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commented
9 years ago I've just started working with the Hough line transform and can answer some of
the
questions for AForge 2.0.0
1. Coordinate system: left/right, translation of origin (in comparison with
GDI+
coordinate system), axes direction.
ANSWER: Coordinate system is polar centered on the image and 0 degrees is
directly
right. GDI+, or at least the Image class, is cartesian, in pixels, with 0,0 at
the
top left and increasing down and right (I think).
2. Degrees or radians are used to measure theta.
ANSWER: Degrees are used to measure theta.
3. Range of theta variation.
ANSWER: I've seen negative Radius and at least 0-180 Theta. I don't know if
those
are the limits or just what I've seen.
4. Range of rho variation.
ANSWER: I don't know what rho is. HoughLine uses Theta in degrees and Radius in
pixels.
5. Actual meaning of absolute/relative intensity.
ANSWER: Relative intensity appears to be measured 0-1.0
I *think* what happens is if you GetLinesByRelativeIntensity with 0.0 you get
all
the lines and 1.0 you get none (maybe one line?). I'm not sure if it's average
or
median, so it's unclear if 0.5 would get you half the lines.
6. Formula of converting linear equation from normal form to slope-intercept
form
and vice versa.
ANSWER: I thought slope-intercept is "normal form". Do you mean converting
from "polar form"?
You can read some of the pointed-to documents to learn about Hough Transform.
Essentially, the HoughLine Theta and Radius--again, measured from the image
center--
describe a vector (line) that is perpendicular to the found line and whose
endpoint
is on the possibly-extrapolated found line. Because of the nature of the
HoughLine,
it is entirely possible that this point lies off the image.
As explained by the author in one of the forums, the line described by
HoughLine
does not indicate the endpoints of the line at all, it only indicates the slope
and
position.
Converting from HoughLine to found line in GDI+ coordinates can be thought of
in
multiple steps.
First convert Theta, Radius to a point in "regular" cartesian coords.
("regular" in this context means 0,0 at center, positive numbers up and right).
Slope of found line is (Theta + 90) degrees.
Transpose and flip the point and slope to match GDI+ coordinate system.
Further, to draw the line on the image, you'll need to find two points outside
(or
on the edge) of the image that are on the found line, to then use GDI+ DrawLine.
// Example code in C#
// Radius and Theta are polar coordinates.
float x, y;
// calculate from polar coords Radius (from center) and Theta
// using geometry:
// sine(theta) = (y / radius);
// cosine(theta) = (x/ radius);
y = (float)Math.Sin(hLine.Theta / 180.0 * (Math.PI)) * hLine.Radius;
x = (float)Math.Cos(hLine.Theta / 180.0 * (Math.PI)) * hLine.Radius;
// Get slope of line, note Math.Tan expects radians, so convert from
degrees.
// Also, Theta (slope of vector) is perpendicular to the found line so
add 90 degrees to get the found line slope.
float m = (float)Math.Tan((Math.PI / 180.0) * (hLine.Theta + 90.0));//
0=>0; 45=>1;90=>inf;135=>-1;180=>0;; tan(theta+90)=y/x
float b = y - m * x;
// found line is now described as a slope of m and y-intercept of b
// Note that the image center is at 0,0 and positive numbers exending up
and right.
// to use with GDI+, you'll need to convert to 0,0 = top-left positive
down and right.
This code and comments are original, mine, and hereby placed in the public
domain.Original comment by ecomput...@gmail.com on 28 Aug 2009 at 2:20
Original issue reported on code.google.com by
Qbi...@gmail.comon 24 Aug 2009 at 3:15