**Name**

**ll_boundaries** Extract meaningful boundaries (contrasted level lines) from a Fimage

**Command Synopsis**

**ll_boundaries** [-e *eps*] [-a] [-w] [-s *step*] [-p *p*] [-t *tree*] [-z] *in* *out*

-eeps: -log10(max. number of false alarms), default 0

-a : get all contrasted level lines (not only maximal ones)

-w : select weak maximality

-sstep: quantization step (bilinear), default 1.

-pp: sampling precision (bilinear), default 2

-ttree: use a precomputed FLST tree

-z : use zero order instead of bilinear interpolation

in: input Fimage

out: output boundaries (Flists)

**Function Summary**

Flists ll_boundaries (in , tree , eps , all , step , precision , z , weak )

Fimage in ;

Shapes tree ;

float *eps , *step ;

int *precision ;

char *all , *z , *weak ;

**Description**

This modules computes all the level lines (that is, the connected
components of the boundaries of the level sets) of an image
(with the same options `-s`

, `-p`

, `-z`

and `-t`

as the `ll_extract`

module) and keeps the most contrasted ones.
The detection is made using a thresholding function balancing between
the minimum contrast (gradient norm) along the curve and the
length of the curve. Unless `-a`

option is specified, only
on representant (the most meaningful one) is kept for each
monotone sequence of meaningful level lines (that is, a sequence
of level lines included in each others, with no inclusion
branching and no contrast reversal).
The thresholding function ensures
that at most 10^{-eps} false detections could occur by chance
with independent random gradient values (see [DMM01]).

Notice that contrary to the `ll_edges`

detection, this
module is constrained to keep full (ie closed) level lines and
cannot break them into parts.

The result is a collection of curves stored in a Flists structure.

**See Also**

`fderiv`, `fhisto`, `flst`, `flstb_boundary`, `flst_bilinear`, `flst_boundary`, `flstb_quantize`, `fsaddles`, `sintegral`.

**Version 1.1**

Last Modification date : Tue Apr 8 16:46:18 2003

**Author**

Lionel Moisan