FUZZBOUND - Fuzzy boundaries extraction.

Contents

Description

Compute the fuzzy boundaries on a fuzzy categorical map following the approach in [ZK00].

Syntax

   fmap = FUZZBOUND(fmemb);
   fmap = FUZZBOUND(fmemb, 'propertyname',propertyvalue,...);

Input

fmemb : array (X,Y,N) of N categorical map providing the N fuzzy memberships of 2D points.

Properties [propertyname propertyvalues]

'thmax' : threshold on the membership value, see part 1 of the algorithm described below.

'thcon' : threshold on the confusion index, see part 2.

'thent' : entropy threshold, see part 3.

Output

fmap : map of fuzzy boundaries.

Algorithm

  1. an individual location x is selected as belonging to a fuzzy boundary if the value of its maximum fuzzy membership p_max is less than a threshold value thmax [Zhang96],
  2. the confusion index for defining fuzzy boundaries, involves two fuzzy membership values for each location: the confusion index is evaluated by 1 minus the difference between the fuzzy membership values of location x belonging to the first most likely and the second most likely classes; a threshold T is applied so that location x defines a fuzzy boundary if the confusion index is greater than a pre-defined threshold thcon [Bur96],
  3. the measure of entropy, for defining fuzzy boundaries, which uses the complete fuzzy membership values for each location. Large values indicate low accuracy in classification, while small values indicate high accuracy in classification. Then, it is logical to assert that boundaries usually occur where locations have high degrees of fuzziness, that is, big values of entropy, larger than a threshold thent [Foo95].

References

[Foo95] G.M. Foody: "Cross-entropy for the evaluation of the accuracy of a fuzzy land cover classification with fuzzy ground data", ISPRS Journal of Photogrammetry and Remote Sensing, 50:2-12, 1995. http://www.sciencedirect.com/science/article/pii/092427169590116V

[Zhang96] J.X. Zhang: "A surface-based approcah to handling uncertainties in an urban-orientated spatial database", PhD Thesis, University of Edinburgh, 1996. See also: "A surface approach to the handling of uncertainties in an integrated spatial database environment", Cartographica: International Journal for Geographic Information and Geovisualization, 33(1):23-31, 1996. http://utpjournals.metapress.com/content/y6036594410t1n3t/

[ZK97] J.X. Zhang and R.P. Kirby: "An evaluation of fuzzy approaches to mapping land cover from aerial photographs", ISPRS Journal of Photogrammetry and Remote Sensing, 52(5):193-201, 1997. http://www.sciencedirect.com/science/article/pii/S0924271697000269

[Bur96] P.A. Burrough: "Natural objects with indeterminate boundaries", in Geographic Objects with Indeterminate Boundaries, P.A. Burrough and A.U. Frank eds., Taylor & Francis (London, UK), pp.3-28, 1996. http://www.mendeley.com/research/natural-objects-indeterminate-boundaries/

[ZK00] J. Zhang and R.P. Kirby: "A comparison of alternative criteria for defining fuzzy boundaries on fuzzy categorical maps", Geo-spatial Information Science, 3(2):26-34, 2000. http://www.springerlink.com/content/p0k58753805p2101/

See also

Requires: FUZZBOUND_BASE.

Function implementation

function fmap = fuzzbound(fmemb,varargin)

parsing parameters

error(nargchk(1, 3, nargin, 'struct'));
error(nargoutchk(1, 1, nargout, 'struct'));

% mandatory parameter
if ~isnumeric(fmemb)
    error('fuzzbound:inputerror','a matrix is required in input');
end

% optional parameters
p = createParser('FUZZBOUND');
% principal optional parameters
p.addParamValue('thmax', [], @(x)isempty(x) || (isscalar(x) && x>=0. && x<=1));
p.addParamValue('thcon', [], @(x)isempty(x) || (isscalar(x) && x>=0. && x<=1));
p.addParamValue('thent', [], @(x)isempty(x) || (isscalar(x) && x>=0. && x<=1));

% parse and validate all input arguments
p.parse(varargin{:});
p = getvarParser(p);

main calculation

fmap = fuzzbound_base(fmemb, p.thmax, p.thcon, p.thent);

end % end of fuzzbound