in the input
of the `amle_init`

module.

**See Also**

`fmse`.

**Version 1.2**

Last Modification date : Thu Nov 29 20:23:56 2001

**Author**

Jean-Pierre D'Ales, Jacques Froment, Catalina Sbert