Future works

desired properties. For example, components on a higher level reveal higher degree of salience than their descendant parts and the components on each level of hierarchy have similar degree of salience. Moreover, the number of boundaries on each level of the hierar-chy is determined automatically. With the aid of the local volume information provided by MSP, the proposed segmentation scheme can decompose object into several levels of parts in more natural ways, and can be applied to objects in different topological types.

The proposed MSP-driven skeletonization framework first transforms the original mesh to a shrunk skeleton-like mesh using MSP information and then employs a greedy edge-swap framework to degenerate the shrunk mesh into an 1D skeleton. In the greedy frame-work, edges that deviate farther from the centerline would be swapped first and vertices are moved towards the centerline. Small branches are removed by checking the salience value of their correspondence surface region whenever a branch is formed. The metric de-signed for the greedy edge-swap framework and salience evaluation are formulated based on the MSP function. The skeleton generated by the proposed method has a dense node distribution at the core parts and around the junctions, and inherently possesses a skeleton-surface mapping. The single salience parameter for branch removal provides a flexible control for deriving skeletons with varying details. Moreover, consistent skeletons can be extracted for a model in different resolutions and poses. We demonstrated the effectiveness of the proposed algorithm by a rather extensive testing and comparison to a state-of-the-art method.

Beyond the intermediate-level shape property and its applications, we also investigated how to interpret and achieve users’ expectation when performing mesh simplification. A new concept of the user-controllable mesh simplification scheme is proposed in which the user-specified weights on some selected regions are used to reorder the simplification oper-ator rather than first altering the simplification costs and then reordering the simplification operator. Our scheme results in a predictable resolution improvement over the selected re-gions and is metric independent since the user-specified weights are not used to alter the simplification cost.

7.2 Future works

There exists some limitations to the proposed minimum slice perimeter. Some small high-lights of MSP value may be noticed on the surface since the slices may pass across multiple

7.2 Future works 72

object parts. A filter that is able to prune those slice segments outside the designate part is required to achieve a MSP that better describes the local volume information.

The existing salience definitions for the 3D object surface [41, 19] are based on the combination of local geometric properties such as curvature and area, which may not reveal the visual significance of object parts. We are also interested in investigating how the salience of a 3D object part can be defined based on the intermediate-level shape properties.

In addition to the derivation of minimum slice perimeter, the normal of the minimum perimeter slices associated with surface points reveals the orientation flow of the object shape, which can be used to guide the vector field generation on the object’s surface. We will investigate how to derive a shape-aware vector field on the surface using the orientation vectors provided by the minimum perimeter slices.

Our proposed skeletonization scheme can extract curved skeleton with dense node dis-tribution directly from 3D model. Such dense node disdis-tribution allows us to establish a reasonable many-to-one mapping between surface and skeleton. Such surface-skeleton mapping may be helpful in geometric modeling applications such as the surface-to-surface correspondence, mesh deformation, and mesh symmetrization. In the future, we will inves-tigate how these geometric modeling problems can be benefited from the skeleton-surface mapping.

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