Action as Space-Time Shapes

Benny YonovichLeon Ribinik

“Actions as Space-Time Shapes”

• Recognize, detect and cluster human actions.

Goal

• Represent actions as space-time shapes.

Approach

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.

Space-Time Shapes

• Induced by a concatenation of 2D silhouettes in the space-time volume.

• Contain both spatial and dynamic information.

Concept

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

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.

Extract the 2D silhouettes and build the space-time volume

• Video is simpler than image.• Background subtraction.

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.

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:

,2 f 2

.

Shape representation using the Poisson equation [1]

• An action and its space-time shape S.• Random walk.

1),,( tyxU• Compute: with ,,, Styx

ttyyxx UUUU

subject to 0),,( tyxU

Laplacian:

• Artificial boundary condition (Neumann): 0tU

on the bounding surface.

• Solution method: geometric multigrid solver.

Let’s get some intuition – 2D Poisson equation

• Consider a conic:• Special case – circle:• Poisson equation solution:

0),( 22 feydxcxybyaxyxP

)4(4

1

)(2

),(),( 22

yx

ba

yxPyxU

• Monotonic decreasing:• Boundary:• Maximum point – center:

04),( 22 yxyxP

xx

U

2

1

yy

U

2

1

0)4,( 22 yxyxU

1)0,0( U

Shape representation using the Poisson equation [2]

• High values of U are attained in the central part of the shape.

Extract space-time shape features [1]

• Space-Time SaliencyDistinguish between different human parts.

Emphasize torso:where:

Emphasize fast moving parts: 2

2

3UU

),,( tyx UUUU

))),,(1(log(max

)),,(1log(1

),,(tyx

tyx

Styx

Extract space-time shape features [2]

• Emphasize fast moving parts:

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

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.

321

• - “stick” structure.• - “plate” structure.• - “ball” structure. 321

321

321

Extract space-time shape features [5]• “Plateness”:• “Stickness”:• “Ballness” – redundant.

• Deviation of dominant eigenvector from principal axes:

• Orientation local features:

1

2

eS pl2

3

)1(

eSS plst

}3,2,1{,),,( jevtyxD jj

),,(),,(),,(, tyxDtyxStyxw jiji

Extract space-time shape features [6]

• Global Features - In order to represent an action with global features, a weighted moments measure is used:

dxdydttyxtyxgtyxwm rqppqr ),,(),,(

where: g(x,y,t) – characteristics function w(x,y,t) – one of the seven possible weighting functions

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.

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.

Results and Experiments [3]

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)!

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:

)min()min(),( 212121jiji

jiijH ccmedianccmedianssD

• Spectral Clustering.• Results: 4 out of 90 misclassification (4.4%

error).

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.

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.

Action Detection [1]• Ballet movie.• Let’s find all the places with the male dancer

performing a “cabriole pa”!• Simple Euclidean distances threshold.

Action Detection [2]Query:

111Kbps, wmv format 192x144x750 ballet movie

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 (http://www.wisdom.weizmann.ac.il/~yelenag).

• Wikipedia.