HOUGH TRANSFORM

BOUNDARY DETECTION BASED ON HOUGH TRANSFORM

Edges vs Boundaries Edges Boundaries Local Intensity discontinuities Points Not Dependent on models Boundaries Extensive Composed of many points Maybe dependent on models Typically our goal is to reconstruct the boundary from local edge elements

Boundaries of Objects from Edges Brightness Gradient (Edge detection) Missing edge continuity, many spurious (bogus, fake) edges

Boundaries of Objects from Edges Multi-scale Brightness Gradient But, low strength edges may be very important

Boundaries of Objects from Edges Machine Edge Detection Image Human Boundary Marking

Boundaries in Medical Imaging Detection of cancerous regions. [Foran, Comaniciu, Meer, Goodell, 00]

Boundaries in Ultrasound Images Hard to detect in the presence of large amount of speckle noise

Boundaries of Objects Sometimes hard even for humans!

Knowledge about Boundary

Finding lines via Hough Transform Useful for detecting any parametric curves (eg. Lines, conics) Relatively unaffected by gaps in curves, and noise Given a set of edge points, find line(s) which best explain the data

Hough Transform

Hough Transform

Contoh y=x+1

Line Detection by Hough Transform Algorithm: Quantize Parameter Space Create Accumulator Array Set For each image edge increment: If lies on the line: Find local maxima in Parameter Space 1 2

Better Parameterization NOTE: Large Accumulator More memory and computations Improvement: Line equation: Here Given points find (Finite Accumulator Array Size) Image Space ? Hough Space Sinusoid Hough Space

Horizontal axis is θ, vertical is rho. Figure 15.1, top half. Note that most points in the vote array are very dark, because they get only one vote. Image space Votes Horizontal axis is θ, vertical is rho.

This is 15.1 lower half Image space votes

15.2; main point is that lots of noise can lead to large peaks in the array

Polar Coordinate Representation of Line

Hough Transform

Example

Example

Contoh Perhitungan x y -90 -45 45 90 0.00 100 70.71 100.00 (100.00) 45 90 0.00 100 70.71 100.00 (100.00) (70.71) 141.42

Pseudocode

Finding Circles by Hough Transform Equation of Circle: If radius is known: (2D Hough Space) Accumulator Array