Deformable registration using shape statistics with applications in sinus surgery Ayushi Sinha March 22 nd , 2018 1
In endoscopic surgery endoscope G. Scadding et al., Diagnostic tools in Rhinology EAACI position paper , Clinical and Translational Allergy, 1(2), 2011 • Restricted field of view • Need ed to know surrounding and occluded structures 2
A Sin inha ha, et al., Automatic segmentation and statistical shape modeling of the paranasal sinuses to estimate natural variations , SPIE Medical Imaging, 2016 A Sin inha ha, et al., Simultaneous segmentation and correspondence improvement using statistical modes , SPIE 3 Medical Imaging, 2017
S Leonard, A Reiter, A Sinh nha, et al., Image-based navigation for functional endoscopic sinus surgery using structure from motion , SPIE Medical Imaging, 2016 S. D. Billings, A. Sin inha ha, et al., Anatomically Constrained Video-CT Registration via the V-IMLOP Algorithm , MICCAI, 2016 S Leonard, A Sin inha ha, et al., Evaluation and Stability Analysis of Video-Based Navigation System for Functional 4 Endoscopic Sinus Surgery on In-Vivo Clinical Data , Trans. Medical Imaging, 2018 ( in submission )
In clinic endoscope G. Scadding et al., Diagnostic tools in Rhinology EAACI position paper , Clinical and Translational Allergy, 1(2), 2011 • For diagnosis and planning • Need ed to know how much patient anatomy diverges from normal 5
Objectives • Surgical/clinical navigation without additional tools • Compensate for deformations in anatomy • Estimate anatomy in the absence of CT 6
Accomplishments Segmentat entation ion Corr rrespondence espondence Deformab ormable le • Technical and modeli eling ng improv ovem ement ent registrati istration on Anatom omica ical l • Clinical Nasal al cyc ycle le Nasal al patency ency variat ation ion 7
Outline Deformable Results and Background registration confidence framework estimates • Statistical shape models • Iterative closest point (ICP) • Iterative most likely point (IMLP) 8
Outline Deformable Results and Background registration confidence framework estimates • Deformable iterative most likely point (D-IMLP) • Deformable iterative most likely oriented point (D-IMLOP) • Generalized deformable iterative most likely oriented point (GD-IMLOP) 9
Outline Deformable Results and Background registration confidence framework estimates • Results on simulation data • Confidence associated with results • Results on in-vivo clinical data 10
Statistical shape models ⋯ v 11 v 21 v 𝑜 s 1 v 12 v 22 v 𝑜 s 2 ⋯ 𝐖 1 = 𝐖 2 = 𝐖 𝑜 s = ⋮ ⋮ ⋮ v 1𝑜 v v 2𝑜 v v 𝑜 s 𝑜 v A Sin inha ha, et al., Automatic segmentation and statistical shape modeling of the paranasal sinuses to estimate natural variations , SPIE Medical Imaging, 2016 A Sin inha ha, et al., Simultaneous segmentation and correspondence improvement using statistical modes , SPIE Medical Imaging, 11 2017
Statistical shape models Mean Variance iance 12
Statistical shape models Variance along the principal mode for the maxillary sinus Front view Left view 13
Statistical shape models Variance along the principal mode for the middle turbinates Front view Right view 14
Shape estimation using statistical shape models (SSMs) Mode we weights hts Estimat mated ed shape pe ∗ v 1 ∗ v 2 𝐖 ∗ = ⋮ ∗ v 𝑜 v 15
Shape estimation using statistical shape models (SSMs) Mode we weights hts Estimat mated ed shape pe ∗ v 1 ∗ v 2 𝐖 ∗ = ⋮ ∗ v 𝑜 v What if correspondences are not available? 16
Iterative closest point (ICP) algorithm Find closest point match on Ψ for all X Compute transformation to align matches y 𝑗 ∈ Ψ X = {x 𝑗 } 17
Iterative most likely point (IMLP) algorithm Find most likely point match on Ψ for all X Compute transformation to align matches y 𝑗 ∈ Ψ X = {x 𝑗 } 18
Outline Deformable Results and Background registration confidence framework estimates • Deformable iterative most likely point (D-IMLP) • Deformable iterative most likely oriented point (D-IMLOP) • Generalized deformable iterative most likely oriented point (GD-IMLOP) 19
Deformable iterative most likely point (D-IMLP) algorithm Find most likely point match on Ψ for all X Compute transformation to align matches y 𝑗 ∈ Ψ X = {x 𝑗 } and deform orm 𝛀 to fit to 𝐘 20
Deformable iterative most likely point (D-IMLP) algorithm y 𝑗 ∈ Ψ X = {x 𝑗 } 𝑔(y i , s) 21
Deformable iterative most likely point (D-IMLP) algorithm Find R, t and a such that x is best aligned with a deformed y Find s such that y deforms to fit x y 𝑗 ∈ Ψ X = {x 𝑗 } 𝑔(y i , s) 22
Deformable iterative most likely oriented point (D-IMLOP) algorithm Find R, t and a such that x is best aligned with a deformed y … and such that the normal of y aligns with that of x Find s such that y deforms to fit x y 𝑗 ∈ Ψ X = {x 𝑗 } 𝑔(y i , s) , 23
Generalized deformable iterative most likely oriented point (GD-IMLOP) algorithm Find R, t and a such that x is best aligned with a deformed y … and such that the normal of y aligns with that of x Find s such that y deforms to fit x y 𝑗 ∈ Ψ X = {x 𝑗 } 𝑔(y i , s) , , 24
What is T ssm (y 𝑗 ) ? (2) 𝐰 𝑗 (3) 𝜈 𝑗 (1) 𝐰 𝑗 y 𝑗 (1) 𝜈 𝑗 (2) 𝜈 𝑗 (3) 𝐰 𝑗 25
Deformable most likely point paradigm 26
Outline Deformable Results and Background registration confidence framework estimates • Results on simulation data • Confidence associated with results • Results on in-vivo clinical data 27
Comparison between… y 𝑗 ∈ Ψ y 𝑗 ∈ Ψ X = {x 𝑗 } y 𝑗 ∈ Ψ X = {x 𝑗 } X = {x 𝑗 } Y = {y 𝑗 } X = {x 𝑗 } D-IMLP D-IMLOP GD-IMLOP SSM estimate Coherent Point Drift (CPD) • Position • • Position • Position • Position • Isotropic • • Anisotropic • Anisotropic • Anisotropic Gaussian noise Gaussian noise Gaussian noise Gaussian noise • Orientation • Orientation • Isotropic Fisher • Anisotropic Kent noise noise 28
Error metrics Registered points Estimated shape Ground truth shape Total al shape pe error or Total al registra stratio tion n error (TSE) (TRE RE) 29
Leave-one-out experiment • # sample point: 1000 (uniformly) • Translational offset: [0, 15] mm • Rotational offset: [0, 9] degrees • Noise: • 1 × 1 × 1mm 3 • 20° (𝑓 = 0.5) • Noise assumed: • 1 × 1 × 1mm 3 Middle turbinate • 20° (𝑓 = 0.5) 30
Leave-one-out experiment Total al shape pe error or Total al registrati stration n error 31
Leave-one-out experiment Total al shape pe error or Time CPD CPD 32
Leave-one-out experiment • # sample point: 1000 (uniformly) • Translational offset: [0, 15] mm • Rotational offset: [0, 9] degrees • Noise: • 1 × 1 × 1mm 3 • 20° (𝑓 = 0.5) • Noise assumed: • 1 × 1 × 1mm 3 Right nostril • 20° (𝑓 = 0.5) 33
Leave-one-out experiment Total al shape pe error or Total al registrati stration n error 34
Parameter sweep • # sample point: 500 (uniformly) • Translational offset: [0, 15] mm • Rotational offset: [0, 9] degrees • Noise: • 2 × 2 × 4mm 3 • 10° (𝑓 = 0.5) Right nostril • Noise assumed: Position Orientation 1x1x1mm 3 , 1x1x2mm 3 , 2x2x2mm 3 , 2x2x3mm 3 , 2x2x4mm 3 , 2°, 10°, 20° 3x3x3mm 3 , 3x3x4mm 3 , 3x3x5mm 3 , 4x4x4mm 3 , 4x4x5mm 3 35
Parameter sweep Actual noise in samples: 2 × 2 × 4mm 3 , 10° (𝑓 = 0.5) Assumed ed Assumed ed Assumed ed (Assumed) (Assumed) (Assumed) Assumed position noise: Isotropic 36
Parameter sweep Actual noise in samples: 2 × 2 × 4mm 3 , 10° (𝑓 = 0.5) Assumed ed Assumed ed Assumed ed (Assumed) (Assumed) (Assumed) Assumed position noise: Anisotropic 37
Leave-one-out experiment • # sample point: 3000 (nasal passage) • Translational offset: [0, 10] mm • Rotational offset: [0, 10] degrees • Noise: • 0.5 × 0.5 × 0.75mm 3 • 10° (𝑓 = 0.5) • Noise assumed: • 1 × 1 × 2mm 3 • 30° (𝑓 = 0.5) Right nostril 38
Leave-one-out experiment Total al shape pe error or 39
Leave-one-out experiment Total al shape pe error or Total al registrati stration n error 40
Success classification: D-IMLP ≈ 𝜓 2 = distribution sity ty ity densi 𝑞 = Pr[E 𝑞 < 𝜓 2 ] abilit Probabil 𝜓 2 Chi-squar square e value lue 41
Success classification: D-IMLP = ≤ sity ty ity densi 𝑞 = Pr[E 𝑞 < 𝜓 2 ] abilit Probabil Chi-squar square e value lue 42
Success classification: D-IMLOP = ≤ ≈ 𝜓 2 distribution = 43
Success classification: D-IMLOP = ≤ ≤ = 44
Success classification: GD-IMLOP = ≤ ≈ 𝜓 2 distribution = 45
Success classification: GD-IMLOP = ≤ ≤ = 46
Success classification (leave-out analysis) • # sample point: 3000 (nasal passage) • Translational offset: [0, 10] mm • Rotational offset: [0, 10] degrees • Noise: • 0.5 × 0.5 × 0.75mm 3 • 10° (𝑓 = 0.5) • Noise assumed: • 1 × 1 × 2mm 3 • 30° (𝑓 = 0.5) Right nostril 47
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