How to find the intersection point on the boundary of the image from the interior point.

I have a set of points (x,y,theta) which are extracted from a fingerprint image(features minutiae).Now if I draw a line from each point along the direction of that point theta from the set of points, every point will definitely intersect on the boundary(x or y axis)(image with origin in the top left corner and it is a closed rectangle or square).Now i want to find the boundary point for each point in the image.

Answer 1

[Image Analyst]

Let's say you have a cluster of points, say 50 of them. Then let's say you call convhull() to get the convex hull and find that 8 of them define the convex hull (like what you'd get if you wrapped a rubber band around the points). This convex hull does not necessarily need to be a rectangle or a square. I'm not sure where that's coming from unless you're talking about the bounding box of the points. OK, so now let's take some arbitrary point inside the convex hull - a cluster point in the middle somewhere. You can send out an infinite number of lines at an infinite number of angles. Each one of those lines will intersect the convex hull, the bounding box, and the edge of the image at some point, so we have an infinite number of intersection points of that line with the "boundary" (however you define that). I think a diagram showing the cluster and the line coming from a point, and the intersection would help explain what you want. Please upload something.

[Image Analyst]

Moved Swathi's "Answer" to a comment here:

I am talking about a fingerprint image(closed square lets say 256*256 image).On the fingerprint i had some points .each point has an angle, along that angle(direction) if we project that point onto the boundary we'll get the point where the actual point meet on the boundary.i am new to imageprocessing and matlab.I need the corresponding boundary point of the original point.

I am unable to upload the image of the fingerprint here.

[Image Analyst]

Use http://tinypic.com or http://snag.gy to upload a picture. I still don't know what the boundary is - is it just the edge of the image? If so, regular algebra can tell you that. You know the point and the slope so the simple point-slope formula of a line

y-yp = slope*(x-xp)

will tell you where it intersects the edge of the image.