Object Detection Using Marked Point Process

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 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