Description
- Model Matching (10 pts): This problem examines the detection of faces by model matching. A face is modeled as a collection of circles and circular arcs, as so:
The basic idea is that face detection begins by finding circles and circular arcs in the image, followed by matching against a stored model. Be sure to give short justifications for each answer below.
- How should the model be represented?
- How should images be processed to detect the features?
- How should matching be performed?
- Is your answer to c. invariant to translation, rotation, and scale?
- Can it handle partial occlusion? If so, how? If not, suggest an extension to your scheme that can.
- Interpretation Tree (5 pts): We have a choice of matching detected image elements (edges) to the model or model elements to the object. Let E be the set of detected image edges and M the set of model edges. In the first case, matching image edge to model edges, we generate a tree of depth |𝐸𝐸| and breadth |𝑀𝑀| with tree size |𝑀𝑀||𝐸𝐸|. In the case of matching the model to image, we generate a tree of size |𝐸𝐸||𝑀𝑀|. We expect many more image elements than model elements – there may be many candidate image edges in a cluttered scene vs. a small number of model edges.
- Which approach is preferable, matching image edges to model or model to image edges? You might consider the case where there are 12 image edges and 5 model edges, for example.
- One advantage to using the interpretation tree approach is that it is possible to match an unknown object in the image to a model even if the object is partially occluded.
We do this by allowing an object element to match a “null element” in the model. Does this change your answer to part a.? How and why? Or why not?
- Binary Image Matching (2 pts): Let 𝐼𝐼1 and 𝐼𝐼2 be binary images. Show that
|𝐼𝐼1 − 𝐼𝐼2|2 = # of pixels where 𝐼𝐼1 ≠ 𝐼𝐼2 Where |𝐼𝐼|2 = ∑𝑖𝑖𝑗𝑗𝑗𝑗2 is the sum of all (pixels squared) in I.
- Classification (5 pts): Suppose we have a 2-class classification problem with class means 𝜇𝜇⃗𝐴𝐴 and 𝜇𝜇⃗𝐵𝐵. Assuming that both classes are equally likely, show that the Nearest Mean classifier decision boundary is the hyper-plane perpendicular to, and midway along, the line segment connecting 𝜇𝜇⃗𝐴𝐴 to 𝜇𝜇⃗𝐵𝐵. You do not need to assume any particular distribution for classes A and B.