[GRASS-dev] some detail questions on i.segment

[Moritz Lennert]

Hi,

Another question concernant i.segment's details:

IIUC, the threshold used in region-growing is normalized using a common 
denominator defined by:

divisor = globals->nrows + globals->ncols;
(BTW, why '+',  not '*' ?)

Row and column numbers come from

globals->nrows = Rast_window_rows();
globals->ncols = Rast_window_cols();

The threshold is then adjusted to take into account object size, i.e. to 
favor merging of smaller regions compared to merging of larger regions:

adjthresh = pow(alpha2, 1. + (double) smaller / divisor);

It is this adjusted threshold that is used to decide whether to merge 
regions or not, depending on whether their similarity is smaller than 
this adjusted threshold or not.:

if (compare_double(Ri_similarity, adjthresh) == -1)

Ri_similarity is normalized by

val /= globals->max_diff;

where globals->max_diff is defined as the difference between max anf min 
values in the input file, as obtained by

Rast_get_fp_range_min_max(&(fp_range[n]), &min[n], &max[n]);

I hope that I've understood all of this correctly.

Now my question:

Are nrows and ncols region-dependent, i.e. will the divisor in the 
calculation of the adjusted vary depending on the region I defined ?

And max->diff do I understand correctly that Rast_get_fp_range_min_max() 
is region-independent, i.e. that if I take different regions of the same 
image, I will always get the same max_diff ?

If this is correct, does this mean the region size might determine 
whether some objects (or pixels) are merged or not ?

This would put into question the determination of a good threshold by 
testing on small regions as the same threshold might not have the same 
effect in larger regions, or ?

Moritz



On 20/05/16 18:40, Markus Metz wrote:
> Hi Moritz,
>
> On Wed, May 18, 2016 at 6:36 PM, Moritz Lennert
> <mlennert at club.worldonline.be> wrote:
>> Hi Markus,
>>
>> I'm working on potentially improbing the i.segment.uspo addon and am looking
>> at the possibility of including the goodness of fit output map somehow in
>> the evaluation of the quality of the segmentation.
>>
>> For that, I need to exactly understand the goodness of fit measure.
>>
>> As a starter: why is the threshold parameter (globals->alpha) squared before
>> being used in create_isegs.c (and in the calculation of the goodness of fit)
>> ? Is it because i.segment works with the squared distance and not the actual
>> distance ?
>
> Yes, i.segment works with the squared distance to avoid sqrt() which
> is slow. All that matters is if the distance is larger or smaller than
> threshold, and this relation is the same with squared values.
>
>>
>> IIUC, the worst goodness of fit measure (i.e. 1 - difference) is equal to
>> the 1 - threshold parameter value. This thus means that if one would want to
>> compare segmentations done with different threshold values by comparing mean
>> goodness of fit, for example, this would have to be scaled taking into
>> account the respective parameter value. Would something like
>>
>> ( goodness of fit - (1 - threshold parameter value) )  / threshold parameter
>> value
>>
>> make sense ?
>
> The goodness of fit is currently 1 - similarity by comparing the
> current cell values to the object's mean values. Similarity is in the
> range [0, 1], 0 means identical, 1 means maximum possible difference.
> With the region growing algorithm, that difference can actually be
> larger than the given threshold if a cell is included in an object and
> subsequent growing of the object shifts the mean away.
>
>>
>> BTW, in write_output.c, in the comments starting at line 82, there is
>> mention of a globals->threshold, but there is not threshold in the globals
>> structure... I guess this should read globals->alpha or threshold->answer,
>> or ?
>
> The comments starting at line 82 in write_output.c are an idea for
> goodness of fit, the actual goodness of fit is calculated in lines 168
> and 182.
>
> HTH,
>
> Markus
>


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