# Multiresolution Techniques

Multiresolution Techniques span an exceptionally broad range of algorithms, models, methods, and concepts. Central to the multiresolution approach is to somehow express short-range, mid-range, and long-range relationships explicitly. The main reasons for a multiresolution approach is one of:

• improving performance, by capturing long-range phenomena that would otherwise not be utilized
• reducing computational complexity, by allowing algorithms to work on both fine and coarse scales, rather than waiting for local pixel-level operations to converge at large scales
• improving numerical robustness (reducing problem conditioning), whereby a multiresolution transformation is essentially an algebraic pre-conditioner
• simplifying the algorithm, by making accessible long-range features that might, in some problems, be much easier to work with than pixel-level features
• improving intuition, by modeling or analyzing the problem over multiple scales, getting deeper insights into the phenomenon at hand.

Although there are, for sure, many mutiresolution approaches and algorithms which have been proposed, broadly these fall into a few groups:

Wavelet Methods

Problems in which a wavelet transform is used to decompose an image or video into multiple scales, very commonly for image/video denoising, or for feeding the coefficients at multiple scales into a classifier for image classification and segmentation.

Hierarchical Models

A model in which a pixellated, finest-scale random field is explicitly represented using a set of random fields over scales. In many cases the multi-scale model may be simpler, using principles of Markov decomposition to decouple the problem into pieces. A multi-scale model allows different models to be asserted at different scales, usually simpler or more meaningful than having a single-scale model which needs to assert all of the various sccale-dependent behaviours simultaneously.

Hierarchical Algorithms

Even if there is no explicitly hierarchical model, it is possible for the processing algorithm to be hierarchical. Best known examples include multigrid methods, whereby a single-scale linear system is solved by casting the problem onto a hierarchy, and wavelet methods in image processing, whereby the image is transferred into a set of multiscale coefficients in the wavelet domain, in which certain operations (like image compression or image denoising) are relatively simple.

## Related publications

### Journal articles

Campaigne, W., and P. Fieguth, "Frozen State Hierarchical Annealing", IEEE Transactions on Image Processing, vol. 22, no. 4, pp. 1486-1497, 2013. Details

Zhang, W.A. WongA. MishraP. Fieguth, and D. A. Clausi, "Efficient globally optimal registration of remote sensing imagery via quasi-random scale-space structural correlation energy functional", IEEE Geoscience and Remote Sensing Letters, vol. 8, issue 5, pp. 997-1001, 2011. Details

Liu, Y.A. Wong, and P. Fieguth, "Synthesis of remote sensing label fields using a tree-structured hierarchical model",IEEE Transactions on Geoscience and Remote Sensing, vol. 49, no. 6, pp. 2060-2070, 2011. Details

Azimifar, Z., M. Amiri, P. Fieguth, and E. Jernigan, "Empirical study of wavelet domain image joint statistics and proposition of an efficient correlation map", Journal of Mathematical Imaging and Vision, pp. 1-15, 2011. Details

Mishra, A.A. WongD. A. Clausi, and P. Fieguth, "Quasi-random nonlinear scale space", Pattern Recognition Letters, vol. 31, issue 13, pp. 1850 - 1859, 2010. Details

Ioannidis, M. A., S. K. AlexanderP. Fieguth, and E. Vrscay, "Hierarchical annealing for synthesis of binary images",Mathematical Geosciences, vol. 41: Springer Berlin / Heidelberg, pp. 357-378, 2009. Details

Jin, F.P. Fieguth, and L. Winger, "Wavelet video denoising with regularized multiresolution motion estimation",EURASIP Journal on Advances in Signal Processing, New York, NY, United States, Hindawi Publishing Corp., pp. 109, 2006. Details

Khellah, F. M.P. Fieguth, M. J. Murray, and M. R. Allen, "Statistical processing of large image sequences", IEEE Transactions on Image Processing, vol. 14, no. 1, pp. 80 - 93, 2005. Details

Ho, T. T., P. Fieguth, and A. S. Willsky, "Computationally efficient steady-state multiscale estimation for 1-D diffusion processes", Automatica, vol. 37, pp. 325–340, 2001. Details

Fieguth, P., "Multiply-rooted multiscale models for large-scale estimation", IEEE Transactions on Image Processing, vol. 10, pp. 1676 - 1686, 2001. Details

Schneider, M., P. Fieguth, W. C. Karl, and A. S. Willsky, "Multiscale statistical methods for the segmentation of signals and images", IEEE Transactions on Image Processing, vol. 9, no. 3, pp. 456 - 468, 2000. Details

Fieguth, P., W. C. Karl, and A. S. Willsky, "Efficient multiresolution counterparts to variational methods for surface reconstruction", Computer Vision & Image Understanding, vol. 70, no. 2: Elsevier Science Inc., pp. 157 - 176, 1998. Details

Fieguth, P., D. Menemenlis, and C. Wunsch, "Mapping Mediterranean altimeter data with a multiresolution optimal interpolation algorithm", Journal of Atmospheric and Oceanic Technology, no. 15, pp. 535-546, 1998. Details

Irving, W. W., P. Fieguth, and A. S. Willsky, "An overlapping tree approach to multiscale stochastic modeling and estimation", IEEE Transactions on Image Processing, vol. 6, no. 11, pp. 1517 - 1529, 1997. Details

Wunsch, C., D. Menemenlis, P. Fieguth, and A. S. Willsky, "Adaptation of a fast optimal interpolation algorithm to the mapping of oceanographic data", Journal of Geophysical Research, vol. 102, issue C5: AGU, pp. 10573 - 10584, 1997. Details

Fieguth, P., and A. S. Willsky, "Fractal estimation using models on multiscale trees", IEEE Transactions on Signal Processing, vol. 44, no. 5, pp. 1297 - 1300, 1996. Details

Fieguth, P., W. C. Karl, A. S. Willsky, and C. Wunsch, "Multiresolution optimal interpolation and statistical analysis of Topex/Poseidon satellite altimetry", IEEE Transactions on Geoscience and Remote Sensing, vol. 33, no. 2, pp. 280 - 292, 1995. Details

### Conference papers

Li, E.M. J. ShafieeF. Kazemzadeh, and A. Wong, "Sparse Reconstruction of Compressed Sensing Multi-spectral Data using Cross-Spectral Multi-layered Conditional Random Field Model", SPIE optics and photonics 2015, San Diego, SPIE , May, Accepted. Details

Liu, L.P. Fieguth, M. Pietikäinen, and S. Lao, "Median Robust Extended Local Binary Pattern for Texture Classification", IEEE International Conference on Image Processing, Accepted. Details

Kasiri, K.P. Fieguth, and D. A. Clausi, "Cross modality label fusion in multi-atlas segmentation", IEEE International Conference on Image Processing, 2014. Details

Barshan, E.C. Scharfenberger, M. Lamm, and P. Fieguth, "Resolution Enhancement Based on Shifted Superposition",Society for Information Display's Week 2015, June, 2015. Details

Gawish, A., and P. Fieguth, "External forces for active contours using the undecimated wavelet transform", accepted, IEEE International Conference on Image Processing, Québec city, Québec, Canada, 2015. Details

Boroomand, A., B. Tan, A. Wong, and K. Bizheva, "Axial resolution improvement in spectral domain optical coherence tomography using a depth-adaptive maximum-a-posterior framework", SPIE Photonics West (BiOS), San Francisco, USA, 2015. Details

Boroomand, A.M. J. ShafieeA. Wong, and K. Bizheva, "Lateral resolution enhancement via imbricated spectral domain optical coherence tomography in a maximum-a-posterior reconstruction framework", SPIE Photonics West (BiOS), San Francisco, USA, 2015. Details

Gawish, A.P. Fieguth, S. Marschall, and K. Bizheva, "Undecimated Hierarchical Active Contours for OCT Image Segmentation", IEEE International Conference on Image Processing ICIP, 2014. Details

Kasiri, K.D. A. Clausi, and P. Fieguth, "Multi-modal image registration using structural features", 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC'14), 2014. Details

Carter, K., S. Marschall, A. GawishP. Fieguth, L. Sorbara, and K. Bizheva, "Accuracy evaluation of scleral lens thickness and radius of curvature using high-resolution SD- and SS-OCT", SPIE Photonics West, 2014. Details

Wong, A., A. K. Scott, E. Li, and R. Amelard, "Continuous sea ice thickness estimation using a joint MODIS and AMSR-E guided variational model", IEEE International Geoscience and Remote Sensing Symposium, March, 2013 Details

Shabani, A. H., J. S. Zelek, and D. A. Clausi, "Evaluation of local spatio-temporal salient feature detectors for human action recognition", IEEE Canadian Conference on Computer and Robot Vision, May. Details

Wong, A., "Perceptual Structure Distortion Ratio: An image quality metric based on complex phase order", 9th Canadian Conference on Computer and Robot Vision, 2012. Details

Kumar, A.A. WongD. A. Clausi, and P. Fieguth, "Multi-scale tensor vector field active contour", IEEE Conference on Image Processing, 2012. Details

Shafiee, M. J.A. Wong, and Z. Azimifar, "A Novel Hierarchical Model-Based Frame Rate Up-Conversion via Spatio-temporal Conditional Random Fields", IEEE International Symposium of Multimedia , 2012. Details

Shabani, A. H.D. A. Clausi, and J. S. Zelek, "Improved Spatio-temporal Salient Feature Detection for Action Recognition", British Machine Vision Conference, University of Dundee, Dundee, UK, August, 2011. Details

Wong, A.A. MishraD. A. Clausi, and P. Fieguth, "Quasi-random scale space approach to robust keypoint extraction in high-noise environments", 7th Canadian Conference on Computer and Robot Vision, Ottawa, Ontario, Canada, March, 2010. Details

Shabani, A. H., J. S. Zelek, and D. A. Clausi, "Human action recognition using salient opponent-based motion features",7th Canadian Conference on Computer and Robotic Vision, Ottawa, Ontario, Canada, pp. 362 - 369, March, 2010. Details

Gangeh, M. J., A. H. Shabani, and M. Kamel, "Nonlinear scale-space theory in texture classification using multiple classifier systems", International Conference on Image Analysis and Recognition, June, 2010. Details

Shabani, A. H., J. S. Zelek, and D. A. Clausi, "Robust Local Video Event Detection for Action Recognition", Advances in Neural Information Processing Systems (NIPS), Machine Learning for Assistive Technology Workshop, Whistler, Canada, December, 2010. Details

Liu, Y.A. Wong, and P. Fieguth, "Remote sensing image synthesis", 2010 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), pp. 2467 -2470, 2010. Details

Shabani, A. H.D. A. Clausi, and J. S. Zelek, "Towards a robust spatio-temporal interest point detection for human action recognition", IEEE Canadian Conference on Computer and Robot Vision, Kelowna, BC, Canada, Kelowna, British Columbia, Canada, pp. 237-243, February, 2009. Details

Mishra, A.P. Fieguth, and D. A. Clausi, "A robust modular wavelet network based symbol classifier", 6th International Conference on Image Analysis and Recognition (ICIAR), Halifax, Nova Scotia, Canada, July 6 - 9, 2009. Details

Mohebi, A.Y. Liu, and P. Fieguth, "Hierarchical sampling with constraints", 6th International Conference on Image Analysis and Recognition, pp. 23 - 32, 2009. Details

Liu, Y., and P. Fieguth, "Image resolution enhancement with hierarchical hidden fields", 6th International Conference on Image Analysis and Recognition, pp. 73 - 82, 2009. Details

Liu, Y., and P. Fieguth, "Parallel hidden hierarchical fields for multi-scale reconstruction", 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, pp. 70–83, 2009. Details

Wong, A.D. A. Clausi, and P. Fieguth, "Phase-adaptive image signal fusion using complex-valued wavelets", 19th International Conference on Pattern Recognition, Tampa, Florida, USA, Dec. 8 - 11, 2008. Details

Wong, A.D. A. Clausi, and P. Fieguth, "Automatic registration of inter-band and inter-sensor images using robust complex wavelet feature representations", 5th Workshop on Pattern Recognition for Remote Sensing, Tampa, Florida, USA, Dec. 7, 2008. Details

Amiri, M., Z. Azimifar, and P. Fieguth, "Correlated non-linear wavelet shrinkage", 15th IEEE International Conference on Image Processing, 2008, pp. 2348 - 2351, 2008. Details

Yu, Q., and D. A. Clausi, "Joint image segmentation and interpretation using iterative semantic region growing on SAR sea ice imagery", 18th International Conference on Pattern Recognition (ICPR), vol. 2, Hong Kong, pp. 223 - 226, Aug. 21 - 24, 2006. Details

Kachouie, N. Nezamoddin, and P. Fieguth, "A combined Bayesshrink wavelet-ridgelet technique for image denoising",2006 IEEE International Conference on Multimedia and Expo, pp. 1917 - 1920, 2006. Details

Wesolkowski, S., and P. Fieguth, "Hierarchical region mean-based image segmentation", 3rd Canadian Conference on Computer and Robot Vision: IEEE Computer Society, pp. 30, 2006. Details

Jin, F.P. Fieguth, and L. Winger, "Image denoising using complex wavelets and Markov prior models", 12th IEEE International Conference on Image Processing: Springer, 2005. Details

Alexander, S. K.P. Fieguth, and E. Vrscay, "Discrete-state modeling of porous media over multiple scales", SIAM Conference on Mathematical and Computational Issues in the Geosciences, Avignon, 2005. Details

Alexander, S. K.P. Fieguth, and E. Vrscay, "Hierarchical annealing of porous media", SIAM Conference on Mathematical and Computational Issues in the Geosciences, Avignon, 2005. Details

Kachouie, N. Nezamoddin, and P. Fieguth, "BayesShrink ridgelets for image denoising", 2004 International Conference on Image Analysis and Recognition, 2004. Details

Fieguth, P., "Hierarchical MCMC sampling", 2004 International Conference on Image Analysis and Recognition, 2004. Details

Wesolkowski, S., and P. Fieguth, "Hierarchical regions for image segmentation", 2004 International Conference on Image Analysis and Recognition, Portugal, 2004. Details

Jin, F.P. Fieguth, and L. Winger, "Motion-compensated wavelet video denoising", 2004 International Conference on Image Analysis and Recognition, Portugal, 2004. Details

Fieguth, P., and S. K. Alexander, "Parameterized hierarchical annealing for scientific models", 2004 International Conference on Image Analysis and Recognition, Portugal, 2004. Details

Azimifar, Z.P. Fieguth, and E. Jernigan, "Textures and wavelet-domain joint statistics", 2004 International Conference on Image Analysis and Recognition, Portugal, 2004. Details

Alexander, S. K.P. Fieguth, and E. Vrscay, "Hierarchical annealing for scientific models", 37th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Montreal, 2004. Details

Azimifar, Z.P. Fieguth, and E. Jernigan, "Hierarchical Markov models for wavelet-domain statistics", 2003 IEEE Workshop on Statistical Signal Processing, 2003. Details

Fieguth, P., "Hierarchical posterior sampling for Gauss-Markov random fields", 2003 International Conference on Image Processing, vol. 1, 2003. Details

Jin, F.P. Fieguth, L. Winger, and E. Jernigan, "Image enhancement by frequency extrapolation using a multiscale edge representation", CCECE '03, Montreal, 2003. Details

Alexander, S. K.P. Fieguth, and E. Vrscay, "Hierarchical annealing for random image synthesis", Fourth International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2003), Portugal, 2003. Details

Fieguth, P., "Hierarchical posterior sampling for images and random fields", ICIP '03, vol. 1, Spain, 2003. Details

Azimifar, Z.P. Fieguth, and E. Jernigan, "Towards random field modeling of wavelet statistics", International Conference on Image Processing, Rochester, NY, 2002. Details

Azimifar, Z.P. Fieguth, and E. Jernigan, "Hierarchical multiscale modeling of wavelet-based correlations",Structural, Syntactic, and Statistical Pattern Recognition, Joint IAPR International Workshops, pp. 850–860, 2002. Details

Azimifar, Z.P. Fieguth, and E. Jernigan, "Modeling the correlation structure of images in the wavelet domain", 14th Canadian Conference on Electrical and Computer Engineering , vol. 2, Toronto, pp. 1123 - 1127, 2001. Details

Azimifar, Z.P. Fieguth, and E. Jernigan, "Wavelet shrinkage with correlated wavelet coefficients", International Conference on Image Processing, vol. 3, Greece, 2001. Details

Carballo, G. F., and P. Fieguth, "Multiresolution Network Flow Phase Unwrapping", IEEE 2000 International Geoscience and Remote Sensing Symposium, vol. 2, pp. 755 -757, 2000. Details

Fieguth, P.F. M. Khellah, M. J. Murray, and M. R. Allen, "Data fusion of sea-surface temperature data", IEEE Geoscience and Remote Sensing Society, vol. 5, pp. 2111 - 2113, 2000. Details

Fieguth, P., "Foveated multiscale models for large-scale estimation", International Conference on Image Processing, 1999. Details

Ho, T. T., P. Fieguth, and A. S. Willski, "Recursive multiscale estimation of space-time random fields", International Conference on Image Processing, vol. 2, 1999. Details

Fieguth, P., M. R. Allen, and M. J. Murray, "Hierarchical methods for global-scale estimation problems", IEEE Canadian Conference on Electrical and Computer Engineering, vol. 1, Waterloo, Canada, pp. 161 - 164, 1998. Details

Fieguth, P., "Global-Scale Three-Dimensional Statistical Estimation", IEEE MDSP '98, Alpbach, Austria, pp. 247 - 250, 1998. Details

Ho, T. T., P. Fieguth, and A. S. Willsky, "Computationally efficient multiscale estimation of large-scale dynamic systems", International Conference on Image Processing, pp. 274 - 278, 1998. Details

Fieguth, P., "Multipole-motivated reduced-state estimation", International Conference on Image Processing, vol. 1, Chicago, 1998. Details

Willsky, A. S., T. T. Ho, and P. Fieguth, "Multiscale modeling with temporal dynamics", 21st International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Atlanta, GA, pp. 3098 - 3101, 1996. Details

Ho, T. T., P. Fieguth, D. Menemenlis, and A. S. Willsky, "TOPEX/POSEIDON and ERS Altimeter Mapping via Efficient Multiresolution Optimal Interpolation", AGU Fall Meeting 1996, San Francisco, 1996. Details

Schneider, M., P. Fieguth, W. C. Karl, and A. S. Willsky, "Multiscale Methods for the Segmentation of Images",ICASSP '96, vol. 4, pp. 2247 - 2250, 1996. Details

Karl, W. C., M. Schneider, W. W. Irving, P. Fieguth, M. M. Daniel, H. Krim, C. H. Fosgate, and A. S. Willsky,"Multiresolution stochastic models: methodology and applications in remote sensing, image processing, and radar",IEEE MDSP '96, pp. 88 - 89, 1996. Details

Fieguth, P., A. S. Willsky, D. Menemenlis, and C. Wunsch, "A general multiresolution approach to the estimation of dense fields in remote sensing", International Conference on Image Processing, vol. 1, Lausanne, Switzerland, pp. 609 - 612, 1996. Details

Fieguth, P., W. C. Karl, and A. S. Willsky, "Multiresolution statistical analysis and assimilation of large ocean data sets",20th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), vol. 5, pp. 2781 -2784 vol.5, 1995. Details

Fieguth, P., and A. S. Willsky, "Multiresolution models for fractals and their uses in statistical signal and image processing", IEEE Conference on Nonlinear Signal and Image Processing, Greece, pp. 779 - 782, 1995. Details

Fieguth, P., W. W. Irving, and A. S. Willsky, "Multiresolution model development for overlapping trees via canonical correlation analysis", International Conference on Image Processing, vol. 1, pp. 45 - 48, 1995. Details

Fieguth, P., A. S. Willsky, and W. C. Karl, "Multiresolution stochastic imaging of satellite oceanographic altimetric data",Image Processing, 1994. Proceedings. ICIP-94., IEEE International Conference, vol. 2, pp. 1 -5 vol.2, nov, 1994. Details

Fieguth, P., W. C. Karl, and A. S. Willsky, "Multiresolution stochastic processing of Topex/Poseidon oceanographic altimetry", IEEE OCEANS'94, vol. 1, pp. 851 - 855, 1994. Details

Willsky, A. S., P. Fieguth, and W. C. Karl, "A Statistical Multiscale Approach To Mapping Altimetric Data", Neural and Stochastic Methods in Image and Signal Processing III, vol. 2304, no. 1: SPIE, pp. 94 - 104, 1994. Details

Irving, W. W., A. S. Willsky, M. M. Daniel, W. C. Karl, and P. Fieguth, "Efficient Algorithms for Gauss-Markov Random Fields", Eighth IEEE Multi-Dimensional Signal Processing Workshop, pp. 160 - 161, 1993. Details

### Book chapters

Fieguth, P, W. Campaigne, and S. K. Alexander, "Frozen-State Hierarchical Annealing", Image Analysis and Recognition, vol. 4141: Springer Berlin / Heidelberg, pp. 41-52, 2006. Details

Fieguth, P., Handbook of Image and Video Processing (2nd Ed.), : Academic Press, pp. 361-276, 2004. Details

Fieguth, P, Handbook of Image and Video Processing, : Academic Press, 1999. Details

### Books

Fieguth, P., "Statistical Image Processing and Multidimensional Modeling", Information Science and Statistics: Springer, 2010. Details

### Theses

Campaigne, W., "Frozen-State Hierarchical Annealing", Department of Systems Design Engineering, 2012. Details

Clausi, D. A., "Texture Segmentation of SAR Sea Ice Imagery", Department of Systems Design Engineering, Waterloo, Ontario, Canada, University of Waterloo, pp. 176, 1996. Details

Fieguth, P., "Application of Multiscale Estimation to Large Multidimensional Imaging and Remote Sensing Problems",Department of Electrical Engineering and Computer Science, Cambridge, Massachusetts, Massachusetts Institute of Technology, 1995. Details