zbMATH — the first resource for mathematics

A wavelet perspective on variational perceptually-inspired color enhancement. (English) Zbl 1328.68281
Summary: The issue of perceptually-inspired correction of color and contrast in digital images has been recently analyzed with the help of variational principles. These techniques allowed building a general framework in which the action of many already existing algorithms can be more easily understood and compared in terms of intensification of local contrast and control of dispersion around the average intensity value. In this paper we analyze this issue from the dual perspective of wavelet theory, showing that it is possible to build energy functionals of wavelet coefficients that lead to a multilevel perceptually-inspired color correction. By computing the Euler-Lagrange equations associated to the wavelet-based functionals we were able to find an analytical formula for the modification of wavelet detail coefficients that overcomes the problem of an ad-hoc selection based on empirical considerations. Besides these theoretical results, the wavelet perspective provides the computational advantage of generating much faster algorithms in comparison with the spatial variational framework.

68U10 Computing methodologies for image processing
68T45 Machine vision and scene understanding
Full Text: DOI
[1] Ambrosio, L., Gigli, N., & Savaré, G. (2005). Gradient flows in metric spaces and in the space of probability measures. Birkhauser: Lectures in Mathematics. · Zbl 1090.35002
[2] Bertalmío, M., Caselles, V., & Provenzi, E. (2009). Issues about the retinex theory and contrast enhancement. International Journal of Computer Vision, 83, 101–119. · Zbl 05671885 · doi:10.1007/s11263-009-0221-5
[3] Bertalmío, M., Caselles, V., Provenzi, E., & Rizzi, A. (2007). Perceptual color correction through variational techniques. IEEE Transactions on Image Processing, 16, 1058–1072. · Zbl 05453797 · doi:10.1109/TIP.2007.891777
[4] Bradley, A. (1999). A wavelet visible difference predictor. IEEE Transactions on Image Processing, 8, 717–730. · doi:10.1109/83.760338
[5] Cho, D., & Bui, T., (2011). Image contrast enhancement in compressed wavelet domain. pp. 3421–3424.
[6] Ciarlet, P. (1989). Introduction to numerical linear algebra and optimisation. Cambridge, MA: Cambridge University Press.
[7] Daly, S. (1992). Visible differences predictor: an algorithm for the assessment of image fidelity. In Proceedings of SPIE 1666. Human Vision, Visual Processing, and Digital Display (vol. III, pp. 2–15).
[8] Daubechies, I. (1992). Ten lectures on wavelets. Philadelphia: SIAM. · Zbl 0776.42018
[9] Di Zenzo, S. (1986). A note on the gradient of multi-image. Computer Vision, Graphics, and Image Processing, 33, 116125. · Zbl 0625.68065
[10] Gonzales, R., & Woods, R. (2002). Digital image processing. Englewood Cliffs, NJ: Prentice Hall.
[11] Held, S., Storath, M., Massopust, P., & Forster, B. (2010). Steerable wavelet frames based on the riesz transform. IEEE Transactions on Image Processing, 19(3), 653–667. · Zbl 1371.42043 · doi:10.1109/TIP.2009.2036713
[12] Laine, A., Fan, J., & Schuler, S. (1994). Mammographic feature enhancement by multiscale analysis. IEEE Transactions on Medical Imaging, 13(4), 725–740. · doi:10.1109/42.363095
[13] Land, E. (1977). The Retinex theory of color vision. Scientific American, 237, 108–128. · doi:10.1038/scientificamerican1277-108
[14] Land, E., & McCann, J. (1971). Lightness and Retinex theory. Journal of the Optical Society of America, 61(1), 1–11. · doi:10.1364/JOSA.61.000001
[15] Li, Y., Sharan, L., & Adelson, E. (2005). Compressing and companding high dynamic range images with subband architecture. In ACM Transactions on Graphics (TOG)–Proceedings of ACM SIGGRAPH 2005 (pp. 836–844).
[16] Loza, A., Bull, D., & Achim, A. (2010). Automatic contrast enhancement of low-light image based on local statistics of wavelet coefficients. In 17th IEEE International Conference on Image Processing (ICIP) (pp. 3553–3556).
[17] Lu, J., & Healy, D, Jr. (1994). Contrast enhancement of medical images using multiscale edge representation. In Proceedings of SPIE in Wavelet Applications (Vol. 2242, pp. 711–719).
[18] Mallat, S. (1999). A wavelet tour of signal processing. New York: Academic Press. · Zbl 0998.94510
[19] Michelson, A. (1927). Studies in optics. Chicago, IL: Chicago University Press. · JFM 53.0876.08
[20] Palma-Amestoy, R., Provenzi, E., Bertalmío, M., & Caselles, V. (2009). A perceptually inspired variational framework for color enhancement. IEEE Transactions on Pattern Analysis and Machine Intelligence, 31(3), 458–474. · doi:10.1109/TPAMI.2008.86
[21] Peli, E. (1990). Contrast in complex images. Journal of the Optical Society of America A, 7(10), 2032–2040. · doi:10.1364/JOSAA.7.002032
[22] Peli, E. (1997). In search of a contrast metric: Matching the perceived contrast of gabor patches at different phases and bandwidths. Vision Research, 37(23), 3217–3224. · doi:10.1016/S0042-6989(96)00262-3
[23] Provenzi, E., De Carli, L., Rizzi, A., & Marini, D. (2005). Mathematical definition and analysis of the retinex algorithm. Journal of the Optical Society of America A, 22(12), 2613–2621. · doi:10.1364/JOSAA.22.002613
[24] Provenzi, E., Fierro, M., Rizzi, A., De Carli, L., Gadia, D., & Marini, D. (2007). Random spray retinex: A new retinex implementation to investigate the local properties of the model. IEEE Transactions on Image Processing, 16, 162–171. · Zbl 05453878 · doi:10.1109/TIP.2006.884946
[25] Provenzi, E., Gatta, C., Fierro, M., & Rizzi, A. (2008). Spatially variant white patch and gray world method for color image enhancement driven by local contrast. IEEE Transactions on Pattern Analysis and Machine Intelligence, 30, 1757–1770. · Zbl 05341019 · doi:10.1109/TPAMI.2007.70827
[26] Pu, T., & Ni, G. (2000). Contrast-based image fusion using the discrete wavelet transform. Optical Engineering, 39(8), 2075–2082. · doi:10.1117/1.1303728
[27] Rizzi, A., Gatta, C., & Marini, D. (2003a). A new algorithm for unsupervised global and local color correction. Pattern Recognition Letters, 24, 1663–1677. · Zbl 01977689 · doi:10.1016/S0167-8655(02)00323-9
[28] Rizzi, A., Gatta, C., & Marini, D. (2003). Yaccd: Yet another color constancy database. In Proceedings of El. Im. 2003, IS &T/SPIEs International Symposium, Color Imaging VIII San Jose, California (USA) (Vol. 5008, pp. 24–35).
[29] Sapiro, G., & Caselles, V. (1997). Histogram modification via differential equations. Journal of Differential Equations, 135, 238–266. · Zbl 0913.35141 · doi:10.1006/jdeq.1996.3237
[30] Scheunders, P. (2002). A multivalued image wavelet representation based on multiscale fundamental forms. IEEE Transactions on Image Processing, 10(5), 568–575. · Zbl 05453292 · doi:10.1109/TIP.2002.1006403
[31] Shapley, R., & Enroth-Cugell, C. (1984). Visual adaptation and retinal gain controls, Ch. 9. In Progress in Retinal Research (Vol. 3, pp. 263–346).
[32] Starck, J., Murtagh, F., Candès, E., & Donoho, D. (2003). Gray and color image contrast enhancement by the curvelet transform. IEEE Transactions on Image Processing, 12(6), 706–717. · Zbl 1288.94013 · doi:10.1109/TIP.2003.813140
[33] Strang, G., & Nguyen, T. (1996). Wavelets and filter banks. Wellesley, MA: Wellesley-Cambridge Press. · Zbl 1254.94002
[34] Tang, J., Liu, X., & Sun, Q. (2009). A direct image contrast enhancement algorithm in the wavelet domain for screening mammograms. Journal of Selected Topics in Signal Processing, 3(1), 74–80. · doi:10.1109/JSTSP.2008.2011108
[35] Velde, K. (1999). Multi-scale color image enhancement. International Conference on Image Processing, 3, 584–587.
[36] Weber, E., (1834). De pulsu, resorptione, audita et tactu–annotationes anatomicae et physiologicae (H.E. Ross, New York: Academic Press 1978, Trans.).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.