The Hough Transform for Vertical Object Recognition in 3D Images Generated from Airborne Lidar Data Christopher Parrish ECE533 Project December 2006

GPS Reference Station Airborne Lidar Airport Obstruction Surveying

Lidar Point Cloud Voxelize 3D Grayscale Intensity Image 3D Sobel operator 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 ImageLaser Point Cloud

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 image Quantize 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 = r 2

Cylinders Detected Using Hough Transform:

Comparison of radii & axes locations of HT-detected cylinders with field-surveyed data: