Colon Visualization UsingShape Preserving Flattening

Joseph Marino and Arie Kaufman

Stony Brook University

Introduction

• Virtual colonoscopy is a popular non-invasive colon screening method

• Various colon flattening methods proposed– Cylindrical projections of segments [Vilanova Bartoli et al.]

– Mass-spring unfolding [Umemoto et al.]

– Conformal mapping [Haker et al., Hong et al.]

• Need methods to visualize flattened colons

Related Work

• Visualize conformally flattened colon meshes– Shape characteristics are of utmost importance

• Polygonal rendering of flattened meshes– Use per-vertex normals of original surface mesh– Encode geometric properties as color at each vertex• E.g., curvature

• These methods do not have the quality or look of the VC endoluminal view

Generating 2D Views

• Use volumetric ray casting– Similar to endoluminal view

• Obtain view position for each ray– For each column of pixels in final image• Average original 3D positions of each pixel• These form a flattened centerline along the entire colon• Use these as view point for ray casting

(each column uses its average position value)

2D Surface Views

• Opaque transfer function– Typical colon surface view– Structures identifiable due to shape preserving map

• This rendering is more natural to view and of higher quality than a simple mesh rendering

Further 2D Views

• Using ray casting also allows for other rendering effects– E.g., electronic biopsy rendering

• Given two flattened colons with a one-to-one and onto correspondence, obtaining matching views in 2D is trivial

Integration for 3D Navigation

• Flattened colon can help guide 3D navigation

• For a location on the flattened colon, obtain the view frustum to view that location in the endoluminal view

• View position either on flattened centerline or volumetric skeleton

Obtaining View Frustums

𝑣0 = 𝑝− 𝑜ȁ�𝑝− 𝑜ȁ� , 𝑣1 = 𝑐1 − 𝑐0ȁ�𝑐1 − 𝑐0ȁ� , 𝑣2 = 𝑣0 × 𝑣1 ,

Given: location p on the surface viewpoint o on centerline (closest to p) neighboring centerline points c0 and c1

{o; v0, v1, v2}

Corresponding View FrustumsIf one-to-one and onto mapping between two flat colons

Given view frustum on supine, find corresponding view frustum in prone

Similar to previous 𝑣𝑝1 = 𝑝0 − 𝑜𝑝ห𝑝0 − 𝑜𝑝ห ,

𝑣𝑝0 = ൫𝑝1 − 𝑜𝑝൯× 𝑣𝑝1ห൫𝑝1 − 𝑜𝑝൯× 𝑣𝑝1ห , 𝑣𝑝2 = 𝑣𝑝0 × 𝑣𝑝1 ,

{op; vp0, vp1, vp2}

Conclusion

• Methods to integrate shape preserving flattening into VC system

• Flattened 2D view with same look and feel as typical 3D endoluminal view

• Use 2D flattened mesh to assist in navigation in the 3D endoluminal view

Acknowledgements

• This work has been supported by NIH grant R01EB7530 and NSF grants IIS0916235, CCF0702699.

• The datasets are provided through the NIH, courtesy of Dr. Richard Choi, Walter Reed Army Medical Center.

Questions & Answers