{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:27:58Z","timestamp":1760239678881,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2020,12,12]],"date-time":"2020-12-12T00:00:00Z","timestamp":1607731200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"publisher","award":["2016\/23\/B\/ST10\/01151"],"award-info":[{"award-number":["2016\/23\/B\/ST10\/01151"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Hyperspectral images provide complex information about the Earth\u2019s surface due to their very high spectral resolution (hundreds of spectral bands per pixel). Effective processing of such a large amount of data requires dedicated analysis methods. Therefore, this research applies, for the first time, the degree of multifractality to the global description of all spectral bands of Airborne Visible\/Infrared Imaging Spectrometer (AVIRIS) data. Subsets of four hyperspectral images, presenting four landscape types, are analysed. In particular, we verify whether multifractality can be detected in all spectral bands. Furthermore, we analyse variability in multifractality as a function of wavelength, for data before and after atmospheric correction. We try to identify absorption bands and discuss whether multifractal parameters provide additional value or can help in the problem of dimensionality reduction in hyperspectral data or landscape type classification.<\/jats:p>","DOI":"10.3390\/rs12244077","type":"journal-article","created":{"date-parts":[[2020,12,13]],"date-time":"2020-12-13T23:39:36Z","timestamp":1607902776000},"page":"4077","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["What Can Multifractal Analysis Tell Us about Hyperspectral Imagery?"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2207-3468","authenticated-orcid":false,"given":"Micha\u0142","family":"Krupi\u0144ski","sequence":"first","affiliation":[{"name":"Centrum Bada\u0144 Kosmicznych Polskiej Akademii Nauk (CBK PAN), Bartycka 18A, 00-716 Warszawa, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9946-3547","authenticated-orcid":false,"given":"Anna","family":"Wawrzaszek","sequence":"additional","affiliation":[{"name":"Centrum Bada\u0144 Kosmicznych Polskiej Akademii Nauk (CBK PAN), Bartycka 18A, 00-716 Warszawa, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9266-0000","authenticated-orcid":false,"given":"Wojciech","family":"Drzewiecki","sequence":"additional","affiliation":[{"name":"Department of Photogrammetry, Remote Sensing of Environment and Spatial Engineering, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1165-0503","authenticated-orcid":false,"given":"Ma\u0142gorzata","family":"Jenerowicz","sequence":"additional","affiliation":[{"name":"Centrum Bada\u0144 Kosmicznych Polskiej Akademii Nauk (CBK PAN), Bartycka 18A, 00-716 Warszawa, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8634-436X","authenticated-orcid":false,"given":"Sebastian","family":"Aleksandrowicz","sequence":"additional","affiliation":[{"name":"Centrum Bada\u0144 Kosmicznych Polskiej Akademii Nauk (CBK PAN), Bartycka 18A, 00-716 Warszawa, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,12]]},"reference":[{"key":"ref_1","unstructured":"Mandelbrot, B.B. (1977). Fractals: Form, Chance, and Dimension, W.H. Freeman & Company."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Mandelbrot, B.B. (1983). The Fractal Geometry of Nature, Henry Holt and Company. Einaudi Paperbacks.","DOI":"10.1119\/1.13295"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/34.368149","article-title":"Texture Segmentation Using Fractal Dimension","volume":"17","author":"Chaudhuri","year":"1995","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Gao, Q., Zribi, M., Escorihuela, J.M., Baghdadi, N., and Segui, Q.P. (2018). Irrigation Mapping Using Sentinel-1 Time Series at Field Scale. Remote Sens., 10.","DOI":"10.3390\/rs10091495"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Di Martino, G., Di Simone, A., and Riccio, D. (2018). Fractal-Based Local Range Slope Estimation from Single SAR Image with Applications to SAR Despeckling and Topographic Mapping. Remote Sens., 10.","DOI":"10.3390\/rs10081294"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Di Martino, G., Iodice, A., Riccio, D., Ruello, G., and Zinno, I. (2018). The Role of Resolution in the Estimation of Fractal Dimension Maps From SAR Data. Remote Sens., 10.","DOI":"10.3390\/rs10010009"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhou, Y., Lin, C., Wang, S., Liu, W., and Tian, Y. (2016). Estimation of Building Density with the Integrated Use of GF-1 PMS and Radarsat-2 Data. Remote Sens., 8.","DOI":"10.3390\/rs8110969"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Chen, Q., Li, L., Xu, Q., Yang, S., Shi, X., and Liu, X. (2017). Multi-Feature Segmentation for High-Resolution Polarimetric SAR Data Based on Fractal Net Evolution Approach. Remote Sens., 9.","DOI":"10.3390\/rs9060570"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1109\/TPAMI.1984.4767557","article-title":"Multiple Resolution Texture Analysis and Classification","volume":"PAMI-6","author":"Peleg","year":"1984","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1016\/0098-3004(86)90047-6","article-title":"Computation of the Fractal Dimension of Topographic Surfaces Using the Triangular Prism Surface Area Method","volume":"12","author":"Clarke","year":"1986","journal-title":"Comput. Geosci."},{"key":"ref_11","unstructured":"Lam, N.S.N., and De Cola, L. (1993). Fractals in Geography, Prentice Hall."},{"key":"ref_12","first-page":"1","article-title":"A Procedure to Estimate the Fractal Dimension of Waveforms","volume":"5","author":"Sevcik","year":"1998","journal-title":"Complex. Int."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Turcotte, D.L. (1997). Fractals and Chaos in Geology and Geophysics, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9781139174695"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s12524-012-0225-4","article-title":"Variogram Fractal Dimension Based Features for Hyperspectral Data Dimensionality Reduction","volume":"41","author":"Mukherjee","year":"2013","journal-title":"J. Indian Soc. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s12524-008-0024-0","article-title":"Fractal-based Dimensionality Reduction of Hyperspectral Images","volume":"36","author":"Ghosh","year":"2008","journal-title":"J. Indian Soc. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.1109\/LGRS.2016.2574940","article-title":"Change Detection Using Global and Local Multifractal Description","volume":"13","author":"Aleksandrowicz","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1733","DOI":"10.1016\/j.asr.2007.04.090","article-title":"Fractal Signatures for Multiscale Processing of Hyperspectral Image Data","volume":"41","author":"Dong","year":"2008","journal-title":"Adv. Space Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.optlaseng.2013.11.018","article-title":"Comparative Performance of Fractal Based and Conventional Methods for Dimensionality Reduction of Hyperspectral Data","volume":"55","author":"Mukherjee","year":"2014","journal-title":"Opt. Lasers Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1080\/10106049.2011.642411","article-title":"Dimensionality Reduction of Hyperspectral Data Using Spectra Fractal Feature","volume":"27","author":"Mukherjee","year":"2012","journal-title":"Geocarto Int."},{"key":"ref_20","first-page":"63","article-title":"Fractal Characterization of Hyperspectral Imagery","volume":"65","author":"Qiu","year":"1999","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1925","DOI":"10.1080\/01431160210155992","article-title":"Fractal Approaches in Texture Analysis and Classification of Remotely Sensed Data: Comparison with Spatial Autocorrelation Techniques and Simple Descriptive Statistics","volume":"24","author":"Myint","year":"2003","journal-title":"Int. J. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Krupinski, M., Wawrzaszek, A., Drzewiecki, W., and Aleksandrowicz, S. (2014, January 17\u201326). Usefulness of the Fractal Dimension in the Context of Hyperspectral Data Description. Proceedings of the 14th SGEM GeoConference on Informatics, Geoinformatics and Remote Sensing; STEF92 Technology, Albena, Bulgaria.","DOI":"10.5593\/SGEM2014\/B23\/S10.046"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1109\/21.259692","article-title":"An efficient differential box-counting approach to compute fractal dimension of image","volume":"24","author":"Sarkar","year":"1994","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4963","DOI":"10.1080\/01431160600676695","article-title":"Fractal analysis of remotely sensed images: A review of methods and applications","volume":"27","author":"Sun","year":"2006","journal-title":"Int. J. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1127\/1432-8364\/2014\/0212","article-title":"Influence of Image Filtering on Land Cover Classification when using Fractal and Multifractal Features","volume":"2014","author":"Wawrzaszek","year":"2014","journal-title":"Photogramm. Fernerkund. Geoinf."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Drzewiecki, W., Wawrzaszek, A., Krupinski, M., Aleksandrowicz, S., and Bernat, K. (2013, January 8\u201311). Comparison of selected textural features as global content-based descriptors of VHR satellite image\u2014The EROS\u2014A study 2013. Proceedings of the 2013 Federated Conference on Computer Science and Information Systems, Krakow, Poland.","DOI":"10.1109\/IGARSS.2013.6723801"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/0920-5632(87)90036-3","article-title":"Fractal measures and their singularities: The characterization of strange sets","volume":"2","author":"Halsey","year":"1987","journal-title":"Nucl. Phys. B Proc. Suppl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/0167-2789(83)90235-X","article-title":"The infinite number of generalized dimensions of fractals and strange attractors","volume":"8","author":"Hentschel","year":"1983","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_29","first-page":"279","article-title":"A New Band Selection Algorithm for Hyperspectral Data Based on Fractal Dimension","volume":"XXXVII","author":"Su","year":"2008","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. Beijing"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Combrexelle, S., Wendt, H., Tourneret, J.-Y., Mclaughlin, S., and Abry, P. (2015, January 2\u20135). Hyperspectral Image Analysis Using Multifractal Attributes. Proceedings of the 7th IEEE Workshop on Hyperspectral Image and SIgnal Processing: Evolution in Remote Sensing (WHISPERS 2015), Tokyo, Japan.","DOI":"10.1109\/WHISPERS.2015.8075453"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Aleksandrowicz, S., Wawrzaszek, A., Jenerowicz, M., Drzewiecki, W., and Krupinski, M. (2019, January 5\u20137). Local Multifractal Description of Bi-Temporal VHR Images. Proceedings of the 2019 10th International Workshop on the Analysis of Multitemporal Remote Sensing Images (MultiTemp), Shanghai, China.","DOI":"10.1109\/Multi-Temp.2019.8866963"},{"key":"ref_32","unstructured":"Grazzini, J., Turiel, A., Yahia, H., Herlin, I., and Rocquencourt, I. (2004, January 12\u201323). Edge-preserving smoothing of high-resolution images with a partial multifractal reconstruction scheme. Proceedings of the ISPRS 2004\u2014International Society for Photogrammetry and Remote Sensing XXXV, Istambul, Turkey."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"8669","DOI":"10.3390\/s91108669","article-title":"Super-resolution reconstruction of remote sensing images using multifractal analysis","volume":"9","author":"Hu","year":"2009","journal-title":"Sensors"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4577","DOI":"10.1109\/TGRS.2019.2891679","article-title":"Effects of Compression on Remote Sensing Image Classification Based on Fractal Analysis","volume":"57","author":"Chen","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Drzewiecki, W., Wawrzaszek, A., Aleksandrowicz, S., Krupinski, M., and Bernat, K. (2013, January 21\u201326). Comparison of selected textural features as global content-based descriptors of VHR satellite image. Proceedings of the 2013 IEEE International Geoscience and Remote Sensing Symposium\u2014IGARSS, Melbourne, Australia.","DOI":"10.1109\/IGARSS.2013.6723801"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Kupidura, P. (2019). The Comparison of Different Methods of Texture Analysis for Their Efficacy for Land Use Classification in Satellite Imagery. Remote Sens., 11.","DOI":"10.3390\/rs11101233"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"103182","DOI":"10.1016\/j.oregeorev.2019.103182","article-title":"Detecting subtle alteration information from ASTER data using a multifractal-based method: A case study from Wuliang Mountain, SW China","volume":"115","author":"Chen","year":"2019","journal-title":"Ore Geol. Rev."},{"key":"ref_38","first-page":"356","article-title":"Fractal Feature for Classification of Hyperspectral Images of Moffit Field, USA","volume":"94","author":"Ghosh","year":"2008","journal-title":"Curr. Sci."},{"key":"ref_39","first-page":"297","article-title":"A Dimensionality Reduction Algorithm of Hyper Spectral Image Based on Fract Analysis","volume":"XXXVII","author":"Junying","year":"2008","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_40","unstructured":"Ziyong, Z. (2010, January 10\u201312). Multifractal Based Hyperion Hyperspectral Data Mining. Proceedings of the 2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery, Yantai, China."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Hosseini, A., and Ghassemian, H. (2012, January 15\u201317). Classification of Hyperspectral and Multifractal Images by Using Fractal Dimension of Spectral Response Curve. Proceedings of the 20th Iranian Conference on Electrical Engineering (ICEE2012), Tehran, Iran.","DOI":"10.1109\/IranianCEE.2012.6292587"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"836","DOI":"10.1080\/00207160.2014.915957","article-title":"A novel logistic multi-class supervised classification model based on multi-fractal spectrum parameters for hyperspectral data","volume":"92","author":"Li","year":"2015","journal-title":"Int. J. Comput. Math."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.infrared.2017.08.021","article-title":"Stacked sparse autoencoder in hyperspectral data classification using spectral-spatial, higher order statistics and multifractal spectrum features","volume":"86","author":"Wan","year":"2017","journal-title":"Infrared Phys. Technol."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Krupi\u0144ski, M., Wawrzaszek, A., Drzewiecki, W., Aleksandrowicz, S., and Jenerowicz, M. (August, January 28). Multifractal Parameters for Spectral Profile Description. Proceedings of the IGARSS 2019\u20142019 IEEE International Geoscience and Remote Sensing Symposium, Yokohama, Japan.","DOI":"10.1109\/IGARSS.2019.8900247"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Jenerowicz, M., Wawrzaszek, A., Krupi\u0144ski, M., Drzewiecki, W., and Aleksandrowicz, S. (August, January 28). Aplicability of Multifractal Features as Descriptors of the Complex Terrain Situation in IDP\/Refugee Camps. Proceedings of the IGARSS 2019\u20142019 IEEE International Geoscience and Remote Sensing Symposium, Yokohama, Japan.","DOI":"10.1109\/IGARSS.2019.8898588"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Jenerowicz, M., Wawrzaszek, A., Drzewiecki, W., Krupi\u0144ski, M., and Aleksandrowicz, S. (2019). Multifractality in Humanitarian Applications: A Case Study of Internally Displaced Persons\/Refugee Camps. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., 1\u20138.","DOI":"10.5194\/egusphere-egu2020-13262"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"809","DOI":"10.5721\/EuJRS20164943","article-title":"Applicability of multifractal features as global characteristics of WorldView-2 panchromatic satellite images","volume":"49","author":"Drzewiecki","year":"2016","journal-title":"Eur. J. Remote Sens."},{"key":"ref_48","first-page":"175","article-title":"Evaluation of degree of multifractality for description of high resolution data aquired by Landsat satellites","volume":"27","author":"Wawrzaszek","year":"2015","journal-title":"Arch. Fotogram. Kartogr. Teledetekcji"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/S0034-4257(98)00064-9","article-title":"Imaging spectroscopy and the Airborne Visible\/Infrared Imaging Spectrometer (AVIRIS)","volume":"65","author":"Green","year":"1998","journal-title":"Remote Sens. Environ."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0034-4257(93)90014-O","article-title":"Derivation of scaled surface reflectances from AVIRIS data","volume":"44","author":"Gao","year":"1993","journal-title":"Remote Sens. Environ."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Gao, B.-C., and Davis, C.O. (1997, January 31). Development of a line-by-line-based atmosphere removal algorithm for airborne and spaceborne imaging spectrometers. Proceedings of the Imaging Spectrometry III, San Diego, CA, USA.","DOI":"10.1117\/12.283822"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Wawrzaszek, A., Krupinski, M., Aleksandrowicz, S., and Drzewiecki, W. (2013, January 21\u201326). Fractal and multifractal characteristics of very high resolution satellite images. Proceedings of the 2013 IEEE International Geoscience and Remote Sensing Symposium\u2014IGARSS, Melbourne, Australia.","DOI":"10.1109\/IGARSS.2013.6723071"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"153","DOI":"10.3847\/1538-4357\/ab1750","article-title":"Multifractal analysis of heliospheric magnetic field fluctuations observed by Ulysses","volume":"876","author":"Wawrzaszek","year":"2019","journal-title":"Astrophys. J."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/24\/4077\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:44:26Z","timestamp":1760179466000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/24\/4077"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,12]]},"references-count":53,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["rs12244077"],"URL":"https:\/\/doi.org\/10.3390\/rs12244077","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2020,12,12]]}}}