Seam Carving for Content-Aware Finding Optimal Seams Image - PowerPoint PPT Presentation

Seam Carving for Image Resizing Overview Definitions Seam Carving for Content-Aware Finding Optimal Seams Image Resizing Optimal Seams Order Results Video Synopsis Ricardo David Casta˜ neda Marin Experiments References Computer Graphics at Instituto de Matematica Pura e Aplicada VISGRAF November 29, 2007

Overview Seam Carving for Image Resizing Overview Content Aware − → Energy Preservation Definitions Finding Optimal Seams Optimal Seams Order Results Video Synopsis Experiments References Figure: Image and its Energy

Overview Seam Carving for Image Resizing Content Aware − → Energy Preservation Overview Definitions Finding Optimal Seams Optimal Seams Order Results Video Synopsis Experiments References Figure: Different strategies for energy preservation

Definitions Seam Carving for Image Resizing Overview Definitions Finding Optimal Seams ◮ Image: I = I ( i , j ) of size n × m . Optimal Seams Order Results Video Synopsis Experiments References

Definitions Seam Carving for Image Resizing ◮ Image: I = I ( i , j ) of size n × m . Overview ◮ Vertical Seam: { ( i , S ( i )) } n i =1 , such that Definitions | S ( i ) − S ( i − 1) | ≤ 1 , ∀ i > 1. Finding Optimal Seams Optimal Seams Order Results Video Synopsis Experiments References Figure: Vertical Seam

Definitions Seam Carving for Image Resizing Overview Definitions Finding Optimal Seams ◮ Image: I = I ( i , j ) of size n × m . Optimal Seams Order ◮ Vertical Seam: { ( i , S ( i )) } n i =1 , such that Results | S ( i ) − S ( i − 1) | ≤ 1 , ∀ i > 1. Video Synopsis Experiments ◮ Energy: e 1 ( I ) = | ∂ I ∂ x | + | ∂ I ∂ y | = E . References

Definitions Seam Carving for Image Resizing Overview Definitions Finding Optimal Seams ◮ Image: I = I ( i , j ) of size n × m . Optimal Seams Order ◮ Vertical Seam: { ( i , S ( i )) } n i =1 , such that Results | S ( i ) − S ( i − 1) | ≤ 1 , ∀ i > 1. Video Synopsis Experiments ◮ Energy: e 1 ( I ) = | ∂ I ∂ x | + | ∂ I ∂ y | = E . References ◮ Seam Cost: cost ( S ) = Σ n i =1 E ( i , S ( i )) .

Definitions Seam Carving for Image Resizing Overview Definitions Finding Optimal Seams ◮ Image: I = I ( i , j ) of size n × m . Optimal Seams Order ◮ Vertical Seam: { ( i , S ( i )) } n i =1 , such that Results | S ( i ) − S ( i − 1) | ≤ 1 , ∀ i > 1. Video Synopsis Experiments ◮ Energy: e 1 ( I ) = | ∂ I ∂ x | + | ∂ I ∂ y | = E . References ◮ Seam Cost: cost ( S ) = Σ n i =1 E ( i , S ( i )) . ◮ Optimal Seam: S ∗ = min S { cost ( S ) } .

How to find Optimal Seams? Seam Carving for Image Resizing Overview ◮ M ( i , j ) = Minimum Cost from Row 1 to ( i , j ) in E. Definitions Finding Optimal Seams Optimal Seams Order Results Video Synopsis Experiments References

How to find Optimal Seams? Seam Carving for Image Resizing Overview ◮ M ( i , j ) = Minimum Cost from Row 1 to ( i , j ) in E. Definitions = E ( i , j ) + min { M ( i − 1 , j − 1) , M ( i − 1 , j ) , M ( i − 1 , j + 1) } Finding Optimal Seams Optimal Seams Order Results Video Synopsis Experiments References

How to find Optimal Seams? Seam Carving for Image Resizing Overview ◮ M ( i , j ) = Minimum Cost from Row 1 to ( i , j ) in E. Definitions = E ( i , j ) + min { M ( i − 1 , j − 1) , M ( i − 1 , j ) , M ( i − 1 , j + 1) } Finding Optimal Seams ◮ S ∗ ( n ) = minArg j M ( n , j ) Optimal Seams Order Results Video Synopsis Experiments References

How to find Optimal Seams? Seam Carving for Image Resizing Overview ◮ M ( i , j ) = Minimum Cost from Row 1 to ( i , j ) in E. Definitions = E ( i , j ) + min { M ( i − 1 , j − 1) , M ( i − 1 , j ) , M ( i − 1 , j + 1) } Finding Optimal Seams ◮ S ∗ ( n ) = minArg j M ( n , j ) Optimal Seams Order ◮ S ∗ ( i ) = minArg S ( i +1) − 1 ≤ j ≤ S ( i +1)+1 M ( i , j ) Results Video Synopsis Experiments References

How to find Optimal Seams? Seam Carving for Image Resizing ◮ M ( i , j ) = Minimum Cost from Row 1 to ( i , j ) in E. Overview = E ( i , j ) + min { M ( i − 1 , j − 1) , M ( i − 1 , j ) , M ( i − 1 , j + 1) } Definitions ◮ S ∗ ( n ) = minArg j M ( n , j ) Finding Optimal ◮ S ∗ ( i ) = minArg S ( i +1) − 1 ≤ j ≤ S ( i +1)+1 M ( i , j ) Seams Optimal Seams Order Results Video Synopsis Experiments References Figure: Finding Optimal Seams

How to find Optimal Seams? Seam Carving for Image Resizing Overview ◮ M ( i , j ) = Minimum Cost from Row 1 to ( i , j ) in E. Definitions = E ( i , j ) + min { M ( i − 1 , j − 1) , M ( i − 1 , j ) , M ( i − 1 , j + 1) } Finding Optimal Seams ◮ S ∗ ( n ) = minArg j M ( n , j ) Optimal Seams Order ◮ S ∗ ( i ) = minArg S ( i +1) − 1 ≤ j ≤ S ( i +1)+1 M ( i , j ) Results Video Synopsis Experiments References Figure: Finding Optimal Seams

Optimal Seams Order Seam Carving for Image Resizing Overview Definitions Finding Optimal Seams Optimal Seams Order ◮ Transport Map: T ( i , j ) = Minimum cost of removing i Results rows and j columns . Video Synopsis Experiments References

Optimal Seams Order Seam Carving for Image Resizing ◮ Transport Map: T ( i , j ) = Minimum cost of removing i Overview Definitions rows and j columns . Finding Optimal ◮ T ( r , c ) = min { T ( r − 1 , c )+ X ( r − 1 , c ) , T ( r , c − 1)+ Y ( r , c − 1) } . Seams Optimal Seams Order Results Video Synopsis Experiments References Figure: Computing T

Optimal Seams Order Seam Carving for Image Resizing Overview ◮ Transport Map: T ( i , j ) = Minimum cost of removing i Definitions rows and j columns . Finding Optimal Seams ◮ T ( r , c ) = min { T ( r − 1 , c )+ X ( r − 1 , c ) , T ( r , c − 1)+ Y ( r , c − 1) } . Optimal Seams ◮ Backtracking 0 = row , 1 = column . Order Results Video Synopsis Experiments References Figure: Backtracking

Seam Removal Seam Carving for Image Resizing Overview Definitions Finding Optimal Seams Optimal Seams Order Results Video Synopsis Experiments References Figure: Seam Removal

Seam Insertion Seam Carving for Image Resizing Overview Definitions Finding Optimal Seams Optimal Seams Order Results Video Synopsis Experiments References Figure: Seam Insertion

Amplification Seam Carving for Image Resizing Overview Definitions Finding Optimal Seams Optimal Seams Order Results Video Synopsis Experiments References Figure: Amplification

Video Synopsis Seam Carving for Image Resizing Overview ⇒ Deleting redundancies in time. Definitions Finding Optimal Seams Optimal Seams Order Results Video Synopsis Experiments References Figure: Synopsis video: The baby and the child appear at different times in the original video, while the synopsis video can represent them at the same time.

Seam Carving in Time Seam Carving for Image Resizing Overview Definitions Finding Optimal Seams ◮ Sequence of Images: f ( i , j , t ), with k frames of size Optimal Seams Order n × m Results Video Synopsis Experiments References

Seam Carving for Content-Aware Finding Optimal Seams Image - PowerPoint PPT Presentation

Seam Carving for Image Resizing Overview Definitions Seam Carving for Content-Aware Finding Optimal Seams Image Resizing Optimal Seams Order Results Video Synopsis Ricardo David Casta neda Marin Experiments References Computer

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Seam Carving for Content-Aware Finding Optimal Seams Image - PowerPoint PPT Presentation

Seam Carving for Image Resizing Overview Definitions Seam Carving for Content-Aware Finding Optimal Seams Image Resizing Optimal Seams Order Results Video Synopsis Ricardo David Casta neda Marin Experiments References Computer

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