HOUGH TRANSFORM BOUNDARY DETECTION BASED ON HOUGH TRANSFORM

HOUGH TRANSFORM

BOUNDARY DETECTION BASED ON HOUGH TRANSFORM

Edges vs Boundaries • Edges – 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

Contoh Grafik pada Ruang Parameter atau Hough Space (m, b) Grafik pada Ruang Cartesian (x-y) 5 y 5 b 4 3 4 2 3 1 y=x+1 2 0 1 -1 0 0 1 2 3 4 5 x 0 1 2 3 4 5 -2 -3 -4 -5 m

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

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

Image space Votes Horizontal axis is θ, vertical is rho.

Image space votes

Polar Coordinate Representation of Line

Hough Transform

Example

Contoh Perhitungan x 0 100 y 0 0 100 -90 0. 00 (100. 00) -45 0. 00 70. 71 (70. 71) 0. 00 0 0. 00 100. 00 45 0. 00 70. 71 141. 42 90 0. 00 100. 00 (200, 00) (150, 00) (100, 00) (50, 00) -100 -50 Titik 1 0 0, 00 50, 00 100, 00 150, 00 200, 00 50 100 Titik 2 Titik 4 Titik 5

Pseudocode

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