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RESEARCH PAPER

SCIENCE CHINA

Information Sciences

July 2012 Vol. 55 No. 7: 1509–1519

doi: 10.1007/s11432-011-4467-5

 Science China Press and Springer-Verlag Berlin H eidelberg 2012 info.scichina.com www.springerlink.com

Radiance-based color calibration for image-based

modeling with multiple cameras

ZHAO Xu

1,2

, ZHOU Zhong

1,2 ∗

&WUWei

1,2

State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing 100191,China;

School of Computer Science and Engineering, Beihang University, Beijing 100191,China

Received February 17, 2011; accepted May 18, 2011; published online April 12, 2012

Abstract Photo-consistency estimation is an important part for many image-based modeling techniques. This

paper presents a novel radiance-based color calibration method to reduce the uncertainty of photo-consistency

estimation across multiple cameras. The idea behind our method is to convert colors into a uniform radiometric

color space in which multiple image data are corrected. Experimental results demonstrate that our method can

achieve comparable color calibration eﬀect without adjusting camera parameters and is more robust than other

existing method. Additionally, we obtain an auto-determined threshold for photo-consistency check, which will

lead to a better performance than existing photo-consistency based reconstruction algorithms.

Keywords color calibration, photo-consistency estimation, multi-camera system, image-based modeling

Citation Zhao X, Zhou Z, Wu W. Radiance-based color calibration for image-based modeling with multiple

cameras. Sci China Inf Sci, 2012, 55: 1509–1519, doi: 10.1007/s11432-011-4467-5

1 Introduction

The development of low-cost acquiring devices and increasing popularity of multi-camera vision systems

are continuously escalating image-based modeling applications [1,2]. One kind of attractive applications

is to well reconstruct the real scene or object with multiple images [3,4]. Although multiple images

can be manually captured with a hand-held camera [5] or automatically using a turntable or robot

based system [6,7], they all suﬀer from a diﬃculty in modeling dynamic scenes. Unlike that, multi-

camera vision systems have been emerged as a popular platform for providing eﬀective support for

applications with real-time requirement. However, it faces the challenge of how to decrease the inﬂuence

introduced by the diﬀerences between cameras, which might further aﬀect many photo-consistency based

reconstruction algorithms [8,9]. Figure 1(b) and (c) illustrate some typical artifacts occurring in space

carving reconstruction caused by the inconsistency of color matching costs, even if camera settings and

types are virtually the same.

As mentioned in [10], diﬀerent cameras-even if they are of the same type-do not exhibit consistent

response. Furthermore, camera responses may diﬀer in settings, illuminations and so on. A direct and

eﬀective method to eliminate these diﬀerences is to adjust camera settings to make their responses sim-

∗

Corresponding author (email: zz@vrlab.buaa.edu.cn)

1510 Zhao X, et al. Sci China Inf Sci July2012Vol.55No.7

Figure 1 Space carving [8] reconstruction of a rabbit toy from six diﬀerent views. (a) One of input toy rabbit images.

(b)(c) A reconstruction using uncalibrated cameras with same settings. The artifacts are marked by circles. (d)(e) A

reconstruction after color calibration. The artifacts are eliminated.

ilar [11]. It assumes that cameras are adjustable and can be physically accessed by calibration system.

Consequently it is not suitable for many low-end acquiring devices.

Besides, color consistency can also be achieved by software processing of multiple images. Porikli [12]

explicitly models pair-wise transfer functions between images, and uses these functions to correct multiple

images. Although it shows consistent appearances, it is ineligible to guarantee numerical consistency for

ignoring diﬀerences between cameras. This would yield a poor reconstructed model with unwanted

artifacts, such as “outlier” or “gap” marked by circles in Figure 1(b) and (c).

Our goal is to achieve color consistency across multiple cameras so as to reduce matching noise for

photo-consistency estimation. The key idea here is to map all captured image data from multiple cameras

into a uniform radiometric color space and then correct them with estimated transformation matrices

to one manually or automatically selected image. After our color calibration, images are consistent

both visually and numerically. Photo-consistency based reconstruction algorithms can produce more

reasonable results, shown in Figure 1(d) and (e).

The remainder of this paper is organized as follows: Section 2 presents the related work. Section 3

discusses the motivation for our work. The detailed radiance-based color calibration method is described

in Section 4. Section 5 shows experiment results and evaluates photo-consistency measurements which

are further applied in 3D reconstruction applications. Finally, further steps are discussed in conclusions.

2 Related work

The direct way to perform color calibrate across multiple cameras is to repeatedly adjust camera pa-

rameters (such as gain and brightness) until all the camera responses are similar enough to each other.

Nanda et al. [11] use scene statistics as feedback to adjust the parameters of multiple cameras in their

RingCam system. The main drawback of this method is that the acquiring devices must be physically

accessible and it is not applicable for many low-end acquiring devices.

Furthermore, several software post processing techniques are proposed. Joshi [13] ﬁts the response

function as linear function, while Ilie [10] tries to minimize a cost function among images by adjusting

hardware parameters. Based on their original work, Malik [14] uses a neural network based transform to

optimize the software correction process, while Yamamoto [15] uses scale invariant feature transform to

detect correspondences instead of a color chart board. However, all methods above need to perform hard-

ware parameter adjustment at ﬁrst. In contrast, our method does not need to adjust camera parameters

but ﬁnally produces consistent colors both visually and numerically.

Another way to achieve color consistency across multiple cameras is by software processing of captured

images. Porikli [12] designs a method based on image color histograms to modeling transfer functions and

pair-wise correct multiple images. However, this method is diﬃcult to ensure numerical color consistency

for ignoring physical diﬀerences between cameras, and it may cause distortions and quantization errors

when some parts of color spectrum are compressed or stretched. In our method, we ﬁrst try to eliminate

the above noise for each camera and then perform color correction with multiple images. Moreover, we

address more attention to the issue of photo-consistency estimation and discuss the application of color

calibration for image-based modeling.

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