Introduction

Visual motion

Many slides adapted from S. Seitz, R. Szeliski, M. Pollefeys1Motion and perceptual organizationSometimes, motion is the only cue

2Motion and perceptual organizationSometimes, motion is the only cue

3Motion and perceptual organizationEven impoverished motion data can evoke a strong percept

G. Johansson, Visual Perception of Biological Motion and a Model For Its Analysis", Perception and Psychophysics 14, 201-211, 1973.4Motion and perceptual organizationEven impoverished motion data can evoke a strong percept

G. Johansson, Visual Perception of Biological Motion and a Model For Its Analysis", Perception and Psychophysics 14, 201-211, 1973.5Motion and perceptual organizationEven impoverished motion data can evoke a strong perceptG. Johansson, Visual Perception of Biological Motion and a Model For Its Analysis", Perception and Psychophysics 14, 201-211, 1973.

6Uses of motionEstimating 3D structureSegmenting objects based on motion cuesLearning and tracking dynamical modelsRecognizing events and activities7Motion fieldThe motion field is the projection of the 3D scene motion into the image

8Motion field and parallaxX(t) is a moving 3D pointVelocity of scene point: V = dX/dtx(t) = (x(t),y(t)) is the projection of X in the imageApparent velocity v in the image: given by components vx = dx/dt and vy = dy/dtThese components are known as the motion field of the imagex(t)x(t+dt)X(t)X(t+dt)Vv9Motion field and parallaxx(t)x(t+dt)X(t)X(t+dt)Vv

To find image velocity v, differentiate x=(x,y) with respect to t (using quotient rule):

Image motion is a function of both the 3D motion (V) and thedepth of the 3D point (Z)

10Quotient rule for differentiation: D(f/g) = (g f g f)/g^2Motion field and parallaxPure translation: V is constant everywhere

11Motion field and parallaxPure translation: V is constant everywhere

The length of the motion vectors is inversely proportional to the depth ZVz is nonzero: Every motion vector points toward (or away from) the vanishing point of the translation direction

12At the vanishing point of the motion location, the visual motion is zeroWe have v = 0 when V_z x = v_0 or x = (f V_x / V_z, f V_y / V_z)Motion field and parallaxPure translation: V is constant everywhere

The length of the motion vectors is inversely proportional to the depth ZVz is nonzero: Every motion vector points toward (or away from) the vanishing point of the translation directionVz is zero: Motion is parallel to the image plane, all the motion vectors are parallel

13Optical flowDefinition: optical flow is the apparent motion of brightness patterns in the imageIdeally, optical flow would be the same as the motion fieldHave to be careful: apparent motion can be caused by lighting changes without any actual motionThink of a uniform rotating sphere under fixed lighting vs. a stationary sphere under moving illumination14