Modelling and segmentation of colour images in polar representations

The suitability of polar representation for quantitative image processing tasks is investigated. The classical colour polar-based representations (HLS, HSV, etc.) lead to brightness and saturation with nonconsistent properties. After a short critical analysis of the gamma 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.