基礎論文 Paper

Novel View Synthesis Based on View-dependent Texture
Mapping with Geometry-aware Color Continuity
Keita Katagiri*1 , Yuta Nakashima*1 , Tomokazu Sato*1 , and Naokazu Yokoya*1

Abstract – Novel view synthesis (NVS) is renowned for its variety of applications, andrecent techniques are based on an image-based approach, which uses multiple input images
to synthesize novel views, with the help of 3D geometry. View-dependent texture mapping is one of the most well-known techniques of this kind. However, it sometimes suﬀers
from blurry or duplicated edges when the geometry is inaccurate because it blends several
input images for alleviating inconsistent lighting conditions among input images. This
paper presents a view-dependent texture mapping-based method for NVS that leverages
geometry-aware color continuity in texture selection. Our color continuity constraint suppresses noticeable texture boundaries in resulting novel views without blending, while ourmethod relaxes the constraint on steep geometric changes. Since such geometric changes
are often followed by surface property changes, our new color continuity constraint canlead to more natural novel views. We formulate our texture selection by an energy minimization problem and solve it with the graph cut algorithm. Our experimental results
have demonstrated the superiority of our method.
Keywords : Novel view synthesis, view-dependent texture mapping, geometry-aware
color continuity, graph cut
1

Introduction

Novel view synthesis (NVS) is a technique to synthesize an image of a scene/object from an arbitrary
viewpoint using a set of multiple images. This technique has received much attention for its various applications, including free-viewpoint television [1]. A
conventional approach for NVS uses a 3D geometry of the scene/object and possibly applies textures,
which are extracted from the image set, to the geometry. Since handcrafting such 3D geometry is demanding and is almost impossible for ordinary users,
automatic techniques have been adopted for 3D reconstruction, such as structure from motion [2, 3]
together with multi-view stereo (MVS) [4]. Unfortunately, these techniques may suﬀer from inaccurate
3D geometry, resulting in the loss of details. Another well-known approach is image-based rendering,which smoothly interpolates diﬀerent images or uses
light ﬁelds obtained from the image set. This approach can synthesize a faithful view but requires avast number of images.
A series of techniques have been proposed in between the geometry- and image-based approaches foralleviating their drawbacks. View-dependent tex*1 Nara Institute of Science and Technology

ture mapping (VDTM) [5] is one of such techniques,
which applies some images to a 3D geometry as its
textures. These images are adaptively selected fromthe image set based on the spatial relationship among
the geometry, the viewpoint speciﬁed by the user
(hereinafter, the novel viewpoint), and the viewpointsof cameras used for capturing the images. It can reconstruct the details of the target while the numberof required images can reduce thanks to the geometry. Due to this desirable features, VDTM has been
widely studied, and a variety of its extensions havebeen proposed [6, 7].
However, the VDTM technique may still suﬀer
from visual artifacts. To alleviate the inﬂuence oflighting condition change while capturing the images, it smoothly blends multiple images and uses
the blended image as a texture [5]. This may lead
duplicated or blurry patterns on the target surface
as shown in Fig. 1(top) if automatic technique for
3D reconstruction are not suﬃciently accurate.
This paper presents a new method for NVS, whichis also an extension of VDTM to remedy the problemof blurry or duplicated patterns. We cast the problem of selecting an appropriate image to be applied as
texture to an energy minimization problem. In addi-

Transactions of the Virtual Reality Society of Japan Vol.21, No.1, 2016

method leverages the geometry in the texture selection through an energy function. This energy function allows our method to relax the color continuity
constraint around steep geometric changes. (ii) We
introduce smooth luminance modiﬁcation to reduce
discontinuities. Compared with image blending, ourluminance modiﬁcation is more robust to misalignment of texture patterns. (iii) We experimentallydemonstrate the eﬀectiveness of our new energy function by comparing synthesized views with various parameters. We also show that luminance modiﬁcation
reduces discontinuities in the views.
2

Related WorkIn recent decades, NVS has been widely studied,and various approaches have been proposed. One of
the major approaches is geometry-based one. Thisapproach uses 3D geometries of objects to synthesize their novel views, possibly with textures on thesurfaces. The 3D geometries can be handcrafted or

Fig. 1 Examples of original VDTM [5] and its
closeup view (top) and our method andits closeup view (bottom).

automatically generated using a 3D reconstruction
technique, such as shape from silhouette [8, 9] andMVS [10, 11, 4]. Depth cameras are also used for
acquiring geometries [12]. The quality of novel views
depends much on the quality of the 3D geometries,
and an automatic 3D reconstruction technique is often insuﬃcient. Another approach for NVS is image-Fig. 2 Diﬀerent lighting conditions for diﬀerent surfaces (left) and diﬀerent surface
properties on the grassy ground andthe concrete wall (right).

tion to the spatial relationship among the viewpoints
and the geometry, our method takes into accountthe color continuity in a resulting view, as Kopf etal. [7] do. Moreover, observing that steep changes
in the geometry imply diﬀerent surface properties
and lighting conditions as shown in Fig. 2, we introduce a novel geometry-aware weighing to the energy function so that steep changes in the geometry
coincide the texture boundaries. Since this texture
selection may not fully remove discontinuities, ourmethod also modiﬁes the luminance of the pixels.
Our main contributions are summarized as follows:(i) Being diﬀerent from Kopf et al.’s method [7], ourbased rendering, which interpolates input images tosynthesize a novel view among them [13, 8, 9] or obtains light ﬁelds from input images [14, 15, 16, 17,18]. This type of technique is sometimes criticized for
its requirement of a large number of input images.
Recent research eﬀorts try to improve image-based
rendering by making use of the 3D geometries of target objects. The unstructured light ﬁeld is one ofsuch techniques proposed by Davis et al. [18]. In order to reduce the number of input images over theoriginal light ﬁeld technique, they use a rough proxyof the object geometry. Debevec et al. proposed
VDTM [5], which much relies on the 3D geometry.
It applies the input images to the 3D geometry as its
textures. VDTM adaptively changes the images tobe applied as texture in accordance with the novel
viewpoint such that the angles formed by the novel
viewpoint, the input image’s viewpoint, and the object are the smallest among the other input images.
Since it can use diﬀerent input images for a single
surface, the texture boundary can be noticeable andKatagiri et al. : Novel View Synthesis Based on View-dependent Texture Mapping with Geometry-aware Color Continuity

degrade the visual quality. In order to alleviate thetexture boundary problem, they blend multiple input images so as to smoothly change the texture.
Nobuhara et al. proposed to ﬁnd plausible geometry
given a viewpoint by minimizing an energy function
with a photo-consistency term [19].
An interesting extension of VDTM is the techniqueproposed by Kopf et al. [7]. They deﬁned an energyfunction that counts the continuity of the adjacenttextures as well as the original VDTM’s angle-based
criterion, which determines the input images to be
used as texture by minimizing the energy function.
In this paper, we propose a method for NVS similar to Kopf et al.’s. The main diﬀerence of our
method from theirs is our new energy function that
relaxes the continuity constraint in texture if the 3D
geometry changes rapidly. Since the surface propertyof the object/scene often changes coincidently withthe geometry changes, our new energy function can
synthesize a more visually natural novel view.
3

Novel View Synthesis Considering
Geometry-aware Color Continuity

Figure 3 shows an overview of the proposed method,which consists of geometry reconstruction (GR) and
NVS stages. In the GR stage, we estimate the intrinsic and extrinsic camera parameters for each image
in an input image set S = {In |n = 1, . . . , N } using
structure from motion [2, 3]. It then reconstructs
the geometry of the target with MVS [4]. The geometry is represented in a 3D mesh model M . In the
NVS stage, provided a viewpoint of a novel view as
the virtual camera’s intrinsic and extrinsic parameters, our method generates a depth map for the view
from M with a standard rendering pipeline and selects an image in S used as the texture for each pixelin the view by energy minimization. Based on the
texture selection result, it colors the pixels in thenovel view and smoothly modiﬁes luminance to reduce color discontinuity. In the following sections, we
describe our texture selection and smooth luminancemodiﬁcation.
3.1

Texture selection

We consider that the requirements for texture selection can be summarized as follows: (1) For pixel
i in the novel view, texture selection must ﬁnd theimage that captures its corresponding 3D point froma direction close to that of the novel viewpoint. (2)The 3D point corresponding to the pixel i is potentially occluded in image In . Texture selection mustverify the visibility of the 3D point in In (visibility
check). (3) Texture selection must take into accountthe color continuity of adjacent pixels in the novelview. (4) Steep changes in the geometry may imply
changes in the target’s surface properties. For suchregions, requirement (3) must be relaxed.
As mentioned above, our method formulates texture selection as an energy minimization problem
with respect to labels xi ∈ {1, . . . , N }, which represents the image used as the texture for pixel i in
the novel view. Encoding above four requirements,
our energy function is deﬁned by
E(X) =αi (xi )fi (xi )+K

i∈Aβij gij (xi , xj ), (1)(i,j)∈B

where A is the set of pixels to which depth values are
assigned, B is the set of pairs of adjacent pixels, andX = {xi |i ∈ A}. Requirements (1)–(4) are encodedin fi , αi , gij , and βij , respectively. K is a parameterto determine the contribution of the pairwise term.
This energy function can be minimized by the graphcut algorithm [20].
Data term fi (xi ) penalizes the label that represents an image in S captured from a direction diﬀerent from that of the novel viewpoint, as in [5]. Let tv
be the 3D position of the novel viewpoint and txi bethat of image Ixi ’s viewpoint. txi can be calculated
from the extrinsic camera parameters of Ixi . From
the depth value di for pixel i in the novel view, we
can regain its corresponding 3D position pi on geometry M using the intrinsic and extrinsic camera
parameters for the novel viewpoint. The data termis deﬁned with respect to pi by the angle, i.e.,fi (xi ) = cos−1(tv − pi ) · (txi − pi ).
tv − pi ) txi − pi 

(2)

Data term weight αi (xi ) is concerned with visibility check, which gives a large value when pi is
occluded in image Ixi . Let dixi denote the depth
value of pi in Ixi , which is calculated using pi andIxi ’s camera parameters, and pi is projected to pixel
k in Ixi . After the GR stage, we can generate thedepth map for each image in S. We denote the depth
value at pixel k in Ixi by ekxi . The depth values dixi
and ekxi are close to each other if pi is not occluded
but not otherwise. Using a certain threshold θd forthe diﬀerence between these depth values, we deﬁneTransactions of the Virtual Reality Society of Japan Vol.21, No.1, 2016

Input images set

Intrinsic/extrinsic
parameter estimation

Geometry reconstruction

Geometry reconstruction (GR) stage
Novel view synthesis (NVS) stage

Synthesized view

Smoothluminance
modification

Depth map
generation

Textureselection

Viewpoint
specification

Fig. 3 Overview of the proposed method.

data term weight αi (xi ) as

1 if |dixi − ekxi | < θdαi (xi ) =,L otherwise(3)

where L is a suﬃciently large value.
Pairwise term gij (xi , xj ) encodes requirement (3),where a pair of pixels (i, j) are in the set B of adjacent pixels. This term gives a large value when
the labels xi and xj disagree and the correspondingcolors cixi and cjxj are diﬀerent, where cixi represents the color (in the RGB color space) at the pixel
corresponding to pi in Ixi . We implement this bygij (xi , xj ) = max(cixi − cixj ∞ , cjxi − cjxj ∞ ),(4)
where ·∞ is the maximum norm. gij is 0 if xi = xj ;Fig. 4 Examples of normal
viewed in color).

maps

(Best

to length 1. We denote the normal for pixel i by ni
and deﬁne the pairwise term weight byn ·n
1 if cos−1 niinjj  < θn
(5)
βij =
 otherwise,otherwise, it gives the maximum diﬀerence of RGB
components in adjacent pixels i and j.
pairwise term weight βij relaxes the inﬂuence ofgij by reducing its value when the geometry changes

where θn is a threshold and  ≤ 1 a factor to reducegij .

steeply. This weight can be viewed as a geometryaware color continuity together with gij . Observing

Our energy minimization-based texture selection
reduces discontinuities in the synthesized view. How-that changes in the geometry can be detected using
its normals, we ﬁrst generate a normal map, as shownin Fig. 4 for the novel viewpoint by calculating thenormal for each face in mesh model M , and assign
the normal to corresponding pixels. Since inaccurate
M causes noisy normal map, we apply a Gaussianﬁlter to the map and normalize each pixel’s normal

ever, it may not fully remove such visual artifacts if
the lighting condition changes while capturing images in S. One approach to alleviating such artifacts can be blending as in [5], but this suﬀers fromblurring or duplicated patterns caused by inaccurate

3.2

Smooth Luminance Modification

camera parameter estimation and 3D geometry reconstruction. Another approach can be globally ad-

Katagiri et al. : Novel View Synthesis Based on View-dependent Texture Mapping with Geometry-aware Color Continuity

Fig. 5 Datasets. From top to bottom: datasets (A), (B), and (C). The leftmost
column shows reconstructed 3D mesh models and others show examples
of input images.

Fig. 6 Cameras that captured the input images (black pyramids) and viewpoints for novel view synthesis in our experiments (red pyramids).

justing luminance of each input image beforehand;
however, it cannot handle, for example, specular reﬂection and local luminance changes caused by the
shadow of the photographer. We instead address thisproblem by locally and smoothly modifying the luminance.
For pixel i, we set a window Wi centered at thatpixel. Let Qi = {xj |j ∈ Wi } be the set of labels in
Wi and thus the elements in Qi are not unique because the same label can be assigned to diﬀerent pixels. Also I¯in denotes a local luminance value aroundi calculated from a novel view whose pixels’ labels
are all n. In other words, I¯in is calculated from anovel view that is synthesized only from In . For asmooth change in luminance, we modify the novel
view’s color ci for pixel i whose label is xi as follows:ci(6)
I¯in .
ci = ¯
Iix |Qi |in∈Qi

This luminance modiﬁcation mixes the luminancevalues I¯in using a weight proportional to the number of pixels in the window, to which label n is as-

Table 1 Speciﬁcation of datasets used in experiments.

DatasetImage size

Number of images

(A)
(B)

1696 × 1280

61

1920 × 1280
1920 × 1280

51
51

(C)

signed. Misalignment of texture patterns does notcause blurring or duplicated patterns.
4

Experimental Results

We experimentally demonstrate the eﬀects of ourpairwise term by comparing synthesized views with
diﬀerent parameter values of K in Eq. (1) and  in
Eq. (5). We also show the advantage of smooth luminance modiﬁcation.
In our implementation, we used VisualSFM [2, 3]
for camera parameter estimation and CMPMVS [4]for 3D geometry reconstruction. The parameter values were heuristically ﬁxed to L = 10000, θd = 0.1,

Transactions of the Virtual Reality Society of Japan Vol.21, No.1, 2016and θn = 5◦ . For smooth luminance modiﬁcation,
we used a 51 × 51 window. Table 1 shows the speciﬁcation of the datasets used in our experiments andFig. 5 shows some examples of input images and3D mesh models by CMPMVS. In Fig. 6, the black
pyramids represent the camera parameters for input images. Dataset (A) contains a stuﬀed penguin, and CMPMVS was able to reconstruct it accurately. Dataset (B) captures a box with grid- anddot-pattern texture. Estimated camera poses andthe 3D mesh model were erroneous. Dataset (C)is a scene with a wall, grassy ground, and a small
structure. CMPMVS worked relatively well with thisdataset. K and  were empirically determined for all
the datasets in Fig. 5. With a larger K, our method
only uses a smaller number of input images because
the pairwise term dominates the energy function. K
may need to be adjusted for each dataset.
Figures 7, 9, and 10 show some examples of synthesized novel views with diﬀerent parameters (K, ),as well as novel views by blending [5], for datasets(A), (B), and (C), respectively. Novel view’s camera parameters are represented in the red pyramids
in Fig. 6. For datasets (A) and (C), closeup views
are provided in Figs. 8 and 11. In these results, luminance modiﬁcation was disabled to demonstrate how
our energy function remedies discontinuities. The
pairwise term is not used with K = 0 (and thus no), which corresponds to VDTM [5], except for blending. A non-zero K with  = 1 roughly mimics Kopf
et al’s method [7].
For dataset (A), as shown in Figs. 7 and 8, thepairwise term successfully reduced the visual artifacts around label boundaries, compared with the
K = 0 case. Diﬀerent parameter values for the pairwise term’s weight  did not change the synthesizedview much. The novel view by blending exhibits aduplicated boundary between the black and gray regions around the penguin’s neck, although the discontinuity around label boundaries are reduced.
The novel view from dataset (B) has discontinuities for K = 0 (horizontal lines are broken) as inFig. 9. For K = 0.4 and  = 1, the horizontal
lines are still disconnected, but the labels change ona certain horizontal line to maintain color continuity. When K = 0.4 and  = 0.5, the labels’ change
coincides with steep change in the geometry. Dueto relatively large errors in the geometry and cam-Fig. 7 Synthesized novel views for dataset(A) (left) and label maps representing xi (right). From top to bottom:
blending, K = 0, (K, ) = (0.4, 1),(K, ) = (0.4, 0.5). White pixels indicate that they are not on the 3D meshmodel.

Katagiri et al. : Novel View Synthesis Based on View-dependent Texture Mapping with Geometry-aware Color Continuity

Fig. 8 Closeups of novel views in Fig. 7.

era poses, all novel views were not satisfactory, but
we conﬁrmed that the proposed method, as well as
VDTM considering color continuity (K = 0.4 and = 1), reduced discontinuities without blending multiple input images. With blending, multiple blacklines appear, especially in the face on the left handside. This is because its geometry is not accurately
compared to the other face, and the rough surface
maps the texture at diﬀerent positions.
For dataset (C), as shown in the closeup viewsin Figs. 10 and 11, the labels change in one of thefaces of the trigonal pyramidal object for K = 0
and (K, ) = (0.4, 1). The novel view by blending
gave similar artifacts. On the other hand, the labels’ boundary coincides the geometry change for(K, ) = (0.4, 0.5), and the labels’ boundary is noFig. 9 Synthesized novel views for dataset(B) (left) and label maps representing xi (right). From top to bottom:
blending, K = 0, (K, ) = (0.4, 1),(K, ) = (0.4, 0.5).

longer signiﬁcant. For this dataset, the data term
basically preferred the labels for K = 0 and (K, ) =(0.4, 1) and the pairwise term was small enough tomaintain the boundary since the diﬀerence in color
was moderate yet noticeable for human viewers. For(K, ) = (0.4, 0.5), the pairwise weight successfully
worked as an incentive to change labels on the geometry change. The resulting views demonstrate thesuperiority of our method’s visual quality.
To show the proposed method’s sensitivity to K,
we synthesized views from dataset (B) with various
K values while ﬁxing  to 0.5 (Fig. 12). Even with
K = 0.2, the pairwise term successfully reduces discontinuities. With K = 1.6, since too much penalty
is imposed to diﬀerent labels, the proposed method

Transactions of the Virtual Reality Society of Japan Vol.21, No.1, 2016

Fig. 10 Synthesized novel views for dataset(C) (left), and label maps representing xi (right). From top to bottom:
blending, K = 0, (K, ) = (0.4, 1),(K, ) = (0.4, 0.5).

Fig. 12 Novel views (left) and their labels(right) for dataset (B) with various K
values. From top to bottom: K = 0,0.2, 0.4, 0.8, 1.6

assigned a single label to most pixels. From this result, the proposed method is not very sensitive to the
choice of K.
Figure 13 compares the novel views before and af-

Fig. 11 Closeups of novel views in Fig. 10(contrast is adjusted for visibility).

ter luminance modiﬁcation. For dataset (A), we cansee color discontinuity below the penguin’s wing before luminance modiﬁcation. Dataset (C) has a clear
boundary around the center of the view (Fig. 13, topleft). It seems that, for these regions, both datasets

Katagiri et al. : Novel View Synthesis Based on View-dependent Texture Mapping with Geometry-aware Color Continuity

Fig. 13 Novel views (top) before and (bottom) after luminance modiﬁcation
for dataset (A) (left) and (C) (right). Best viewed in color.

5Conclusion

This paper has presented a new method for NVS,
which leverages the geometry of the object to ﬁndsuitable images for coloring pixels in novel views andFig. 14 Original image (left) removed fromdataset (A) and novel view (right)
synthesized using the image’s camera
parameters.

have no better images than those used in Fig. 13,
and thus our texture selection was not able to ﬁndsmoother label transition than those in Fig. 13. After
luminance modiﬁcation, these discontinuities weresuccessfully reduced.
To demonstrate our novel view’s faithfulness andits quality when the input images are distant fromthe speciﬁed viewpoint, we removed one input image from the dataset and used the image’s camera
parameters to specify those of the novel view. Figure 14 shows the result. Since the original image,which is the most reasonable choice as the texture
for this novel view, was not used, we can observe
some artifacts. However, we consider that the proposed method reproduced the original image withconvincing quality.

alleviate visual artifacts due to texture changes. We
have also introduced smooth luminance modiﬁcation
to further reduce discontinuities in texture. Experimental results have demonstrated the superiority of
our method. Its main limitation is sensitivity to thegeometry: If the geometrical change is even slightly
above the threshold, the pairwise term is completely
spoiled, which may cause extra discontinuities. We
need a weighting scheme that deal with this problem.
Acknowledgments
This work was supported in part by JSPS KAKENHI Nos. 23240024 and 25540086.

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(2015 年 7 月 15 日受付)

［Authors’ Introduction］

Keita Katagiri
Keita Katagiri received his B.E.
from Kyushu Institute of Technology
in 2013 and the M.E. from Nara Institute of Science and Technology in 2015.
Currently he is with Ricoh Company
Ltd.

Yuta Nakashima
Yuta Nakashima received the B.E.,
M.E., Ph.D. degrees from Osaka University, in 2006, 2008, and 2012, respectively. He is currently an assistantprofessor at Nara Institute of Scienceand Technology and is also a Visiting
Scholar at Carnegie Mellon University.
He was a Visiting Scholar at the University of North Carolina at Charlotte
in 2012.

Tomokazu Sato （正会員）
Tomokazu Sato received his B.E.
degree in computer and system science from Osaka Prefecture University in 1999. He received his M.E.
and Ph.D. degrees in information science from Nara Institute of Science andTechnology in 2001 and 2003, respectively. He was appointed as an assistant professor at Nara Institute of Science and Technology in 2003 and became an associate professor in 2011.

Naokazu Yokoya （正会員）
Naokazu Yokoya received his B.E.,
M.E., and Ph.D. degrees in information and computer sciences from Osaka
University in 1974, 1976, and 1979, respectively. He joined ElectrotechnicalLaboratory (ETL) in 1979. He was avisiting professor at McGill University
in 1986-87 and has been a professor at
Nara Institute of Science and Technology since 1992. He has also been a vicepresident at Nara Institute of Scienceand Technology since April 2013.