Summary: Modelling and segmentation of colour images in polar representations
Jesu´s Angulo a,*, Jean Serra b
Centre de Morphologie Mathe´matique Ecole des Mines de Paris, 35 rue Saint Honore´, 77300 Fontainebleau, France
Laboratoire A2SI ESIEE, B.P. 99 93162, Noisy-le-Grand, France
Received 20 September 2005; received in revised form 14 June 2006; accepted 31 July 2006
The suitability of polar representation for quantitative image processing tasks is investigated. The classical colour polar-based rep-
resentations (HLS, HSV, etc.) lead to brightness and saturation with nonconsistent properties. After a short critical analysis of the gam-
ma correction, a new polar representation using the L1 norm is proposed. It satisfies several quantitative requirements.
The relevance of this representation is demonstrated by means of luminance/saturation histograms, which exhibit typical alignments.
Their physical interpretation leads to a model for light reception in terms of linearly regionalized spectra. A full example illustrates the
application of the histogram approach.
Colour images are multivariable functions, and for segmenting them one must go through a reducing step. It is classically obtained by
calculating a gradient module, which is then segmented as a grey tone image. An alternative solution is proposed. It is based on separated
segmentations, followed by a final merging into a unique partition. The generalisation of the top-hat transformation for extracting colour
details is also considered. These new marginal colour operators take advantage of an adaptive combination of the chromatic and the
achromatic (or the spectral and the spatio-geometric) colour components.
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