Accuracy of the zero crossings of the second directional derivative as an edge detector

1993 ◽  
Vol 4 (3) ◽  
pp. 227-251 ◽  
Author(s):  
Johan de Vriendt
Keyword(s):  
Directional Derivative ◽  
Edge Detector ◽  
Zero Crossings ◽  
Second Directional Derivative

Noise-robust color edge detector using gradient matrix and anisotropic Gaussian directional derivative matrix

2016 ◽  
Vol 52 ◽  
pp. 346-357 ◽  
Author(s):  
Fu-Ping Wang ◽  
Peng-Lang Shui
Keyword(s):  
Directional Derivative ◽  
Edge Detector ◽  
Derivative Matrix ◽  
Noise Robust

Mesh adaptive direct search with second directional derivative-based Hessian update

2015 ◽  
Vol 62 (3) ◽  
pp. 693-715 ◽  
Author(s):  
Árpád Bűrmen ◽  
Jernej Olenšek ◽  
Tadej Tuma
Keyword(s):  
Directional Derivative ◽  
Direct Search ◽  
Mesh Adaptive Direct Search ◽  
Second Directional Derivative

scholarly journals RECONSTRUCTING BUILDINGS WITH DISCONTINUITIES AND ROOF OVERHANGS FROM OBLIQUE AERIAL IMAGERY

2017 ◽  
Vol XLII-1/W1 ◽  
pp. 465-471 ◽  
Author(s):  
D. Frommholz ◽  
M. Linkiewicz ◽  
H. Meissner ◽  
D. Dahlke
Keyword(s):  
Point Cloud ◽  
Structural Breaks ◽  
Directional Derivative ◽  
Texture Mapping ◽  
Aerial Images ◽  
Surface Model ◽  
Real World Data ◽  
Zero Crossings ◽  
Building Models ◽  
Dense Point

This paper proposes a two-stage method for the reconstruction of city buildings with discontinuities and roof overhangs from oriented nadir and oblique aerial images. To model the structures the input data is transformed into a dense point cloud, segmented and filtered with a modified marching cubes algorithm to reduce the positional noise. Assuming a monolithic building the remaining vertices are initially projected onto a 2D grid and passed to RANSAC-based regression and topology analysis to geometrically determine finite wall, ground and roof planes. If this should fail due to the presence of discontinuities the regression will be repeated on a 3D level by traversing voxels within the regularly subdivided bounding box of the building point set. For each cube a planar piece of the current surface is approximated and expanded. The resulting segments get mutually intersected yielding both topological and geometrical nodes and edges. These entities will be eliminated if their distance-based affiliation to the defining point sets is violated leaving a consistent building hull including its structural breaks. To add the roof overhangs the computed polygonal meshes are projected onto the digital surface model derived from the point cloud. Their shapes are offset equally along the edge normals with subpixel accuracy by detecting the zero-crossings of the second-order directional derivative in the gradient direction of the height bitmap and translated back into world space to become a component of the building. As soon as the reconstructed objects are finished the aerial images are further used to generate a compact texture atlas for visualization purposes. An optimized atlas bitmap is generated that allows perspectivecorrect multi-source texture mapping without prior rectification involving a partially parallel placement algorithm. Moreover, the texture atlases undergo object-based image analysis (OBIA) to detect window areas which get reintegrated into the building models. To evaluate the performance of the proposed method a proof-of-concept test on sample structures obtained from real-world data of Heligoland/Germany has been conducted. It revealed good reconstruction accuracy in comparison to the cadastral map, a speed-up in texture atlas optimization and visually attractive render results.

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