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Temporal Scale-Spaces ScSp03

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D
Daniel Fagerstrom

Presented at Scale-Space 03

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Temporal Scale Spaces Daniel Fagerström CVAP/NADA/KTH [email_address]
Measurement of Temporal Signals ,[object Object],[object Object],[object Object],[object Object]
Earlier Approaches ,[object Object],[object Object],[object Object]
Current Approach ,[object Object]
Space vs. Time Space All directions simultaneously available Time The past can be memorized, the future can not Memory
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object]
Principles ,[object Object],[object Object],[object Object]
Measurement
Meaurement ,[object Object],[object Object]
Examples ,[object Object],[object Object],[object Object]
Causality ,[object Object],[object Object]
Embodiment of Geometry ,[object Object],[object Object],[object Object]
Covariance ,[object Object],[object Object]
Orbits
Convolution ,[object Object],[object Object]
Cascade Property (Semi-Group)
Extended Point ,[object Object],[object Object]
Temporal Scale Space Kernels ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Characterization Laplace transform Semi-group and causality Continuity (Cauchy’s functional equation)
Characterization (Cont) Dilatation covariance Positivity (Bernstein)
Temporal Scale Space Kernels 0.3 0.5 0.8
Extremal Stable Density Functions ,[object Object],[object Object],[object Object]
Explicit Form
Markov Property? ,[object Object],[object Object],[object Object], t L(0,  )=0 L(t,  )=f(t)
Fractional Derivatives ,[object Object],[object Object],[object Object]
Evaluation Equations ,[object Object],[object Object],[object Object],[object Object],[object Object]
Uniquenes of the Signaling Equation ,[object Object],[object Object],[object Object]
Signaling Equation ,[object Object],[object Object]
Numerical Scheme ,[object Object],[object Object],[object Object],t  3/2 -1/2
Example
Example
Comparison with Previous Work ,[object Object],[object Object]
Comparison with Earlier Work ,[object Object],[object Object]
Comparison with Earlier Work ,[object Object],[object Object],[object Object]
Conclusion ,[object Object],[object Object],[object Object],[object Object]

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Temporal Scale-Spaces ScSp03