Substitutability of Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud Jaya Sreevalsan-Nair Beena Kumari Motivation: Augmented Classification Covariance Matrix: an Alternative Discussions Substitutability of Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud Beena Kumari Jaya Sreevalsan-Nair Graphics-Visualization-Computing Lab (GVCL), International Institute of Information Technology, Bangalore (IIITB), India. Dagstuhl Seminar 16142: Multidisciplinary Approaches to Multivalued Data: Modeling, Visualization, Analysis April 3-8, 2016.
Substitutability of Agenda Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud Jaya Sreevalsan-Nair Beena Kumari Motivation: Augmented Classification Motivation: Augmented Classification Covariance Matrix: an Alternative Discussions Covariance Matrix: an Alternative Discussions
Substitutability of Agenda Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud Jaya Sreevalsan-Nair Beena Kumari Motivation: Augmented Classification Motivation: Augmented Classification Covariance Matrix: an Alternative Discussions Covariance Matrix: an Alternative Discussions
Substitutability of 3D Urban LiDAR Point Cloud Symmetric Second-order Tensor Fields: An Application Data acquisition using airborne LiDAR, where point cloud (3D points) in Urban LiDAR 3D Point Cloud describes topography; Jaya Sreevalsan-Nair Depending on acquisition settings, dataset could contain additional Beena Kumari information such as multiple returns, intensity, color, etc. Motivation: Region of our interest: urban settings, usually consisting of buildings, asphalt Augmented & natural ground, vegetation, etc. Classification Covariance Matrix: an Alternative Discussions Image courtesy: Keil Schmid, Kirk Waters, Lindy Dingerson, Brian Hadley, Rebecca Mataosky, Jamie Carter, and Jennifer Dare. Lidar 101: An introduction to lidar technology, data, and applications. NOAA Coastal Services Center, 2012.
Substitutability of What is Augmented Classification ? Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud Jaya Sreevalsan-Nair Beena Kumari A combination of structural and contextual classifications ∗ – explicitly building class tuples in order to enable structural operations on points in Motivation: Augmented specific object classes, such as curve extractions in buildings, asphalt ground Classification (road), etc. Covariance Matrix: an Alternative Discussions * B. Kumari and J. Sreevalsan-Nair. 2015. An interactive visual analytic tool for semantic classification of 3D urban LiDAR point cloud. In Proceedings of the 23rd SIGSPATIAL International Conference on Advances in Geographic Information Systems (GIS ’15). ACM, New York, NY, USA, Article 73.
Substitutability of Structural Classification Symmetric Second-order Tensor Fields: An Application [Keller11] proposed structural classification using principal component in Urban LiDAR 3D Point Cloud analysis of covariance matrix in local (spherical) neighborhood ; Jaya Sreevalsan-Nair Beena Kumari Motivation: Augmented Classification Covariance Matrix: an Alternative Discussions
Substitutability of Structural Classification Symmetric Second-order Tensor Fields: An Application [Keller11] proposed structural classification using principal component in Urban LiDAR 3D Point Cloud analysis of covariance matrix in local (spherical) neighborhood ; Jaya Sreevalsan-Nair Structural classes, given λ 2 ≥ λ 1 ≥ λ 0 : Beena Kumari ◮ (L) disc-shaped neighborhood = planar type , i.e. Motivation: Augmented P d = { p ∈ P | λ 0 /λ 2 < ǫ } ; Classification ◮ (M) cylindrical-shaped neighborhood = line/curve type , i.e. Covariance Matrix: an Alternative P c = { p ∈ P | λ 1 /λ 2 < ǫ } ; Discussions ◮ (R) spherical neighborhood = point type , i.e. P s = { p ∈ P | λ 0 /λ 2 ≥ ǫ } .
Substitutability of Contextual Classification Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud We proposed hierarchical clustering, using visualization in choosing clustering Jaya Sreevalsan-Nair Beena Kumari parameters (3D color maps/heatmaps of parameters) – in our implementation: Motivation: Augmented ◮ we classify into 4 object classes: buildings, asphalt ground, natural Classification ground, vegetation ; Covariance Matrix: an Alternative ◮ we use hierarchical expectation-maximization (HEM); Discussions ◮ we use one parameter for clustering at a time, from a n-dimensional parameter space; ◮ we use a tree-visualizer which enables user to decide the parameter based on heatmaps of parameters;
Substitutability of Contextual Classification Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud We proposed hierarchical clustering, using visualization in choosing clustering Jaya Sreevalsan-Nair Beena Kumari parameters (3D color maps/heatmaps of parameters) – in our implementation: Motivation: Augmented ◮ we classify into 4 object classes: buildings, asphalt ground, natural Classification ground, vegetation ; Covariance Matrix: an Alternative ◮ we use hierarchical expectation-maximization (HEM); Discussions ◮ we use one parameter for clustering at a time, from a n-dimensional parameter space; ◮ we use a tree-visualizer which enables user to decide the parameter based on heatmaps of parameters; Clustering parameters used: normalized height, height-difference, intensity, properties derived from local geometry (linearity, planarity, curvature, difference of normals, surface residual, etc.)
Substitutability of Contextual Classification Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud We proposed hierarchical clustering, using visualization in choosing clustering Jaya Sreevalsan-Nair Beena Kumari parameters (3D color maps/heatmaps of parameters) – in our implementation: Motivation: Augmented ◮ we classify into 4 object classes: buildings, asphalt ground, natural Classification ground, vegetation ; Covariance Matrix: an Alternative ◮ we use hierarchical expectation-maximization (HEM); Discussions ◮ we use one parameter for clustering at a time, from a n-dimensional parameter space; ◮ we use a tree-visualizer which enables user to decide the parameter based on heatmaps of parameters; Clustering parameters used: normalized height, height-difference, intensity, properties derived from local geometry (linearity, planarity, curvature, difference of normals, surface residual, etc.) Preserved spatial locality using region-growing , with post-processing of merging clusters in the leaf nodes of our tree visualizer, to form 4 classes.
Substitutability of Contextual Classification Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud Jaya Sreevalsan-Nair Beena Kumari Motivation: Augmented Classification Covariance Matrix: an Alternative Discussions
Substitutability of Contextual Classification Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud Jaya Sreevalsan-Nair Beena Kumari Motivation: Augmented Classification Covariance Matrix: an Alternative Discussions
Substitutability of Contextual Classification Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud Jaya Sreevalsan-Nair Beena Kumari Motivation: Augmented Classification Covariance Matrix: an Alternative Discussions
Substitutability of Contextual Classification Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud Jaya Sreevalsan-Nair Beena Kumari Motivation: Augmented Classification Covariance Matrix: an Alternative Discussions
Substitutability of Results: Contextual Classification Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud Jaya Sreevalsan-Nair Beena Kumari Motivation: Augmented Classification Covariance Matrix: an Alternative Discussions Area 1 of the Vaihingen dataset (1,79,997 points): (L) Orthoimage, (R) our contextual classification.
Substitutability of Results: Augmented Classification Symmetric Second-order Tensor Fields: An Application in Urban LiDAR 3D Point Cloud Jaya Sreevalsan-Nair Structural classification + contextual classification = augmented classification Beena Kumari (using class tuples) Motivation: Augmented Classification Covariance Matrix: an Alternative Discussions Area 1 of the Vaihingen dataset (1,79,997 points) Expected benefits: preserving structural classification explicitly for curve extraction in object classes.
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