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:: ROAD ROUNDABOUT EXTRACTION FROM VERY HIGH RESOLUTION AERIAL IMAGERY M. Ravenbakhsh, C. S. Fraser

Document type:: Monograph

Structure type:: Chapter

In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009 disturbances may destabilize the ziplock’s active vertices. As a result convergence may not occur or the snake may get trapped near the initial position. As a means of overcoming this problem, an external force with a large capture range can be applied. The Gradient Vector Flow (GVF) field (Xu & Prince, 1997), which is an example for such an external force, is used in the proposed approach. The GVF field was aimed at addressing two issues: a poor convergence to concave regions, and problems associated with the initialisation. It is computed as a spatial diffusion of the gradient of an edge map derived from the image. This computation causes diffuse forces to exist far from the object, and crisp force vectors to be near the edges. The GVF field points toward the object boundary when very near to the boundary, but varies smoothly over homogeneous image regions, extending to the image border. The main advantage of the GVF field is that it can capture a snake from a long range. Thus, the problem of far initialization can be alleviated. The Evolution of a ziplock snake is illustrated in Fig. 8. The snake is fixed at the head and tail, and it consists of two parts, the active and the passive vertices. These parts are separated by moving force boundaries. The active parts of the snake consist of the head and tail segments. O Passive Vertex • Active Vertex Figure 8. Evolution of a ziplock snake. The GVF is defined to be the vector field G(x,y) = (u(x,y),v(x, y)) that minimizes the energy functional: £= ¡¡p{« x 2 +u y 2 + v x 2 +v v 2 ) + IY/| 2 |G-Y/f dxdy (8) where V/ is the vector field computed from f(x,y) having vectors pointing toward the edges. f(x,y) is derived from the image and it has the property that it is larger near the image edges. The regularization parameter ju should be set according to the amount of noise present in the image; more noise requires a higher value of ¡u . Through use of calculus of variations (Courant & Hilbert, 1953), the GVF can be found by solving the following Euler equations: ¿iV 2 u-(ti-f)(f 2 +f 2 ) = 0 (9) (U V 2 v-(v-/ v )(//+/ v 2 ) = 0 where V“ is the Laplacian operator and f x and f are partial derivatives of f with respect to x and y. Let ^( 5 ) = (jc(s), y(s)) be a parametric active contour in which s is the curve length and x and y are the image coordinates of the 2D-curve. The internal snake energy is then defined as E mx (V(s)) = j [a(s) | V s (s) | 2 +fi(s) | V ss (s) | 2 ] (10) where y and F vs are the first and second derivatives of V with respect to 5. The functions a(s) and /3(s) control the elasticity and the rigidity of the contour, respectively. The global energy E = E int (V(s)) + E img (V(s)) (11) needs to be minimized, with a(s) = a and /?(.?) = /? being constants. Minimization of the energy function of Eq. 11 gives rise to the following Euler equations: dE jm „ (V(s)) .... - aV ss (5) + PV SSSS (s) + 8 =0 (12) oV(s) where V(5) stands for either x(j') or ^(5), and V ss and V ssss denote the second and fourth derivatives of V, respectively. After approximation of the derivatives with finite differences, and conversion to vector notation with Vj = (x,-,>' ; ), the Euler equations take the form (13) -2A[K-, -2V, + V M ]+[V, -2V M + V M ] + G(u,v) = 0 where G(w,v) is the GVF vector field . Eq. 13 can be written in matrix form as KV + G(u,v) = 0 (14) where AT is a pentadiagonal matrix. Finally, the motion of the GVF ziplock snake can be written in the form (Kass et al., 1988) V [,] =(K + yIY l *(y F [, " ,1 -/rG(u,v)| vM ) (15) where y stands for the viscosity factor (step size) determining the rate of convergence and / is the iteration index, k alters the strength of the external force. It is noteworthy that the proposed model still might fail to detect the correct boundaries in the following cases: • High variation of curvature at the roundabout border resulting in an initialization that is too poor in some parts, with the consequence that the snakes becomes and remain straight. • The roundabout central area lacks sufficient contrast with the surroundings, causing the curve to converge to nearby features.

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