A geometric framework for channel network extraction from lidar: Nonlinear diffusion and geodesic paths

[1] A geometric framework for the automatic extraction of channels and channel networks from high-resolution digital elevation data is introduced in this paper. The proposed approach incorporates nonlinear diffusion for the preprocessing of the data, both to remove noise and to enhance features that are critical to the network extraction. Following this preprocessing, channels are defined as curves of minimal effort, or geodesics, where the effort is measured on the basis of fundamental geomorphological characteristics such as flow accumulation area and isoheight contours curvature. The merits of the proposed methodology, and especially the computational efficiency and accurate localization of the extracted channels, are demonstrated using light detection and ranging (lidar) data of the Skunk Creek, a tributary of the South Fork Eel River basin in northern California.

[1]  Phillip Colella,et al.  Two new methods for simulating photolithography development in 3D , 1996, Advanced Lithography.

[2]  P. Reichenbach,et al.  Identification and mapping of recent rainfall-induced landslides using elevation data collected by airborne Lidar , 2007 .

[3]  Andrea Tribe,et al.  Automated recognition of valley lines and drainage networks from grid digital elevation models: a review and a new method , 1992 .

[4]  Ron Kimmel,et al.  Numerical geometry of images - theory, algorithms, and applications , 2003 .

[5]  Paolo Tarolli,et al.  Hillslope-to-valley transition morphology: new opportunities from high resolution DTMs. , 2009 .

[6]  J. Koenderink The structure of images , 2004, Biological Cybernetics.

[7]  Kai Borre,et al.  Lecture Notes in Earth Sciences , 1987 .

[8]  David G. Tarboton,et al.  On the extraction of channel networks from digital elevation data , 1991 .

[9]  K. L. Frankel,et al.  Characterizing arid region alluvial fan surface roughness with airborne laser swath mapping digital topographic data , 2007 .

[10]  Guillermo Sapiro,et al.  Fair polyline networks for constrained smoothing of digital terrain elevation data , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[11]  Paolo Tarolli,et al.  LiDAR-derived slopes for headwater channel network analysis , 2009 .

[12]  J. Dvořák,et al.  Analysis of erosion. , 1994 .

[13]  T. Banchoff,et al.  Differential Geometry of Curves and Surfaces , 2010 .

[14]  I. Rodríguez‐Iturbe,et al.  The fractal nature of river networks , 1988 .

[15]  John F. O'Callaghan,et al.  The extraction of drainage networks from digital elevation data , 1984, Comput. Vis. Graph. Image Process..

[16]  Clemens Simmer,et al.  Dynamics of Multiscale Earth Systems , 2003 .

[17]  William E. Dietrich,et al.  Evidence for nonlinear, diffusive sediment transport on hillslopes and implications for landscape morphology , 1999 .

[18]  D. Montgomery,et al.  Channel Initiation and the Problem of Landscape Scale , 1992, Science.

[19]  E. Barnes,et al.  Scaling in river corridor widths depicts organization in valley morphology , 2007 .

[20]  Guillermo Sapiro,et al.  O(N) implementation of the fast marching algorithm , 2006, Journal of Computational Physics.

[21]  G. Sapiro,et al.  Geometric partial differential equations and image analysis [Book Reviews] , 2001, IEEE Transactions on Medical Imaging.

[22]  D. Montgomery,et al.  Erosion thresholds and land surface morphology , 1992 .

[23]  J. Tsitsiklis,et al.  Efficient algorithms for globally optimal trajectories , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[24]  Stanley Osher,et al.  Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations , 2003, SIAM J. Numer. Anal..

[25]  Mark S. Wigmosta,et al.  Land use and watersheds : human influence on hydrology and geomorphology in urban and forest areas , 2001 .

[26]  Hans-Peter Helfrich,et al.  Diffusion Methods for Form Generalisation , 2003 .

[27]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[28]  David G. Tarboton,et al.  The analysis of river basins and channel networks using digital terrain data , 1989 .

[29]  D. Montgomery,et al.  Where do channels begin? , 1988, Nature.

[30]  P. Tarolli,et al.  The effectiveness of airborne LiDAR data in the recognition of channel-bed morphology , 2008 .

[31]  D. Montgomery,et al.  Analysis of Erosion Thresholds, Channel Networks, and Landscape Morphology Using a Digital Terrain Model , 1993, The Journal of Geology.

[32]  Kevin J. McMaster Effects of digital elevation model resolution on derived stream network positions , 2002 .

[33]  Guillermo Sapiro,et al.  A geometric method for automatic extraction of sulcal fundi , 2006, 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006..

[34]  Jochen Schmidt,et al.  Comparison of polynomial models for land surface curvature calculation , 2003, Int. J. Geogr. Inf. Sci..

[35]  Yann Gousseau,et al.  Interpolation of digital elevation models using AMLE and related methods , 2002, IEEE Trans. Geosci. Remote. Sens..

[36]  Robert B. Dial,et al.  Algorithm 360: shortest-path forest with topological ordering [H] , 1969, CACM.

[37]  P. Lions,et al.  Image selective smoothing and edge detection by nonlinear diffusion. II , 1992 .

[38]  D. Montgomery,et al.  Source areas, drainage density, and channel initiation , 1989 .

[39]  Alan D. Howard,et al.  BADLAND MORPHOLOGY AND EVOLUTION: INTERPRETATION USING A SIMULATION MODEL , 1997 .

[40]  Robert S. Anderson,et al.  Evolution of the Santa Cruz Mountains, California, through tectonic growth and geomorphic decay , 1994 .

[41]  Guillermo Sapiro,et al.  Distance Functions and Geodesics on Submanifolds of Rd and Point Clouds , 2005, SIAM J. Appl. Math..

[42]  Lorenzo Marchi,et al.  Characterisation of the surface morphology of an alpine alluvial fan using airborne LiDAR , 2008 .

[43]  L. Band Topographic Partition of Watersheds with Digital Elevation Models , 1986 .

[44]  Guillermo Sapiro,et al.  Robust anisotropic diffusion , 1998, IEEE Trans. Image Process..

[45]  R. David,et al.  Landscape dissection and drainage area-slope thresholds , 1994 .

[46]  D. J. Andrews,et al.  Fitting degradation of shoreline scarps by a nonlinear diffusion model , 1987 .

[47]  Efi Foufoula-Georgiou,et al.  Channel network extraction from high resolution topography using wavelets , 2007 .

[48]  Guillermo Sapiro,et al.  Morse description and geometric encoding of digital elevation maps , 2004, IEEE Transactions on Image Processing.

[49]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[50]  D. Staley,et al.  Surficial patterns of debris flow deposition on alluvial fans in Death Valley, CA using airborne laser swath mapping data , 2006 .

[51]  R. M. Wallace,et al.  Terrain Analysis Using Digital Elevation Models , 2001 .

[52]  D. J. Chadwick,et al.  Analysis of LiDAR-derived topographic information for characterizing and differentiating landslide morphology and activity , 2006 .

[53]  James Rose,et al.  Geomorphological mapping of glacial landforms from remotely sensed data : An evaluation of the principal data sources and an assessment of their quality , 2006 .

[54]  A. Rinaldo,et al.  Fractal River Basins: Chance and Self-Organization , 1997 .

[55]  Raja Sengupta,et al.  Utah State University From the SelectedWorks of Christopher L . Lant 2004 Development and Comparison of Approaches for Automated Mapping of Stream Channel Networks , 2017 .

[56]  John B. Vogler,et al.  Channel head locations with respect to geomorphologic thresholds derived from a digital elevation model: A case study in northern Thailand , 2006 .

[57]  A. Howard A detachment-limited model of drainage basin evolution , 1994 .

[58]  E. Foufoula‐Georgiou,et al.  Channel network source representation using digital elevation models , 1993 .

[59]  Andrea Tribe,et al.  Automated recognition of valley heads from digital elevation models , 1991 .

[60]  J. McKean,et al.  Objective landslide detection and surface morphology mapping using high-resolution airborne laser altimetry , 2004 .

[61]  P. Troch,et al.  Curvature distribution within hillslopes and catchments and its effect on the hydrological response , 2006 .

[62]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[63]  Hongkai Zhao,et al.  A fast sweeping method for Eikonal equations , 2004, Math. Comput..

[64]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[65]  Elbridge Gerry Puckett,et al.  Two new methods for simulating photolithography development in 3D , 1997 .

[66]  D. Tarboton A new method for the determination of flow directions and upslope areas in grid digital elevation models , 1997 .

[67]  SapiroGuillermo,et al.  Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces , 2001 .

[68]  G. Hancock,et al.  Channel head location and characteristics using digital elevation models , 2006 .

[69]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[70]  David G. Tarboton,et al.  A New Method for Determination of Most Likely Landslide Initiation Points and the Evaluation of Digital Terrain Model Scale in Terrain Stability Mapping , 2006 .

[71]  Roberto Rudari,et al.  A procedure for drainage network identification from geomorphology and its application to the prediction of the hydrologic response , 2005 .

[72]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods , 1999 .

[73]  M. Costa-Cabral,et al.  Digital Elevation Model Networks (DEMON): A model of flow over hillslopes for computation of contributing and dispersal areas , 1994 .

[74]  A. Rinaldo,et al.  Fractal River Basins , 2001 .

[75]  J. McKeana,et al.  Objective landslide detection and surface morphology mapping using high-resolution airborne laser altimetry , 2004 .