CMRT09

Stilla, Uwe

Bibliographic data

Monograph

Persistent identifier:: 856955019

Author:: Stilla, Uwe

Title:: CMRT09

Sub title:: object extraction for 3D city models, road databases, and traffic monitoring ; concepts, algorithms and evaluation ; Paris, France, September 3 - 4, 2009 ; [joint conference of ISPRS working groups III/4 and III/5]

Scope:: X, 234 Seiten

Year of publication:: 2009

Place of publication:: Lemmer

Publisher of the original:: GITC

Identifier (digital):: 856955019

Illustration:: Illustrationen, Diagramme, Karten

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Monograph

Collection:: Earth sciences

Chapter

Title:: VEHICLE ACTIVITY INDICATION FROM AIRBORNE LIDAR DATA OF URBAN AREAS BY BINARY SHAPE CLASSIFICATION OF POINT SETS W. Yaoa, S. Hinz, U. Stilla

Document type:: Monograph

Structure type:: Chapter

CMRT09: Object Extraction for 3D City Models, Road Databases and Traffic Monitoring - Concepts, Algorithms, and Evaluation 38 other than as parallelogram (Fig.4, bottom row), but e.g. trapezoid, common quadrilaterals, etc, due to unstable sampling characteristics of LiDAR or clutter objects in urban areas. It is difficult to decide whether it is actually a moving vehicle part or a point set of stationary vehicle with missing parts. Generally, these vehicle point sets confuse the shape analysis and deliverer only ambiguous geometric features that cannot be adopted for robust classification. Therefore, this category of vehicle point sets have to be identified and then excluded from candidates delivered to movement classification, which means that they could be only attributed to uncertain motion status at the moment. Those point sets are also undergone the same shape analysis process and can be found when the parallelogram fitting fails. 3.2 Movement classification G at the identity e, T, , is called the Lie algebra g. The exponential map exp is a mapping from Lie algebra elements to Lie group elements. The inverse of the exponential map is called logarithmic map log. The Lie algebra element of T is obtained by performing component-wise log operation on each of the M i : flog W) log(7’) = (1) l 0 • log (K)J (\ 0^ (0 -l'] where log(A/ ( ) = a t I 1 + ^.1 I. Equation (1) expresses the Lie algebra element of an individual spoke in terms of the generator matrices for scaling and 2-d rotation factors. As indicated in section 3.1, the point sets of extracted vehicle can generally be denoted by spoke model with two parameters, whose configuration is formulated as 'U ' x = , u,= i a i \ Vs, K E > J where k denotes the number of spokes in the model. As inspired by the works of Fletcher et al., (2003) and Yarlagadda et ah, (2008), the 3D vehicle shape variability is nonlinear and represented as a transformation space. Thus the similarity between vehicle instances can be measured by group distance metric. It has been also confirmed that Lie group PCA can better describe the variability of data that is inherently nonlinear and statistics on linear models may benefit from the addition of nonlinear information. Since our task is intended to classify the vehicle motion based on the shape features of vehicle point sets, the classification framework for distinguishing generic vehicle category can be easily adapted to motion analysis. Consequently, a new vehicle configuration Y can be obtained by a transformation of X written in matrix form: Y=T(X) where f M, . 0 ^ r = 0 . M , M' = Rf o 0 e ai , R, denotes the 2-d k / rotation acting on the angle of shear 0 SA . e“‘ denotes the scale acting on the extent E. By varying T, different vehicle shape (motion status) can be represented as transformations of X. based on elaborations in Rossmann (2002), M i is a Cartesian product of the scale and angle value groups 'R x SO(2), which are the Lie group of 1-d real value and the Lie group of 2-d rotation, respectively. Since the Cartesian product of Lie group elements is a Lie group and T is the Cartesian product of transformation matrices M acting on the individual spokes, T forms a Lie group. The group T is a transformation group that acts on shape parameters M. However, any vehicle shape X may be represented in T as the transformation of a fixed identity atom. A group is defined as a set of elements together with a binary operation (multiplication) satisfying the closure, associative, identity and the inverse axioms. A Lie group G is a group defined on differentiable manifold. The tangent space of group The intrinsic mean p of a set of transformation matrices 7j , T 2 , T n of vehicle spoke models is defined as p = argmin]Tt/(7j,r 2 ) 2 (2) k=\ where denotes Riemannian distance on G, and d(T t ,T 2 ) = ||log(7]' l 7’ 2 )|| where ||| is the Frobenius norm of the resulting algebra elements. The 1-parameter Lie algebra element of the spoke model of vehicle point sets is given by (AS>) • o ^ A M = (3) v 0 ■ A« where A r (/) = / log(Afy), denoting that the Lie algebra element is defined at a fixed (a,.,#,) for each spoke, which represents the tangent to a geodesic curve parameterized by /. The parameter t in (3) sweeps out a 1-parameter sub-group, H v (t) of the Lie group G of spoke transformations. For any g e G , the distance between g and //,,(/) is defined as d{g,H y ) = mind(g,exp[A v (/)]), (4) Analogous to the principle components of a vector space, there exist 1-parameter subgroups called the principle geodesic curves (Fletcher et al., 2003) which describe the essential variability of the data points lying on the manifold. The first principle geodesic curve for elements of a Lie group G is defined as the 1-parameter subgroup H tU (/), where n v (,) =argmin ^d 2 (fi~ l g„H v ) (5) i=i Let p n be the projection of p'g, on //,„ , and define g <n = pjl/j-'gf. The higher A-th principle geodesic curve can be determined recursively based on (5). The motion analysis can then be formulated as a binary classification problem using Lie distance metrics. The input to the Lie distance classifier comprises a set of labeled samples Tj from two categories of vehicle status C i - moving vehicles and stationary ones. n Y denotes the number of training samples for each category. The intrinsic mean p } and the principal geodesics H Ul) are computed for each vehicle class C j using

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