1. Action as Space-Time Shapes
Benny Yonovich
Leon Ribinik

2. “Actions as Space-Time Shapes”
Goal
Recognize, detect and cluster human actions.
Approach
Represent actions as space-time shapes.

3. Motivation Limitations in current methods:
Optical flow estimation is difficult.
Periodicity analysis is limited to cyclic actions.
Treating video sequence as a space-time volume is useful for analyzing actions.
Silhouettes contain detailed information about the shape of objects.

4. Space-Time Shapes
Induced by a concatenation of 2D silhouettes in the space-time volume.
Contain both spatial and dynamic information. 4

5. Concept
Generalization of a method developed for the analysis of 2D shapes to deal with volumetric space-time shapes induced by human actions. 5

6. Algorithm Overview Input: Video sequence
Extract the 2D silhouettes and build the space-time volume.
Calculate shape descriptor by solving a Poisson equation.
Use the solution to extract space-time shape features and global features measure.
Classify, cluster and detect actions using the global features measure. 6

7. Extract the 2D silhouettes and build the space-time volume
Video is simpler than image.
Background subtraction. 7

8. Calculate shape descriptor
First approach: Medial axis distance transform.
Assign each internal pixel a value reflecting its minimum distance to the boundary contour.
Does not reflect global properties of a silhouette.
Article approach: Shape representation using the Poisson equation.
A measure that “senses” the boundaries and assigns each pixel a value reflecting its relative position. 8

9. Poisson equation
Partial differential equation with broad utility in electrostatics, mechanical engineering and theoretical physics.
In Euclidean space:
where
is the Laplace Operator, also denoted by
In three-dimensional Cartesian coordinates, the equation takes the form: 9

10. Shape representation using the Poisson equation [1]
An action and its space-time shape S.
Random walk.
Compute:
with
subject to
on the bounding surface.
Laplacian:
Artificial boundary condition (Neumann):
Solution method: geometric multigrid solver. 10

11. Let’s get some intuition – 2D Poisson equation
Consider a conic:
Special case – circle:
Poisson equation solution:
Monotonic decreasing:
Boundary:
Maximum point – center: 11

12. Shape representation using the Poisson equation [2]
High values of U are attained in the central part of the shape. 12

13. Extract space-time shape features [1]
Space-Time Saliency
Distinguish between different human parts.
Emphasize torso: where:
Emphasize fast moving parts: 13

14. Extract space-time shape features [2]
Emphasize fast moving parts: 14

15. Extract space-time shape features [3]
Space-Time Orientations
Estimate the local orientation and aspect ratio of different space-time parts.
Use the 3x3 Hessian H of U.
Hessian matrix - square matrix of second-order partial derivatives of a function 15

16. Extract space-time shape features [4]
Let be the eigenvalues of H.
The first principal eigenvector corresponds to the shortest direction.
The third principal eigenvector corresponds to the elongated direction.
- “stick” structure.
- “plate” structure.
- “ball” structure. 16

17. Extract space-time shape features [5]
“Plateness”:
“Stickness”:
“Ballness” – redundant.
Deviation of dominant eigenvector from principal axes:
Orientation local features: 17

18. Extract space-time shape features [6]
Global Features - In order to represent an action with global features, a weighted moments measure is used:
where:
g(x,y,t) – characteristics function
w(x,y,t) – one of the seven possible weighting functions 18

19. Results and Experiments [1]
Action classification and Clustering:
90 low-resolution (180x144, deinterlaced 50 fps) video sequences showing 9 different people, each performing 10 natural actions (“run”, “walk”, “jumping-jack” and more).
Silhouettes obtained by subtracting the median background from each of the sequences.
Poisson equation and seven features were computed. 19

20. Results and Experiments [2]
Action classification and Clustering:
Sliding window in time to extract 8 frames space-time cubes, with an overlap of 4 frames between the consecutive space-time cubes.
Centered each space-time cube around its space-time centroid.
Procedure does not involve any global video alignment!
Computed global features measure vector with moments. 20

21. Results and Experiments [3]21

22. Action Classification
Leave-one-out procedure: remove the entire sequence from the database, keep other actions of the same person.
Compare each cube of the removed sequence to all the cubes in database.
Classify using the nearest neighbor procedure on global features measure (Euclidean distance).
Results: The algorithm misclassified 20 out of 923 space-cubes (2.17% error)! 22

23. Action Clustering
A common spectral clustering algorithm was applied to 90 unlabeled action sequences, representing 10 different actions.
Distance between two sequences is a variant of he Median Hausdorff Distance:
Spectral Clustering.
Results: 4 out of 90 misclassification (4.4% error). 23

24. Robustness [1]
10 test video sequences, people walking in various difficult scenarios.
10 additional sequences, each showing the “walk” action captured from a different viewpoint.
Measured the Median Hausdorff Distance between each sequence and each action type, Classified each sequence as the smallest distance action. 24

25. Robustness [2] Results:
First group sequences were classified correctly as the “walk” action, with relatively large difference between the first and second choices.
Second group sequences were classified correctly, viewpoints between 0 degree and 54 degree with relatively large difference. For Larger view points, a gradual deterioration occurs. 25

26. Action Detection [1] Ballet movie.
Let’s find all the places with the male dancer performing a “cabriole pa”!
Simple Euclidean distances threshold. 26

27. 111Kbps, wmv format 192x144x750 ballet movie
Action Detection [2]
111Kbps, wmv format 192x144x750 ballet movie
Query: 27

28. Bibliography
“Shape Representation and Classification Using the Poisson Equation”, L. Gorelick, M. Galun, E. Sharon, A. Brandt, and R. Basri.
“On Spectral Clustering: Analysis and an Algorithm”, A. Ng, M. Jordan, and Y. Weiss.
Lena Gorelick’s website and materials (
Wikipedia. 28