An Improved ‘Gas of Circles’ Higher-Order Active Contour Model and Its Application to Tree Crown Extraction
A central task in image processing is to find the region in the image corresponding to an entity. In a number of problems, the region takes the form of a collection of circles, e.g. tree crowns in remote sensing imagery; cells in biological and medical imagery. In , a model of such regions, the ‘gas of circles’ model, was developed based on higher-order active contours, a recently developed framework for the inclusion of prior knowledge in active contour energies. However, the model suffers from a defect. In , the model parameters were adjusted so that the circles were local energy minima. Gradient descent can become stuck in these minima, producing phantom circles even with no supporting data. We solve this problem by calculating, via a Taylor expansion of the energy, parameter values that make circles into energy inflection points rather than minima. As a bonus, the constraint halves the number of model parameters, and severely constrains one of the two that remain, a major advantage for an energy-based model. We use the model for tree crown extraction from aerial images. Experiments show that despite the lack of parametric freedom, the new model performs better than the old, and much better than a classical active contour.
KeywordsActive Contour Gradient Descent Algorithm Local Energy Minimum Marked Point Process Phantom Region
Unable to display preview. Download preview PDF.
- 1.Horváth, P., Jermyn, I.H., Kato, Z., Zerubia, J.: A higher-order active contour model for tree detection. In: Proc. International Conference on Pattern Recognition (ICPR), Hong Kong, China (2006)Google Scholar
- 4.Foulonneau, A., Charbonnier, P., Heitz, F.: Geometric shape priors for region-based active contours. In: Proc. IEEE International Conference on Image Processing (ICIP), vol. 3, pp. 413–416 (2003)Google Scholar
- 5.Paragios, N., Rousson, M.: Shape priors for level set representations. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 78–92. Springer, Heidelberg (2002)Google Scholar
- 6.Leventon, M., Grimson, W., Faugeras, O.: Statistical shape influence in geodesic active contours. In: Proc. IEEE Computer Vision and Pattern Recognition (CVPR), Hilton Head Island, South Carolina, USA, vol. 1, pp. 316–322 (2000)Google Scholar
- 7.Rochery, M., Jermyn, I.H., Zerubia, J.: Higher order active contours and their application to the detection of line networks in satellite imagery. In: Proc. IEEE Workshop Variational, Geometric and Level Set Methods in Computer Vision, at ICCV, Nice, France (2003)Google Scholar
- 8.Gougeon, F.A.: Automatic individual tree crown delineation using a valley-following algorithm and rule-based system. In: Hill, D., Leckie, D. (eds.) Proc. Int’l Forum on Automated Interpretation of High Spatial Resolution Digital Imagery for Forestry, Victoria, British Columbia, Canada, pp. 11–23 (1998)Google Scholar
- 9.Larsen, M.: Finding an optimal match window for Spruce top detection based on an optical tree model. In: Hill, D., Leckie, D. (eds.) Proc. of the International Forum on Automated Interpretation of High Spatial Resolution Digital Imagery for Forestry, Victoria, British Columbia, Canada, pp. 55–66 (1998)Google Scholar
- 10.Perrin, G., Descombes, X., Zerubia, J.: A marked point process model for tree crown extraction in plantations. In: Proc. IEEE International Conference on Image Processing (ICIP), Genova, Italy (2005)Google Scholar