¹Universidad Simón Bolívar, División de Física y Matemática, Departamento de Cómputo Científico y Estadística, Caracas, Venezuela. Professor and Researcher. Email: zmartinez@usb.ve

We present a methodology for extracting processes of curves in images, using a statistical summary of the directional information given in measures of location, curvature and direction associated with the pixels that compose each curve. The main purpose is to obtain measures that serve as input for the reconstruction, in vector format, of a process of curves which are of interest, so that the extracted curves can be easily stored and reconstructed based on few parameters conserving representative information of its curvature at each pixel. As starting point, the directional information obtained from a methodology of consistent curves detection is used, which includes the decomposition of the image in a directional domain contained in \mathbb{R}^2-k, with k\in\mathbb {N}. Basic summary measures criteria are proposed for this type of data and the application to four cases of satellite images for extraction of sections of rivers in these images are shown.

Key words: Curvature, Detection, Energy, Feature Selection, Image Processing, Maximum, Median, Trajectory.

Presentamos una metodología para la extracción de procesos de curvas en imágenes, mediante un resumen estadístico de la información direccional dado en medidas de localización, curvatura y dirección asociadas a los pixels que componen cada curva. El propósito principal es obtener medidas que sirvan como insumo para la reconstrucción de los procesos de curvas que sean de interés, en formato de vector, de manera que las curvas extraídas puedan ser almacenadas fácilmente y reconstruidas en base a pocos parámetros conservando información representativa de su curvatura en cada pixel. Como punto de partida se usa la información direccional obtenida a partir de la metodología de detección consistente de curvas, la cual comprende la descomposición de la imagen en un dominio direccional contenido en \mathbb{R}^2-k, con k\in\mathbb{N}. Para este tipo de datos se proponen criterios básicos para las medidas de resumen y se muestra la aplicación a cuatro casos de imágenes satelitales para la extracción de tramos de río en dichas imágenes.

Palabras clave: curvatura, detección, máximo, mediana, selección de características, procesamiento de imágenes, trayectoria.

Texto completo disponible en PDF

References

1. Candès, E., Demanet, L., Donoho, D. & Ying, L. (2006), 'Fast discrete curvelet transforms', Multiscale Modeling Simulation 5(3), 861-899.         [ Links ]

2. Candès, E. & Donoho, D. (2000a), 'Curvelets - A suprisingly efective nonadaptive representation for objects with edges', Curves and Surfaces C(2), 1-10.         [ Links ]

3. Candès, E. & Donoho, D. (2000b), 'Curvelets, multiresolution representation, and scaling laws', SPIE Wavelet Applications in Signal and Image Processing VIII 4119(1), 1-12.         [ Links ]

4. Candès, E. & Donoho, D. (2002), 'Recovering edges in ill-posed inverse problems optimality of curvelet frames', Annals of Statistics 30(3), 784-842.         [ Links ]

5. Candès, E. & Donoho, D. (2004), 'New tight frames of curvelets and optimal representations of objects with piecewise C-2 singularities', Communications on Pure and Applied Mathematics 57(2), 219-266.         [ Links ]

6. Chang, W. & Coghill, G. (2000), Line and Curve Feature Discrimination, 'Proceedings of the International ICSC Congress on Intelligent Systems and Applications (ISA 2000)', Symposium on Computational Intelligence (CI 2000), , , Wollongong, Australia.         [ Links ]

7. Cheriet, M., Kharma, N., Liu, C. & Suen, C. (2007), Character Recognition Systems, John Wiley & Sons, Inc., Hoboken, New Jersey, USA.         [ Links ]

8. Do, M. N. (2001), Directional multiresolution image representations, PhD thesis, Swiss Federal Institute of Technology, Lausanne, Switzerland.         [ Links ]

9. Do, M. & Vetterli, M. (2001), 'Contourlets: A directional multiresolution image representation', Proceedings International Conference on Image Processing 1, 357-360.         [ Links ]

10. Do, M. & Vetterli, M. (2005), 'The Contourlet Transform: An Efficient Directional Multiresolution Image Representation', IEEE Transactions on Image Processing 14(12), 2091-2106.         [ Links ]

11. Gonzalez, R. & Woods, R. (2002), Digital Image Processing, Second edn, Prentice Hall, Upper Saddle River, New Jersey, USA.         [ Links ]

12. Gonzalez, R., Woods, R. & Eddins, S. (2004), Digital Image Processing Using MATLAB, Prentice Hall.         [ Links ]

13. Martinez, Z. (2011), Detección automática de curvas en imágenes, Tesis Doctoral, Universidad Central de Venezuela, Facultad de Ciencias, Postgrado de Matemáticas, Caracas, Venezuela.         [ Links ]

14. Martínez, Z. & Ludeña, C. (2011), 'An algorithm for automatic curve detection', Computational Statistics & Data Analysis 55(6), 2158-2171.         [ Links ]

15. Myler, H. R. & Weeks, A. R. (1993), Computer Imaging Recipes in C, Prentice-Hall, Inc.         [ Links ].

16. Nixon, M. & Aguado, A. (2008), Feature Extraction & Image Processing, Second edn, Academic Press, London.         [ Links ]

17. Phoong, S., Kim, C., Vaidyanathan, P. & Ansari, R. (1995), 'A new class of two-channel biorthogonal filter banks and wavelet bases', IEEE Transactions on Signal Processing 43(3), 649-665.         [ Links ]

18. Sezgin, M. & Sankur, B. (2004), 'Survey over image thresholding techniques and quantitative performance evaluation', Journal of Electronic Imaging 13(1), 146-165.         [ Links ]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX: