A Hybrid Object/Image Space Approach for Efficient and Robust Line Drawings

彬彬

1 Introduction

Line drawings are an effective way to convey shapes in a relatively

succinct manner by ignoring the less important or distracting details.

In the past decade, many promising computer-generated line

drawing algorithms have been proposed, which can be roughly classified

into two categories: object-space and image-space.

The object-space algorithms, e.g., suggestive contours [DeCarlo

et al. 2003], apparent ridges [Judd et al. 2007], PELs [Xie et al.

2007], demarcating curves [Kolomenkin et al. 2008], Laplacian

lines [Zhang et al. 2011], etc, adopt a two-pass algorithmic framework:

in the first pass, certain geometric properties (such as curvatures,

principal directions and their derivatives) are computed for

each vertex and the geometry of the feature lines are extracted; then

the extracted lines are rendered in the second pass. In spite of its

popularity, this two-pass framework usually requires that the input

model is smooth and has good triangulation quality, since computing

high order geometric properties using discrete differential

geometry is very sensitive to mesh tessellation and noises. Thus,

for real-world models obtained from 3D scanning, a careful preprocessing

(e.g., denoising, remeshing, etc) must be done before

applying the line drawing algorithms. The image-space algorithms

(e.g., [Lee et al. 2007]) are usually efficient since they avoid the expensive

computations of differential properties on surfaces. However,

image-space algorithms suffer pixel-level artifacts and are difficult

for shape stylization.

This paper presents a new hybrid approach for efficient and robust

line drawing on general triangle meshes. Our method naturally integrates

object- and image-spaces in that it computes the geometric

features in the object space and then adopts a simple fragment

shader to render the lines in the image space. As a result, our algorithm

is more efficient than the existing object-space approaches,

since we bypass the process of line geometry extraction, which

is normally the most time-consuming operation in traditional line

drawing algorithms. On the other hand, our algorithm is also more

robust than the conventional image-space techniques, since the geometric

features are extracted in the object space, which is independent

of the image resolution.

Our approach is strongly inspired by the Difference-of-Gaussian

(DoG) image edge detector. Given a grey-scale image, the DoG

edge detector first convolutes it with two Gaussian filters with different

kernel sizes. Then subtracting one image from the other preserves

spatial information that lies between the range of frequencies

that are preserved in the two blurred images. Thus, the DoG operator

is a band-pass filter that discards all but a handful of spatial

frequencies that are present in the original grayscale image.

A na¨ıve approach for 3D line drawings is to apply image edge detectors

(e.g., DoG detector, Canny edge detector, etc) to the rendered

diffuse shading image. However, these approaches severely

suffer the pixel level artifacts and the quality of resulting drawings

are usually poor. In this sketch, we present an elegant algorithm

to generalize DoG operator to 3D models. We show that the DoG

of illumination can be decomposed into the view-independent and

view-dependent components, where the former, the most computational

expensive part, can be completely precomputed. Furthermore,

the run-time line drawing can be done with very simple arithmetic

calculations using the GPU.

彬彬

tc

再看一看，再顶楼主

菜刀吻电线

沙发不解释

tc

有意思！学习了！

奇

我是老实人,我来也!

奇

呵呵，很好，方便罗。