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Unstructured Lumigraph Rendering.PDF
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Unstructured Lumigraph Rendering
Chris Buehler Michael Bosse Leonard McMillan Steven Gortler Michael Cohen
MIT Laboratory for Computer Science Harvard University Microsoft Research
Abstract
We describe an image based rendering approach that generalizes
many current image based rendering algorithms, including light
field rendering and view-dependent texture mapping. In particular,
it allows for lumigraph-style rendering from a set of input cameras
in arbitrary configurations (i.e., not restricted to a plane or to any
specific manifold). In the case of regular and planar input camera
positions, our algorithm reduces to a typical lumigraph approach.
When presented with fewer cameras and good approximate geom-
etry, our algorithm behaves like view-dependent texture mapping.
The algorithm achieves this flexibility because it is designed to meet
a set of specific goals that we describe. We demonstrate this flexi-
bility with a variety of examples.
Keyword Image-Based Rendering
1 Introduction
Image-based rendering (IBR) has become a popular alternative to
traditional three-dimensional graphics. Two effective IBR meth-
ods are view-dependent texture mapping (VDTM) [3] and the light
field/lumigraph [10, 5] approaches. The light field and VDTM algo-
rithms are in many ways quite different in their assumptions and in-
put. Light field rendering requires a large collection of images from
cameras whose centers lie on a regularly sampled two-dimensional
patch, but it makes few if any assumptions about the geometry of
the scene. In contrast, VDTM assumes a relatively accurate ge-
ometric model, but requires only a small number of images from
input cameras that can be in general positions. These images are
then “projected” onto the geometry for rendering.
We suggest that, at their core, these two approaches are quite
similar. Both are methods for interpolating color values for a de-
sired ray as some combination of input rays. In VDTM this inter-
polation is performed using a geometric model to determine which
pixel from each input image “corresponds” to the desired ray in the
output image. Of these corresponding rays, those that are closest in
angle to the desired ray are weighted to make the greatest contribu-
tion to the interpolated result.
Light field rendering can be similarly interpreted. For each de-
sired ray (s, t, u, v), one searches the image database for rays that
intersect near some (u, v) point on a “focal plane” and have a simi-
lar angle to the desired ray, as measured by the ray’s intersection on
the “camera plane” (s, t). In a depth-corrected lumigraph, the focal
plane is effectively replaced with an approximate geometric model,
making this approach even more similar to view dependent texture
mapping.
Given these related IBR approaches, we attempt to address the
following questions: Is there a generalized rendering framework
that spans all of these image-based rendering algorithms, having
VDTM and lumigraph/light fields as extremes? Might such an al-
gorithm adapt well to various numbers of input images from cam-
eras in general configurations while also permitting various levels
of geometric accuracy?
In this paper we approach the problem by suggesting a set of
goals that any image based rendering algorithm should have. We
find that no previous IBR algorithm simultaneously satisfies all of
these goals. Therefore these algorithms behave quite well under
appropriate assumptions on their input, but may produce unneces-
sarily poor renderings when these assumptions are violated.
We then describe an algorithm for “unstructured lumigraph ren-
dering” (ULR), that generalizes both lumigraph and VDTM render-
ing. Our algorithm is designed specifically with the stated goals in
mind. As a result, our renderer behaves well with a wide variety
of inputs. These include source cameras that are not on a com-
mon plane, such as source images taken by moving forward into a
scene, a configuration that would be problematic for previous IBR
approaches.
It should be no surprise that our algorithm bears many resem-
blances to earlier approaches. The main contribution of our algo-
rithm is that, unlike previously published methods, it is designed to
meet a set of listed goals. Thus, it works well on a wide range of
differing inputs, from few images with an accurate geometric model
to many images with minimal geometric information.
2 Previous Work
The basic approach to view dependent texture mapping (VDTM) is
put forth by Debevec et al. [3] in their Fac¸ade image-based model-
ing and rendering system. Fac¸ade is designed to estimate geometric
models consistent with a small set of source images. As part of this
system, a rendering algorithm was developed where pixels from all
relevant cameras were combined and weighted to determine a view-
dependent texture for the derived geometric models. In later work,
Debevec et al [4] describe a real-time VDTM algorithm. In this
algorithm, each polygon in the geometric model maintains a “view
map” data structure that is used to quickly determine a set of three
input cameras that should be used to texture it. Like most real-time
VDTM algorithms, this algorithm uses hardware supported projec-
tive texture mapping [6] for efficiency.
At the other extreme, Levoy and Hanrahan [10] describe the light
field rendering algorithm, in which a large collection of images are
used to render novel views of a scene. This collection of images
is captured from cameras whose centers lie on a regularly sampled
two-dimensional plane. Light fields otherwise make few assump-
tions about the geometry of the scene. Gortler et al. [5] describe
a similar rendering algorithm called the lumigraph. In addition,
the authors of the lumigraph paper suggest many workarounds to
overcome limitations of the basic approach, including a “rebinning”
process to handle source images acquired from general camera po-
sitions and a “depth-correction” extension to allow for more ac-
curate ray reconstructions from an insufficient number of source
cameras.
Many extensions, enhancements, alternatives, and variations
to these basic algorithms have since been suggested. These in-
clude techniques for rendering digitized three-dimensional models
in combination with acquired images such as Pulli et al. [13] and
Wood et al. [18]. Shum et al. [17] suggests alternate lower di-
mensional lumigraph approximations that use approximate depth
correction. Heigl et al. [7] describe an algorithm to perform IBR
from an unstructured set of data cameras where the projections of
the source cameras’ centers were projected into the desired im-
age plane, triangulated, and used to reconstruct the interior pixels.
Isaksen et al. [9] show how the common “image-space” coordinate
frames used in light field rendering can be viewed as a focal plane
for dynamically generating alternative ray reconstructions. A for-
mal analysis of the trade off between the number of cameras and
the fidelity of geometry is presented in [1].
3 Goals
We begin by presenting a list of desirable properties that we feel an
ideal image-based rendering algorithm should have. No previously
published method satisfies all of these goals. In the following sec-
tion we describe a new algorithm that attempts to meet these goals
while maintaining interactive rendering rates.
Use of geometric proxies: When geometric knowledge is
present, it should be used to assist in the reconstruction of a desired
ray (see Figure 1). We refer to such approximate geometric infor-
mation as a proxy. The combination of accurate geometric proxies
with nearly Lambertian surface properties allows for high quality
reconstructions from relatively few source images. The reconstruc-
tion process merely entails looking for rays from source cameras
that see the “same” point. This idea is central to all VDTM algo-
rithms. It is also the distinguishing factor in geometry-corrected lu-
migraphs and surface light field algorithms. Approximate proxies,
such as the focal-plane abstraction used by Isaksen [9], allow for
the accurate reconstruction of rays at specific depths from standard
light fields.
With a highly accurate geometric model, the visibility of any
surface point relative to a particular source camera can also be de-
termined. If a camera’s view of the point is occluded by some other
point on the geometric model, then that camera should not be used
in the reconstruction of the desired ray. When possible, image-
based algorithms should consider visibility in their reconstruction.
C
1
C
5
C
4
C
3
D
C
2
C
6
Figure 1: When available, approximate geometric information
should be used to determine which source rays correspond well to
a desired ray. Here C
x
denotes the position of a reference camera,
and D is desired novel viewpoint.
Unstructured input: It is also desirable for an image-based
rendering algorithm to accept input images from cameras in gen-
eral position. The original light field method assumes that the cam-
eras are arranged at evenly spaced positions on a single plane. This
limits the applicability of this method since it requires a special
capture gantry that is both expensive and difficult to use in many
settings [11].
The lumigraph paper describes an acquisition system that uses a
hand-held video camera to acquire input images [5]. They apply a
preprocessing step, called rebinning, that resamples the input im-
ages from virtual source cameras situated on a regular grid. This
rebinning process adds an additional reconstruction and sampling
step to lumigraph creation. This extra step tends to degrade the
overall quality of the representation. This can be demonstrated by
noting that a rebinned lumigraph cannot, in general, reproduce its
input images. The surface light field algorithm suffers from essen-
tially the same resampling problem.
Epipole consistency: When a desired ray passes through the
center of projection of a source camera it can be trivially re-
constructed from the ray database (assuming a sufficiently high-
resolution input image and the ray falls within the camera’s field-
of-view) (see Figure 2). In this case, an ideal algorithm should
return a ray from the source image. An algorithm with epipole
consistency will reconstruct this ray correctly without any geomet-
ric information. With large numbers of source cameras, algorithms
with epipole consistency can create accurate reconstructions with
essentially no geometric information. Light field and lumigraph al-
gorithms are designed specifically to maintain this property.
Surprisingly, many real-time VDTM algorithms do not ensure
this property, even approximately, and therefore, will not work
properly when given poor geometry. The algorithms described
in [13, 2] reconstruct all of the rays in a fixed desired view using
a fixed selection of three source images but, as shown by the origi-
nal light field paper, proper reconstruction of a desired image may
involve using some rays from each of the source images. The algo-
rithm described in [4] always uses three source cameras to recon-
struct all of the desired pixels on a polygon of the geometry proxy.
This departs from epipole consistency if the proxy is coarse. The
algorithm of Heigl et al. [7] is an notable exception that, like a light
field or lumigraph, maintains epipole consistency.
C
1
C
5
C
4
C
3
C
2
D
C
6
Figure 2: When a desired ray passes through a source camera cen-
ter, that source camera should be emphasized most in the recon-
struction. Here this case occurs for cameras C
1
, C
2
, C
3
, and C
6
.
Minimal angular deviation: In general, the choice of which
input images are used to reconstruct a desired ray should be based
on a natural and consistent measure of closeness (See Figure 3). In
particular, source image rays with similar angles to the desired ray
should be used when possible.
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