Scale-space segmentation
When Witkin coined the term [scale-space] [1][2] he observed that the zero-crossings of the second derivative formed a nesting tree, which defined hierarchical relations between local maxima and local minima at different scales. Specifically, zero-crossing features at coarse scales could be traced back to corresponding zero-crossing features at fine scales. This general idea has inspired several other authors to investigate coarse-to-fine schemes for image segmentation. Koenderink [3] proposed to study how iso-intensity contours evolve over scales and this approach was investigated in more detail by Lifshitz and Pizer [4]. Unfortunately, however, the intensity of image features change over scales, which implies that it is hard to trace coarse-scale image features to finer scales using intensity information. Lindeberg [5]studied the problem of linking local extrema and saddle points over scales, and proposed an image representation called the scale-space primal sketch which makes explicit the relations between structures at different scales, and also makes explicit which image features are stable over large ranges of scale including locally appropriate scales for those. Gauch and Pizer [6] studied the complementary problem of ridges and valleys in at multiple scales and developed a tool for interactive image segmentation based on multi-scale watersheds. The use of multi-scale watershed with application to the gradient map has also been investigated by Olsen and Nielsen [7] Vincken et al [8] proposed a hyperstack for defining probabilistic relations between image structures at different scales. The use of stable image structures over scales has been furthered by Ahuja and his co-workers [9] More recently, these ideas for multi-scale image segmentation by linking image structures over scales have been picked up by Florack and Kuijper [10].
There have also been numerous other works on multi-scale image segmentation. This is only a brief overview of some of the main ideas.
References
- ^ Witkin, A. P. "Scale-space filtering", Proc. 8th Int. Joint Conf. Art. Intell., Karlsruhe, Germany,1019--1022, 1983.
- ^ A. Witkin, "Scale-space filtering: A new approach to multi-scale description," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP), vol. 9, San Diego, CA, Mar. 1984, pp. 150--153.
- ^ Koenderink, Jan "The structure of images", Biological Cybernetics, 50:363--370, 1984
- ^ Lifshitz, L. and Pizer, S.: A multiresolution hierarchical approach to image segmentation based on intensity extrema, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12:6, 529 - 540, 1990.
- ^ Lindeberg, T.: Detecting Salient Blob-Like Image Structures and Their Scales with a Scale-Space Primal Sketch: A Method for Focus-of-Attention, International Journal of Computer Vision, 11(3), 283--318, 1993.
- ^ Gauch, J. and Pizer, S.: Multiresolution analysis of ridges and valleys in grey-scale images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 15:6 (June 1993), pages: 635 - 646, 1993.
- ^ Olsen, O. and Nielsen, M.: Multi-scale gradient magnitude watershed segmentation, Proc. of ICIAP 97, Florence, Italy, Lecture Notes in Computer Science, pages 6--13. Springer Verlag, September 1997.
- ^ Vincken, K., Koster, A. and Viergever, M.: Probabilistic multiscale image segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 19:2, pp. 109-120, 1997.
- ^ M. Tabb and N. Ahuja, Unsupervised multiscale image segmentation by integrated edge and region detection, IEEE Transactions on Image Processing, Vol. 6, No. 5, May 1997, 642-655.
- ^ Florack, L. and Kuijper, A.: The topological structure of scale-space images, Journal of Mathematical Imaging and Vision, 12:1, 65-79 (2000).