The Hough Transform for Vertical Object Recognition in 3D Images

Generated from Airborne Lidar Data

Christopher ParrishECE533 ProjectDecember 2006

GPS Reference Station

Airborne Lidar

Airport Obstruction

Surveying

Lidar Point Cloud

Voxelize

3D Grayscale Intensity Image

3D Sobeloperator

3D Grayscale Edge Image

Threshold segmentation

3D Binary Edge Image

Hough Transform to identify vertical cylinders

Vertical objects of interest

Hough transform- based approach for detecting vertical objects of cylindrical shape:

3D Grayscale Image2D Color Image Laser Point Cloud

T

Tzyx z

fyf

xfGGG

f

222zyx GGGf f

242000242

,484000484

,242000242

:xG

202404202

,404808404

,202404202

:yG

242484242

,000000000

,242484242

:zG

otherwise0 if 1

),,(Tf(x,y,z)

zyxg

Gradient of a 3D image, f(x,y,z):

Magnitude of the gradient:

3D Sobel operator (three 3x3x3 filters expressed here as sets of three 2D matrices)

Thresholded (binary) edge image

Computing Binary Edge Image:

3D Binary Edge Images

HT Cylinder Detection Algorithm:

Input = 3D binary edge imageQuantize 3D parameter space. Initialize all accumulator cells to zero. For each nonzero voxel in 3D binary edge image,

step through all values of s and t. At each location:

Solve for r Round r to its nearest accumulator cell value Increment counter for that (s,t,r) accumulator cell.

Find entry in 3D accumulator array with highest # of votes.

Assume cylinders are vertical (axes parallel to mapping frame Z axis) => # of parameters reduced from 5 to 3. Representation: (X-s)2+(Y-t)2 = r2

Cylinders Detected Using Hough Transform:

Comparison of radii & axes locations of HT-detected cylinders with

field-surveyed data: