Geometry seam carving

Highlights

• Mesh deformation with preservation of salient features.

• Transfer of the concept of seam carving from images to 3D meshes.

• Combination of elastic mesh editing with a novel discrete mesh deformation approach.

• Adaptation of the surface tessellation to the degree of the deformation distortion.

Abstract

We present a novel approach to feature-aware mesh deformation. Previous mesh editing methods are based on an elastic deformation model and thus tend to uniformly distribute the distortion in a least-squares sense over the entire deformation region. Recent results from image resizing, however, show that discrete local modifications such as deleting or adding connected seams of image pixels in regions with low saliency lead to far superior preservation of local features compared to uniform scaling — the image retargeting analog to least-squares mesh deformation. Hence, we propose a discrete mesh editing scheme that combines elastic as well as plastic deformation (in regions with little geometric detail) by transferring the concept of seam carving from image retargeting to the mesh deformation scenario. A geometry seam consists of a connected strip of triangles within the mesh’s deformation region. By collapsing or splitting the interior edges of this strip, we perform a deletion or insertion operation that is equivalent to image seam carving and can be interpreted as a local plastic deformation. We use a feature measure to rate the geometric saliency of each triangle in the mesh and a well-adjusted distortion measure to determine where the current mesh distortion asks for plastic deformations, i.e., for deletion or insertion of geometry seams. Precomputing a fixed set of low-saliency seams in the deformation region allows us to perform fast seam deletion and insertion operations in a predetermined order such that the local mesh modifications are properly restored when a mesh editing operation is (partially) undone. Geometry seam carving hence enables the deformation of a given mesh in a way that causes stronger distortion in homogeneous mesh regions while salient features are preserved much better.

Introduction

The deformation of three-dimensional (3D) models has a wide range of applications in artistic as well as industrial design. Nowadays, the predominant representations of surfaces are triangle meshes which come at high resolution, often acquired using 3D laser scanning, and exhibiting geometric details at various scales. For a deformation technique to be considered useful for editing of such meshes, it is hence crucial that it meets certain requirements: apart from providing visual feedback for interactive application, it should provide easy to control modeling metaphors. Most importantly, it should generate intuitive and predictable deformation results that are physically plausible and aesthetically pleasing. In order to meet these quality requirements, a deformation method has to preserve local characteristics of a surface, i.e., geometric detail or features, under deformation.

This paper presents a novel mesh deformation technique that puts special emphasis on the aspect of feature preservation. Previous mesh editing approaches are mostly based on an elastic deformation model and usually distribute the distortion over the entire deformation region in a least-squares sense. Recent research on image resizing, however, demonstrated that discrete modifications produce results that are far superior to those obtained by applying uniform scaling, which can be considered as the analog in the image processing world to a least-squares deformation in the mesh editing world.

In their work on image seam carving, Avidan and Shamir  [1] insert or delete a connected seam of image pixels in regions with low energy, yielding realistically looking and visually pleasing resizing results. In our work, we transfer the concept of discrete modifications from the image retargeting to the mesh deformation scenario. Our definition of a seam is closely related to the image setting: a geometry seam is a closed and connected path of low-energy triangles and runs through the modeling region of a mesh. Depending on the characteristics of the deformation, geometry seams can be removed from the mesh by collapsing their interior edges and they can be inserted by splitting these edges, which resembles the delete or insert operations in image seam carving. By precomputing a set of low-saliency seams, we can perform deletion and insertion operations at interactive rates. Furthermore, applying the operations in a predetermined order allows us to properly undo previous editing operations and hence to restore the original model. We use a well-established elastic mesh deformation method which we significantly adapt such that it jointly works with this novel plastic and discrete modification scheme which intervenes when the surface distortion exceeds certain thresholds and calls for additional remeshing. This enables editing of a 3D model, thereby distributing the distortion non-homogeneously over the model, and hence causing stronger deformations in low-saliency mesh regions, while features are preserved much better compared to purely elastic mesh editing methods.