Automatic cylinder detection using Hough Transform T Rabbani

Automatic cylinder detection using Hough Transform. T. Rabbani t. rabbani@citg. tudelft. nl 9/18/2020 1 Section of Photogrammetry and Remote Sensing

Hough Transform for automatic cylinder detection • 85% of objects found in industrial scenes can be approximated by planes, spheres, cones and cylinders • 5 -free parameters for cylinder. 9/18/2020 2

Hough Transform for automatic cylinder detection • Space Complexity • Time complexity • Example: • S=100 Cs = 9. 3 GB • S=200 Cs = 300 GB • Solution: Two-step approach • Orientation Estimation • Position and Radius estimation 9/18/2020 3

Basic Idea Behaviour of normals on Gaussian sphere 9/18/2020 4

Step 1: Orientation Estimation 9/18/2020 5

Step 2: Position and Radius Estimation 9/18/2020 6

Uniform Sampling of orientation space • Uniform sampling essential for Hough transform • Place points so that each point represents equal area on sphere surface • No closed form solution • Iterative solution too slow, as Hough transform needs bidirectional mapping 9/18/2020 7

Spherical sampling • linear sampling of and • Highly nonlinear 9/18/2020 8

Cartesian sampling • Use implicit equation of sphere • Uniformaly sample x and y 9/18/2020 9

Approximate Uniform Sampling Number of samples in phi = For mapping back and forth: 9/18/2020 10

Approximate Uniform Sampling 9/18/2020 11

Example 9/18/2020 12

Example 9/18/2020 13

Results 9/18/2020 14

Results on NAM modeling • 20 million points • Processing: q. Segmentation q. Automatic cylinder and plane detection ØPlanar patches: 946 ØCylinders: 1392 9/18/2020 15

Problem: Model Selection • Domains of planes and cylinders overlap • A cylinder can be represented by a number of planar patches • A plane by a set of cylindrical segments (a) (b) 9/18/2020 16

Solution: Hypothesis verification • • Hough transform will always give a hit Consider each hit as a strong hypothesis Employ model matching for hypothesis verification Accept only if hypothesis verification is successful 9/18/2020 17

Planarity Test • Histogram of • Distances • Angles with normal • Aspect ratio = Max Extent/Min Extent Max-extent Min-extent 9/18/2020 18

Cylindricality Test • Difference between predicted and actual normal • Distribution of points on cylinder surface • Max min radius 9/18/2020 theta 19

Results on NAM modeling 9/18/2020 20

Future Plans • Results refinements • Merging of multiple hits • Connection of separated segments due to occlusions etc • Automatic constraint detection • Detection and fitting of curves 9/18/2020 21

Questions: 9/18/2020 22