USER-GUIDED FEATURE SENSITIVE HOLE FILLING

FOR 3D MESHES

Hanh T.-M. Ngo and Won-Sook Lee

School of Information Technology and Engineeing, University of Ottawa, Ontario, Canada

Keywords: Hole filling, Surface reconstruction, 3D modelling, Real time user interaction.

Abstract: Most hole filling approaches use techniques to fill up a hole first and then to smooth it. Very few tries

rebuild features on the filled surface of the original 3D model. We propose an efficient hole-filling

methodology which preserves sharp features of the geometry of the original model. The main idea is that we

reconstruct feature curves in the missing parts of the given mesh before filling the hole with smoothing

surface. The feature curves in the missing part are reconstructed by extending salient features of the

existing parts. The hole is partitioned into several smaller and more planar sub-holes divided by the feature

curves and then the hole-filling step follows. User intervention is available to design the features to be

desired shape to guide feature curve reconstruction wherever ambiguity exists or results are unsatisfactory.

Our hole filling techniques is different from other existing techniques as features are taken as the first

subject to reconstruct, which eventually drive the feature-definite surface filling process. It is also very

efficient as a user is interfering only with features and the actual hole-filling step is dealing with only planar

holes.

1 INTRODUCTION

3D computer models of real life objects can be

obtained by several ways such as 3D scanning

devices, or computer-aided design software

(Autodesk Maya, 3DS Max, etc.). A common

scenario, especially when dealing with 3D shapes

obtained from 3D scanning, is to have incomplete

surfaces. These appear in areas where the object

geometry occludes the scanning device, notable

examples when scanning human bodies include the

area under the chin, armpits or between the fingers,

hence limiting the information obtained. Because of

these issues, many post processing techniques are

needed to be applied onto the raw models before

being able to use them as the input of design or

animation applications. The repair of incomplete

polygon meshes is a fundamental problem in the

reconstruction of 3D models in the field of computer

graphics.

One of key aspects of reconstruction of 3D

models is hole-filling. This is to complete the shape

of the 3D object where surface information is

missing. This is essential for a wide range of

applications such as computer animation, pattern

recognition, or character design. Hole-filling

techniques aim to keep the filled surface

continuously and smoothly fitted at the boundary of

the hole to conform to the shape of the original

model. Although there is a large body of research on

hole filling, very little attention has been devoted to

the problem of recovering fine features of the 3D

object, for instance the sharpness of the edge

geometry. Most research focuses on automatic

methods that require performing complex

optimization processes (Chui and Lai, 2000; Attene

et al., 2003; Liepa, 2003; Jun, 2005; Podolak and

Rusinkiewicz, 2005; Zhao et al., 2007; Chen and

Cheng, 2008). In many cases, although the models

obtained are hole-free, interpolation algorithms fail

to preserve fine details, ignoring sharp edges and

corner shapes.

Due to the complexity of the regions where holes

are generated, automatic model modification

methods may not give satisfactory results in dealing

with holes. Complex optimization frameworks are

computationally expensive. In addition, processing

large and complicated models is a time consuming

task. Despite of the great computational overhead,

fine features in models are not recovered. Since

there are potentially several possible results for the

surface recovery process, the user should have the

T.-M. Ngo H. and Lee W..

USER-GUIDED FEATURE SENSITIVE HOLE FILLING FOR 3D MESHES.

DOI: 10.5220/0003324700490058

In Proceedings of the International Conference on Computer Graphics Theory and Applications (GRAPP-2011), pages 49-58

ISBN: 978-989-8425-45-4

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

ability to influence the quality of the output surface.

Furthermore, although there are ways to set the

constraints for automatic methods to resolve

ambiguous topology problem, there will always be

the cases that require high-level knowledge to

disambiguate or have multiple answers, where the

selection depends on user’s preference. We believe a

program interface that allows user intervention

efficiently helps to reduce the implementation effort,

to give better visually plausible results and to

enhance the versatility of the system since the user

would have the ability to choose the desired feature-

topology and the shape of the filled mesh.

We are motivated by the need of a hole filling

system that is able to plausibly recover the fine

geometry features of the 3D models, especially the

sharp features, with some possible simple guidance

by users at the hole locations using a real time

Graphics User Interface (GUI). Our goal is to

develop a system that can repair the holes of the 3D

models and, at the same time, aesthetically preserve

the sharpness of the model at the hole locations with

the aid from user intervention.

Our main contributions are two-fold: (i) salient

features of the mesh geometry are taken as the first

subject to reconstruct, which eventually drive the

feature-definite surface filling process; (ii) the user

is allowed to influence the hole filling process at

feature designing level while the rest is taken care by

the automatic functions. Our results show missing

hole features are recovered with high quality while

supporting flexibility.

2 RELATED WORKS

Many researches on hole filling topic have been

done up to now. However, there are only few hole-

filling approaches attempting to preserve and to

recover the sharp features of the 3D model. In this

section we focus our discussion on feature sensitive

recovering methods for 3D meshes as they are of our

special interest.

Barequet and Kumar (Barequet and Kumar,

1997) proposed a method that allows users to inspect

the automatic results of the first iteration and also to

mark the areas to be corrected. The second iteration

produces the final results. The approach can produce

“intuitively-correct” filling of the holes with the aid

of the user.

In (Ohtake and Belyaey, 2003), to preserve the

shape of sharp edges and corners at the hole

locations, a multilevel piecewise surface fitting

method is employed to represent a mesh model that

has fine structures. Local approximation for fitting

edges and corners are based on the piecewise

quadric surface fitting method. It consists of a

number of tests (edge tests and corner tests) in order

to determine the type of approximation surface or

shape function that should be used. Edges and

corners are automatically recognized by clustering

the normals of the mesh vertices.

In (Sharf et al., 2004), a context-based

completion method is proposed to recover the

missing fine details in a repaired hole. The method

employs the idea of texture synthesis, by replicating

portions of regions from adequate examples. Based

on this idea, the fine structure of the 3D model is

recovered by finding a piece in the original model or

in the template models that is similar in shape to

replace the initial repaired hole. Hence, this method

is particularly efficient for repairing holes in

textured mesh model.

Attene et al. (Attene et al., 2003) proposed a

method to recover the sharp features of 3D mesh

model which are lost by reverse engineering or by

remeshing processes that use a non-adaptive

sampling of the original surface. The algorithm

starts by identifying the smooth edges in the mesh

model then applying the filters to get the chamfer

edges. Each chamfer edge and its incident triangles

are subdivided by inserting new vertices. These

vertices are calculated so that they lie on

intersections of planes that locally approximate the

smooth surfaces that meet at the sharp features.

In (Chen et al., 2005), holes are filled and

sharpness is recovered by applying a sharpness-

dependent filter. The filter operates based on the

distribution of the sharpness values of triangle faces

in the vicinity of a hole boundary. In this context,

the vicinity of a hole boundary is defined as its two-

ring neighborhood. For any triangle face, its

sharpness value is computed as the variance of the

angles between its normal and each of the normals

of the neighboring faces.

In (He and Chen, 2006), both automatic and

interactive methods are employed for hole-filling. A

novel hole-filling system that makes use of a haptic

device is proposed. After the hole identification

phase, the hole boundaries are smoothed in the

interpolation step. This step is to correct boundary

topologies and to adjust the boundary edge lengths

in order to avoid the uneven distribution of points at

the hole boundary. Then the user can decompose

those complex holes into simpler ones in stitching

process. Sub-holes are then automatically

triangulated using regular triangulation methods.

The user can repeat the intervention process until

GRAPP 2011 - International Conference on Computer Graphics Theory and Applications

obtaining satisfactory results. The authors proposed

an interesting idea about using haptic for 3D user

intervention. However, the limitation of this method

is the lack of an automatic method to detect the fine

features of the mesh to serve as the guidance for the

user.

In (Zhao et al., 2006), holes are detected then

triangulated using the modified minimum-weight

triangulation technique. Sharp features are recovered

by crest line fairing. The system makes use of the

crest line detection technique in (Yoshizawa et al.,

2005) to detect the feature lines in the original mesh.

Crest lines are the salient surface features defined

via the first- and the second-order curvature

derivatives. Detected crest lines are then used in

region growing and fairing processes to recover the

sharp features at the hole areas. The users are also

able to connect some crest lines before the region

growing step.

Chen and Cheng (Chen and Cheng, 2008)

presented a sharpness-based method for filling holes.

The whole algorithm performs in two steps: an

interpolation step for filling the hole which produces

the first approximation of the final model, and a

post-processing step which modifies the

approximation model to match the original. The

patch for the hole is interpolated using the radial

basis function to create a smooth implicit surface to

fill the holes. The implicit surface is triangulated

using a regularized matching tetrahedral algorithm.

Then the triangulated surface patch is stitched to the

hole boundary to obtain the repaired model. In the

post-processing step, a sharpness-dependent filter is

applied to the repaired model to recover its sharp

features. In this paper, the sharpness-dependent filter

is an improvement of the one presented in (Chen et

al., 2005). Although the algorithm works quite

effectively in repairing the models, the system is

difficult to implement.

Although an automatic system is always

desirable, dealing with fine features at the hole areas

is a challenging task. In spite of a complicated hole-

filling optimization engine to get the results

automatically as in (Zhao et al., 2007), the fine

features are not adequately recovered in many cases.

Most of the systems require user intervention

(Barequet and Kuma, 1997; He and Chen, 2006;

Zhao et al., 2006) to obtain the best guess of fine

features at the hole areas and to correct the

automatic results.

Our hole-filling system provides both fully

automatic and semi-automatic capabilities where

semi-automatic allows user to be comfortable

dealing with only several feature elements. If there is

no ambiguity in pairing the feature points and no

inaccurate crest lines detected at the hole vicinities,

our system can fully automatically produce

aesthetical results. Furthermore, while most hole

filling algorithms provide only automatic function

and manual hole filling takes a lot of user's time and

effort as it is at surface mesh level with numerous

points to touch and requires expert knowledge about

the objects and about how to manipulate on the 3D

mesh, our hole filling method, in the more complex

cases, need a very limited user intervention at the

feature level to support the hole filling procedure.

3 USER-GUIDED FEATURE

SENSITIVE HOLE FILLING

Our hole filling algorithm can completely fill the

holes of a model and aesthetically recover the

sharpness of the model at the hole areas, if any. It

includes the solution for efficient preservation of

sharpness properties of 3D mesh models during the

hole filling procedure; the solution for

implementation of a user-friendly interface to

support user intervention in real-time.

3.1 Algorithm Overview

Figure 1 shows a high level view of our user-guided

feature sensitive hole filling system. The input

model information is loaded into our designed data

structure for further usage in two modules: Crest

Incomplete model

Crest Line Detection Hole Identification

Feature pts Interpolation User Intervention

Feature Line Interpolation

Patch Generation

Patch Regulation

Repaired model

Figure 1: The framework of our system.

USER-GUIDED FEATURE SENSITIVE HOLE FILLING FOR 3D MESHES

Line Detection and Hole Identification. Crest line

information helps to find feature points in the holes

and their vicinities, which are used later for sharp

feature interpolation. Here, the user can interfere the

crest point positions and design the shape of the

patch mesh. Using this corrected information, our

system performs a feature line interpolation

procedure over the holes. This process defines the

expected fine features of the hole geometries and

also divides large complex holes into smaller and

more planar ones. For each of these simpler holes,

patch is generated by projecting the hole on its

projection plane, performing triangulation and then

mapping the triangulated topology back to 3D space.

The 3D patch is then stitched into the 3D model, and

it is regularized to make the patch consistent with

the original mesh, in order to produce the final

repaired mesh model.

3.2 Crest Line Detection

Defined in (Yoshizawa et al., 2005), the crest lines

are the salient surface features defined via the first-

and the second-order curvature derivatives. Crest

line detection has a significant role in our system

since it guides the user to pair the feature points on

the hole boundaries and to correctly interpolate the

feature lines over the holes. In our implementation,

we employed the crest line detection approach

proposed in (Yoshizawa et al., 2005).

Consider an oriented surface S and denote k

max

and k

min

its maximal and minimal principal

curvatures. Denote by t

max

and t

min

the corresponding

principal directions. Denote c

max

and c

min

the

derivatives of the principal curvatures along their

corresponding curvature directions. The convex crest

lines, also called ridges, are given by

max

= 0, δc

max

/δt

max

< 0,

max

> |k

min

(1)

while the concave crest lines, also called ravines, are

characterized by

min

= 0, δc

min

/δt

min

> 0,

min

< -|k

min

(2)

It also turns out that in our cases, the mesh

models are usually with holes, the crest lines that

suppose to pass over the holes areas are missing

after the crest line detection phase and need to be

recovered by some way. Furthermore, since there is

no surface information at the hole areas the detected

crest lines in the hole vicinity are usually go

incorrectly comparing to the case when the mesh

model is complete. In our algorithm, the detected

crest line information is used to interpolate the

missing parts. Hence, in order to have the accurate

interpolation results it is necessary to correct the

crest information at the hole vicinities first before

the interpolation is proceeded. We believe user

intervention to correct the crest line information is

the most efficient way and it is chosen in our

method. An example of inaccurately detected crest

lines at the hole’s vicinity and the corrected ones by

user through our GUI is showed in Figure 2.

Figure 2: (a) An example of inaccurate crest line detection

at the hole area: detected crest lines and crest points are

colored in green and blue correspondingly; (b) Crest lines

are corrected by user intervention.

3.3 Hole Identification

In the loading phase, all of the 1-ring neighbourhood

and connected component information of vertices,

edges and triangles of the input mesh model are

calculated and stored in our designed data structures

to facilitate further processing. Hence, at this step,

all boundary edges can be easily identified by

checking the numbers of their adjacent triangles, i.e.

for an edge, if the number of its adjacent triangles is

equal to one then that edge is a boundary edge. Its

two end vertices are the boundary vertices and its

adjacent triangle is the boundary triangle. Once the

boundary edge is detected, its two end vertices are

used as seeds to trace along the connected boundary

edges and vertices. If all identified points form a

closed loop they make up a hole.

3.4 Feature Line Interpolation

At this step, before doing the filling work, we

attempt to recover the sharp features, i.e. the feature

lines that suppose to pass over the hole areas. After

the feature lines are interpolated, the holes are also

subdivided by these feature lines into the smaller

and more planar ones. This indeed facilitates the

later hole filling procedure.

3.4.1 Basic Concepts

In our system convention, feature points are defined

GRAPP 2011 - International Conference on Computer Graphics Theory and Applications

as the crest points, either detected or interpolated,

that lie on the feature line segment passing over a

hole. Detected feature point is defined as the

intersection point between the crest line, either ridge

or ravine, with the hole boundary (see Figure 3).

Intersection point are the detected crest point, either

ridge- or ravine- point, that lies on hole edge, also

called boundary edge. Interpolated feature point is

the feature point obtained during the feature line

interpolation process. Figure 3 provides illustration

of these concepts.

Figure 3: An example of interpolating the feature lines

over a hole using spline interpolation: the interpolated

feature line is colored in blue, the interpolated feature

points are colored in green.

In the same way with Jun (Jun, 2005), we

consider two types of holes: simple hole and

complex hole. Simple holes are those that can be

filled with planar triangulations, which is the case

when all boundary edges can be projected into a

plane, without self-intersection (as illustrated in

Figure 4(a)). It is not adequate to fill the complex

hole with planar triangulations since there are

usually self-intersections when projecting the

complex hole boundaries into a plane (Figure 4(b)).

Thus, in our perspective, we attempt to properly

subdivide the complex holes into simple ones in

order to fill the holes by planar triangulation (see

Section 3.4.4).

Figure 4: Example of projecting holes onto planes: (a)

Simple hole makes no self-intersections; (b) Complex hole

creates self-intersections (colored in red) on the projection

plane.

3.4.2 User Intervention

Once feature points are detected in the previous step,

some limited user intervention at feature level is

needed

• To pair the detected feature points to avoid

ambiguity for the case there are multiple feature

lines passing over the hole;

• To adjust the inaccurately detected crest points

to enhance the accuracy and the quality of the

final result; and to specify the hole at the corner

of the object model by specifying the triple of

detected feature points lying on the hole

boundary at the corner area.

3.4.3 Feature Line Interpolation

To interpolate the missing feature lines passing over

the holes, the following issue should be addressed:

since we try to make use of the crest line

information which is automatically detected by the

system, the interpolated feature lines passing over

the hole should be interpolated by the available crest

lines and crest points.

We choose spline interpolation for interpolating

the feature lines at the hole areas. A spline is a

mathematical representation of a curve. It consists of

a series of points, called control points, at certain

intervals along the curve, and a function that allows

defining additional points within an interval.

Two requirements for the spline interpolation in

our case are

i. The curve should pass through all the control

points, as they define feature line, and its segments

act as the edges in the polygonal mesh model;

ii. It is necessary to be able to calculate the exact

positions of missing control points of the spline

based on the available ones.

There are various functions available for

approximating a curve and Catmull-Rom spline is

the one that satisfy the above requirements.

Figure 5: The Catmull-Rom spline passes through all of its

control points.

Recall the properties of Catmull-Rom spline

interpolation, a new point can be found between two

control points. This point is specified by a value t

USER-GUIDED FEATURE SENSITIVE HOLE FILLING FOR 3D MESHES

that represents a proportion of the distance from one

control point to the next one, as shown in Figure 5.

Given the control points P

, P

and parameter

t, 0≤ t ≤1.0, we can compute the new point location

q using the following equation:

0200

10 1 0

() 0.5 (1.0,, , )

2541

13 31

qt tt t

⎛⎞

⎜⎟

−

⎜⎟

=∗ ∗ ∗

⎜⎟

−−

⎜⎟

−−

⎝⎠

(3)

Figure 3 illustrates our method to interpolate a

feature line passing over a hole using the detected

crest line information. In our implementation, to

interpolate a feature line passing over a hole, the pair

of feature points on the hole boundary and their

adjacent crest points make four initial control points

for the Catmull-Rom interpolation equation (3).

Since we attempt to interpolate a feature line that has

the point density as consistent as possible to the

original mesh, the value t that appears in equation

(3) is approximated in our implementation as follow:

Given a hole that has n edges on its boundary.

Denote length(e

) the length of boundary edge e

;

denote a the average edge length of the hole

boundary. We have

elength

∑

)

(

(4)

Denote d the Euclidean distance between the

feature points F

and F

then we have

t =

(5)

3.4.4 Hole Partitioning

Once all the feature lines at the holes are

interpolated, a hole tracing procedure is executed.

For each hole, the procedure starts with a vertex on

the hole boundary, then it does the tracing along the

connected boundary edges and its corresponding

feature lines. If all identified points form a closed

loop they make up a hole. By involving feature lines

in the hole identification process at this step, the

original complex holes are indeed subdivided into

smaller, more planar and simpler sub-holes right at

the feature line locations.

In (Jun, 2005), the author discusses the self-

intersection problem when projecting a complex

hole onto a plane. This means some edges on the

hole boundary may overlap each other in the

projection plane. In our system, since the holes are

split at the salient feature curves, the sub-holes

obtained are already quite planar. In addition, by

using of the tangent plane of the hole boundary as its

projection plane our approach avoids efficiently the

self-intersection of the hole boundary.

3.5 Hole Filling

After all the polygonal holes in the original mesh

model are identified, for each hole its boundary

edges are then projected onto a projection plane for

further triangulation.

3.5.1 Projection Plane Calculation

For each hole or sub-hole identified in the input

mesh, we need to calculate the plane to project its

boundary onto. The requirement for such a plane is

that the projection of the boundary edges of a

polygonal hole on it is a bounded domain and it

should limit the possibility of creating the problem

of self-intersecting of the projected boundary as

much as possible.

We use the method to calculate the projection

plane that is based on the maximum area vector

method. The direction of the plane is derived from

the normalized sum of the normals of the boundary

triangles. The illustration of a hole and the direction

of its projection plane are shown in Figure 6. The

formula for computing the normal N of the

projection plane P for a hole is as follow:

∑

(6)

where v is the number of the boundary triangles of

the hole, n

is the normal of the i

boundary triangle

of the hole.

Figure 6: An example of a hole and the direction of its

projection plane.

GRAPP 2011 - International Conference on Computer Graphics Theory and Applications

3.5.2 Filling Holes through Planar

Triangulation

In our system, for each hole, once its boundary in

the original mesh model are projected onto its

corresponding projection plane, the projected

boundary vertices are used as the input for the

constrained Delaunay triangulation to get the patch

mesh for the hole in 2D. The procedure of mapping

back to 3D space of the patch mesh is done by

applying the topological structure of the constructed

2D triangulation to the original 3D boundary.

4 RESULTS AND VALIDATION

The visualization system Hole3D was developed as

the implementation to demonstrate our user-guided

feature sensitive hole filling system presented in this

paper. The visualization and user interface were

implemented in MS Visual Studio 2005

Development Environment with Coin3D (a high-

level 3D graphics toolkit for developing cross-

platform real-time 3D visualization and visual

simulation software), VTK (the Visualization

Toolkit) and MFC (Microsoft® Foundation Classes).

The programming language used is C++.

(a)

(b)

Figure 7: Applied our algorithm: (a) The input moai model

with two holes and concave sharp edges; (b) Hole filling

result obtained in our system with user intervention to pair

the feature points.

We demonstrate how the proposed algorithm can

be used to reconstruct hole regions. Basically, the

test cases are processed in two mesh models, the

moai model and the stripped fandisk model. Many

possible cases of hole are created and filled by our

system to verify its effectiveness.

Figure 7 shows the input moai model with two holes

and concave sharp edges at the neck area. The sharp

features are recovered properly using our method.

The patches stitched to the hole areas are marked

with the yellow boundary. Although we do not

implement mesh refinement and fairing techniques

in our system, the patch is adequate to complete the

model in expected way. Figure 12 shows the result

of filling a fandisk model with a concave corner hole

(Figure 12(a)). The final mesh model after applying

our feature sensitive hole filling algorithm are

displayed in Figure 12(b)(c).

As shown in Figure 9, with the hole at the convex

sharp edge, our system can achieve the proper

results. Figure 9(b) shows the hole filling result

obtained automatically by our system without a user

correcting the detected crest lines. Better result can

be obtained with user interaction to correct the

detected crest lines before interpolating feature lines

passing over the hole as shown in Figure 9(c).

We demonstrate the robustness of our system by

comparing our experiment results with the results

presented in papers (Chen et al., 2005; Zhao et al.,

2006). As shown in Figure 10, there are three holes

in fandisk mesh model, which has one, two and three

ridges passed through them (Figure 10(a)). As

presented in (Zhao et al., 2006), the method in

(Liepa, 2003) can only close the holes (Figure

10(b)), the method in (Zhao et al., 2006) produces

better result but the geometry at the corner hole is

not recovered properly (Figure 10(c)). Figure 11

demonstrates the hole filling results for convex and

concave corner holes obtained after applying the

sharpness dependent filter hole filling method in

(Chen et al., 2005).

(a) (b) (c)

Figure 8: Applied our algorithm: (a) The input moai model with a convex corner hole; (b) Our final hole filling result with

polygonal presentation, the hole patch is colored in red; (c) Flat shaded render of the final result.

USER-GUIDED FEATURE SENSITIVE HOLE FILLING FOR 3D MESHES

(a)

(b) (c)

Figure 9: Applied our algorithm: (a) The input stripped fan

disk model with a hole on the convex sharp edge; (b) Our

hole filling result without the user intervention to correct

the detected crest points at the hole area; (c) Our hole

filling result where the detected crest points are corrected

at the hole area.

To have a visual comparison with the

aforementioned algorithms, as shown in Figure 13,

we applied our hole filling method to the fandisk

model with holes at the same locations as in the

input mesh model in Figure 10 that reproduced from

(Zhao et al., 2006). Indeed, the modified mesh

model shows three typical kinds of holes that have

sharp features need to be recovered: one hole with

one feature line passing over, one hole with two

feature lines passing over and one hole at the corner.

The results of our hole filling technique are shown in

Figure 13: the sharp edges are recovered

aesthetically; the corner shape is reconstructed

consistently with the original shape. Figure 13(b)

shows the final hole filling result with the hole

highlighted in green. Figure 13(c) shows the hole

filling result obtained by our system, the patches are

stitched to the input mesh as the hole areas to get the

final mesh model. The sharp features at the concave

corner hole in Figure 12 are recovered nicely using

our method comparing to the result shown in Figure

11(b).

Figure 10: Applied the algorithms in (Liepa, 2003) and

(Zhao et al., 2006): (a) The input mesh model with 3

holes; (b) The result obtained by using method in (Liepa,

2003); (c) The result obtained by using method in (Zhao et

al., 2006) (reproduced from (Zhao et al., 2006)).

Figure 11: Applied the hole filling algorithm in (Chen et

al., 2005) to the holes at the corners: (a) A original mesh

model with a convex corner hole; (b) The result after

filling the hole in the model in (a); (c) A original mesh

model with a concave corner hole; (d) The result after

filling the hole in the model in (c) (reproduced from (Chen

et al., 2005)).

The experiments show that our method can

produce excellent results for filling the holes at the

corners. The mesh quality of the patches could be

improved to make them more consistent with the

original mesh quality by applying mesh refinement

techniques.

5 DISCUSSION

Certainly, fully automated methods for hole filling

have several advantages over a method that requires

user intervention. However, from the point of view

of the complexity of the hole, a fully automated

method may not work correctly for holes with

complex geometries. Our research aims to combine

manual and automatic methods to improve current

hole-filling methods, making this process more

versatile, robust and effective.

Most of the feature sensitive hole-filling methods

rely significantly on the normals of the vertices

around the hole areas to decide whether or not there

exist fine features. This makes those methods

sensitive to the mesh quality, e.g. the point density,

the shapes of triangles and the point distribution. In

our algorithm, since the feature curves are

interpolated from the salient information detected in

the mesh model, user intervention allows to correct

the detected crest line information. This enables the

whole algorithm to produce the final results quite

independently from the quality of the input mesh



GRAPP 2011 - International Conference on Computer Graphics Theory and Applications

Figure 12: Our algorithm results: (a) The input stripped fandisk model with a concave corner hole; (b) Our final hole filling

result with polygonal presentation, the hole patch is colored in green; (d) Flat shaded render of the final result model.

(a) (b) (c)

Figure 13: Applied our algorithm to a moai model with 3 types of holes: (a) The original mesh model with 3 kinds of holes;

(b) The final result obtained by our system with the highlighted patches; (c) Flat shaded render of the final mesh result.

model.

The core idea of our algorithm using the salient

information to recover the sharp feature is simple

but effective. Among the existing techniques that

have attempted to reconstruct fine features of the

original mesh at the hole areas, our hole filling

techniques is different since the fine features are

taken as the first subjects to reconstruct, which

eventually drive the feature-definite surface filling

process. Our results show the effectiveness of our

method in filling the hole and preserving

aesthetically the sharp edges.

The accuracy of our method depends to a great

extent on the accuracy of the crest line detection

method. We expect that improvements in crest line

detection will produce a higher quality results from a

fully automatic procedure based on our approach. In

our implementation, all of the salient and polygonal-

based information of the input mesh model are

extracted and stored in our designed data structures

in the loading phase then further computation is

limited to areas near holes. This makes the algorithm

efficient to run on large models.

Our system improves the visual quality of the

results with respect to previous approaches and

provides real-time user interaction. On the other

hand, it strongly relies on crest line detection, and

therefore it is very sensitive to changes in this

geometrical feature. Our system is able to recover

efficiently the sharp features, especially when the

feature curves or the profile of the sharp edges are

close to the cubic splines. However, if the profile of

the sharp edges in the input mesh is more complex

than cubic splines, the results may not be necessarily

accurate and may even be far from the real

geometry.

Further mesh refinement and fairing methods

may be used to improve the quality of the generated

patch meshes. By doing this, the point density and

triangle shape in the patch mesh will be consistent

with the input mesh.

6 CONCLUSIONS

We have presented a novel technique for filling

holes in 3D triangulated mesh models which is able

to recover efficiently the sharp features of the

original geometry, producing plausible results which

are consistent with the geometry of the original

mesh models. For each input mesh, our system

identifies its hole and crest line information. Then it

USER-GUIDED FEATURE SENSITIVE HOLE FILLING FOR 3D MESHES

uses this information to geometrically segment

complex holes into simple approximately planar

holes, called sub-holes. The patch meshes that are

used to fill those sub-holes are generated by using

planar triangulation algorithm for the point set at the

hole boundaries. Then these patch meshes are

mapped back to the 3D space and stitched to the

original model at the hole areas to achieve the final

result. The user is able to interact with our system

through correcting the crest lines, adjusting the

feature points defined by the crest lines and the hole

boundaries, pairing the feature points or specifying

the corner hole locations. The adjustment of the

location of the crest lines by users results in

modification in the shape of the patch mesh which is

later stitched to the original model, as holes are

filled using different geometric information. To

validate our approach, we have tested our technique

on different mesh models with many possible cases,

and the results show that our methods effectively

reconstruct the sharp features. Most approaches for

hole filling in literature do not reconstruct these fine

details due to the interpolation schemes used. We

overcome this limitation by including additional

information on the object shape in areas of high

curvature and by limited user intervention.

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