A mathematical approach to the segmentation of sea-ice SAR images

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Abstract
This paper discusses basic mathematical formulations to clarify the problem of automatic segmentation of sea-ice remote sensing imagery. The work is illustrated with a SAR image. The main issue is a robust and automatic analysis of sea-ice conditions from remotely sensed data. The paper reveals some of the potential and essential features that are hidden in a class of filters often known as simple ‘shrink and expand operators’. The intensity of radiation from the ground is idealized as a measure which may have singularities. Absolutely calibrated digital images represent this measure where the measurable set are restricted to unions of picture elements. A related proposed martingale stopping time scheme makes image segmentation robust to changes in resolution. Tunable segmentations based on mathematical morphology can be controlled to give optimal ‘physically proper’ sets which are independent of calibration. This approach introduces physical knowledge, time aspects, and random geometry to the problem of image segmentation.

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