week 3: structural descriptions (cont.)

• a brief overview of the Dynamic Link Architecture (von der Malsburg)
• learning geons (Shams and von der Malsburg)

DLA

slide 2

slide 3

slide 4

details here.

slide 5

hypothesized processing hierarchy

[on motion-based segmentation]

hypothesized processing hierarchy (cont.)

slide 7

some of the objects in the database

• 3 primitives: cones, cubes, cylinders (+ other parts that do not recur often);
• variation in: size (60%), position, (partial) occlusion;
• some variation in orientation in depth (but notice that two out of the three primitives are rotationally symmetric w.r.t. the vertical axis).

slide 8

the representation of an objects as a labeled graph

• object = lattice of nodes
• each node labeled with a Gabor jet
• 4 orientations at 3 spatial frequencies used in the model

slide 9

Gabor jets

slide 10

similarity between two jets

slide 11

cost function for graph matching

slide 12

adding lateral excitation, nonlinearity

slide 13

effect of lateral excitation

slide 14

effect of lateral excitation

Receiver Operating Characteristics (ROCs) for graph matching with and without lateral excitation:

1. matching a cylinder against 103 objects
2. matching a a cone+cylinder against the 103 objects

slide 15

two schematic examples of successfull matching

bright areas = high similarity

slide 16

calculating SIMILARITY HISTORY for an object

slide 17

history of jet similarity across matches

M_i^k represents the similarity of the jet at node i to its corresponding jet (at varying coordinates j) in different matches.

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to detect correlated patterns of similarity...

slide 19

...consider the history correlation matrix

slide 20

final learned patterns from segmented parts

slide 21

decomposition into "partial primitives"

slide 22

several extracted versions of the cone primitive

(before merging and clean-up)

slide 23

cleaned-up primitives

slide 24

recognition with learned vs. ideal primitives

slide 25

digital embryos

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... embedded into complex 3D scenes

slide 27

learning the "embryo"

1. the recurring embryo
2. the shape learned from scene examples

slide 28

an algorithm for clique finding

complexity: the problem is NP-complete

intuitive approach: use dynamics of "gravitational" collapse

slide 29

detecting two cliques

slide 30

detecting one clique

slide 31

NP-completeness a non-issue???

not really; the "gravitational collapse" does not actually solve the clique problem as originally posed!

lesson: many (all?) NP-complete problems can be turned into deterministic polynomial ones by relaxing the original requirements (as in the present work) or by imposing restrictions (e.g., subgraph isomorphism admits a polynomial solution if the degree of the graphs is bounded by a constant)

slide 32

supplementary material

• Face Recognition by Dynamic Link Matching (Laurenz Wiskott and Christoph von der Malsburg)
• slides of the talk (courtesy of Ladan Shams)
•