Galilean Differential Geometry Of Moving Images

Galilean Differential Geometry of Moving Images Daniel Fagerström CVAP/NADA/KTH [email_address]

Differential Structure of Movies ,[object Object],[object Object],[object Object]

Approaches for Motion Analysis ,[object Object],[object Object],[object Object]

Optical Flow ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Spatio-Temporal Differential Invariants ,[object Object],[object Object],[object Object],[object Object],[object Object]

Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Galilean Geometry ,[object Object],Shear x t x t

Galilean Geometry ,[object Object],[object Object],[object Object],[object Object],[object Object]

Galilean Invariants ,[object Object],[object Object],[object Object]

Galilean ON-System ,[object Object]

Moving Frames ,[object Object],[object Object],[object Object],[object Object],[object Object]

Moving Frames C(A) contains the differential geometric invariants expressed in the global frame i

Image Geometry ,[object Object],[object Object],[object Object],[object Object],[object Object]

Gradient Gauge ,[object Object],[object Object]

Hessian Gauge ,[object Object],[object Object]

Galilean 1+1 D ,[object Object],[object Object],[object Object]

Tangent Gauge ,[object Object]

Hessian Gauge ,[object Object]

Galilean 2+1 D ,[object Object],[object Object],[object Object],[object Object]

Invariants in the General Case ,[object Object],[object Object],[object Object],[object Object],[object Object]

More Descriptive Invariants ,[object Object],[object Object],[object Object]

Tangent Gauge ,[object Object],[object Object],[object Object]

Hessian Gauge ,[object Object],[object Object],[object Object]

Real Image Sequences ,[object Object],[object Object]

Conclusion ,[object Object],[object Object],[object Object],[object Object],[object Object]

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