Deformable Image Registration Adrien Bartoli ALCoV – ISIT Université d’Auvergne Clermont-Ferrand, France Fourth Tutorial on Computer Vision in a Nonrigid World ICCV’11, Barcelona, Spain – octobre 6, 2011 Lourdes Agapito, Adrien Bartoli, Alessio Del Bue
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Deformable Image Registration
Adrien Bartoli
ALCoV – ISIT
Université d’Auvergne
Clermont-Ferrand, France
Fourth Tutorial on Computer Vision in a Nonrigid World ICCV’11, Barcelona, Spain – octobre 6, 2011
Lourdes Agapito, Adrien Bartoli, Alessio Del Bue
The Equations of Registration
Deformable Image Registration
The warp 𝜑𝑖: Ω → ℝ2 is a function that transfers pixels between images
Warp visualization grid
→ To relate the content of at least two images
𝜑1 𝜑2
𝜑3 ROI Ω ∈ ℕ2
Difficulty: Variation of the Imaged Appearance
External occlusions, color Self-occlusion Field of view + lighting
Scene geometry Surface appearance Imaging conditions
• External occlusions • Self-occlusions • Wrinkles and foldings • Temporal continuity • Extensibility • Etc.
• Lighting • Lack of / repeating texture • Reflectance • Specularities • Transparency • Etc.
• Pose • Field of view • Affine vs perspective • Optical and motion blur • Auto-exposure, saturation • Etc.
Template
Semantic Matching
The Warp Function 𝜑
The warp 𝜑:Ω → ℝ2 is continuous and piecewise ‘smooth’
3D deformation Ψ ∈ 𝐶0
Warp 𝜑 ∈ 𝐶0
Image Pair Versus Video Registration
𝜑1
𝜑2 𝜑3
Video registration
Image pair registration
𝜑
min𝜑∈𝐶0ℰ[𝜑]
A variational optimization problem
ℰ is the cost functional
Computational Warp Representation
A warp 𝜑 is an interpolant between pairs of fixed/moving driving features
source target
fixed
moving
Computational Warp Representation
Encompasses the Flow-Field, Mesh Interpolation, Radial Basis Functions (and so the Thin-Plate Spline), Tensors Product (and so the Cubic B-Spline Free-Form Deformation), etc.
[Brunet et al., IJCV’11 ; Bartoli et al., IJCV’10]
The Cost Functional
Data term • Relates the warp to the image content • Bayesian likelihood
Regularization term • Measures closeness to prior knowledge • Bayesian prior
From left to right • Subspace trajectory constraints, PCA basis [Garg et al, EMMCVPR’11] • Subspace trajectory constraints, DCT basis [Garg et al, EMMCVPR’11] • Large Displacement Optical Flow [Brox et al, ECCV’10] • Baseline method (no motion basis) [Wedel et al, 2009] • Pairwise B-Spline pixel-based estimation [Pizarro et al, IJCV]
Deformable Image Registration
Adrien Bartoli
ALCoV – ISIT
Université d’Auvergne
Clermont-Ferrand, France
Fourth Tutorial on Computer Vision in a Nonrigid World ICCV’11, Barcelona, Spain – octobre 6, 2011