1. Object Detection Using Marked Point Process
CMPUT 615
Nilanjan Ray

2. Object Detection
Often we are asked to detect objects in an image, where the number of objects is not known a priori
We may have knowledge about object likelihood, i.e., a good sense of what is a good measurement, what is not
We may also have some knowledge about spatial distribution of the objects
Can we put together all the pieces of information in a nice computational framework for object detection?
Yes! Marked point process framework can be utilized here

3. Object Detection: Point Process
A point process (aka spatial point process) can attach a probability to a configuration of points on a space
A point can have its marks. For example, an ellipse center is the point and its marks are the orientation and two radii
Thus, a point together with its marks can represent an object that we want to detect from an image

4. Point Process Prior g1 marks Interaction function:
a ~ U(amin, amax),
b ~ U(bmin, bmax),
θ ~ M(ξ), g1
marks
Interaction function:
A point consists of a center and its marks (mi)

5. Simulations From Marked PP Prior
Four realizations

6. Metropolis-Hastings Algorithm
Has 3 move types
Birth of a new point
Death of an existing point
Altering marks of an existing point
Each such move type is accepted or rejected via a ratio (a dimensionless number) called MH ratio
This process simulation is run a long time– until the configuration converges

7. Detection Result

8. Road Network Extraction

9. Building Extraction

10. Hydrographic Network Extraction

11. Summary
Spatial point process is excellent in modeling object level information
Can deal with variable number of objects in an image
The downside is long computations: sampling based techniques take a long time