Copyright is held by the author / owner(s). SIGGRAPH Asia 2011, Hong Kong, China, December 12 – 15, 2011. ISBN 978-1-4503-0807-6/11/0012

Local Oscillation Suppression Based on Joint Bilateral Filtering Framework

Zhuo Su ∗ Xiaonan Luo † Zhengjie Deng ‡

School of Information Science and Technology, Sun Yat-sen UniversityNational Engineering Research Center of Digital Life, China

(a) Local extrema vs our approach (b) Bilateral filter vs our approachFigure 1: Comparisons of local extrema [Subr et al. 2009], bilateral filter [Paris et al. 2009] and our approach. With two magnified localoscillation regions in (a) and the mesh of pixel intensity in (b), we demonstrate that our approach has a sound texture oscillations suppression.

1 IntroductionImage details are mainly composed of edges and textures. Fromthe view of pixel intensity or gradient magnitude, both edges andtextures are the drastic variances among the pixels of local imageregions. However, because of the similarity of textures, they usu-ally feature some regular local oscillations [Subr et al. 2009]. Itmakes great sense to distinguishes edges and textures exactly formany image applications, e.g. detail manipulation. But the currentmajor bilateral-based [Paris and Durand 2009] and optimization-based [Farbman et al. 2008] approaches usually emphasize more onedge-preserving, incompletely preserving some textures instead ofsmoothing. These results will produce serious interferences in bothedge preservation and texture extraction. On the basis of the jointbilateral filtering framework, we take advantage of our degenerativeimage to suppress the local oscillations and produce better outputwith dual properties of edge-preserving and texture-smoothing, seeFigure 1(e).

2 Joint Bilateral Filtering Framework with De-generative Range Input

Bilateral filter (BF) is an popular edge-preserving smoothing ap-proach and the joint bilateral filter (JBF) is one of its extension[Paris and Durand 2009]. The JBF takes a flexible image E re-lated with the input image I , called joint image, as the input ofthe weighted range function.

IJ(p) =

∑GS (∥p− q∥)GR (|E(p)− E(q)|) I(q)∑

GS (∥p− q∥)GR (|E(p)− E(q)|) , (1)

where S and R denote the spatial and range domain, respectively.The pixel p is the center of S and q = p+ k, where k = [kx, ky]with −r ≤ kx, ky ≤ r, and r denotes the radius of spatial do-main S. In addition, the weighted spatial function GS(·) and theweighted range function GR(·) are defined by one dimensionalGaussian function. With the flexibility of choosing the joint imageE, the improvement (1) can be expected to achieve sound resultsof both edge-preserving and texture-smoothing. For this reason,we propose a scheme to construct a degenerative image as the jointimage in the following.

2.1 Degenerating by Iterative Asymmetric SamplingThe spatial sampling can effectively reduce the texture oscillations.Inspired by Gaussian pyramid algorithm and the flexibility of iter-

∗E-mail:suzhuoi@gmail.com†E-mail:lnslxn@mail.sysu.edu.cn‡E-mail:jet dunn@hotmail.com

ation, we proposed an iterative asymmetric sampling operation toobtain our expected degenerative image. A sample rate d is appliedto obtain the downsampling image L = I ′↓d and d−1 is applied forupsampling. This procedure is formulated as

Lt =(g ⊗ It

)↓d, It+1 = Lt↑d

−1

, (2)

where t denotes the iterative times. Some efficient image samplingapproaches can be applied in this asymmetric operation. Finally,the output It+1 are taken as the degenerative image E.

Figure 2: Plots of 1D signal. Our approach achieves effects com-parable to those of bilateral filter in edge preserving (block a andb), and better oscillations suppression than Gaussian smoothing(block c).

3 Conclusion and AcknowledgementIn summary, a novel approach is proposed to suppress the localoscillation based on the degenerative image in the joint bilateral fil-tering framework. And a compact iterative asymmetric samplingscheme is developed to produce the degenerative images. Our re-sults are shown in Figure 1 and the 1D signal analysis is given inFigure 2. Compared with [Subr et al. 2009], our approach not onlyavoids complicated interpolations of local extremas, but also avoidssolving weighted optimization equation. In addition, our approachcan be further extended to several applications, such as detail en-hancement, texture manipulation, and edge detection.

This work is supported by the NSFC-Guangdong Joint Fund (No.U0735001, U0935004), and the National Key Basic Research andDevelopment Program of China 973 (No. 2011CB302204).

References

FARBMAN, Z., FATTAL, R., LISCHINSKI, D., AND SZELISKI, R.2008. Edge-preserving decompositions for multi-scale tone anddetail manipulation. ACM Trans. Graph. 27, 3, 67:1–10.

PARIS, S., AND DURAND, F. 2009. A fast approximation of thebilateral filter using a signal processing approach. InternationalJournal of Computer Vision 81, 1, 24–52.

SUBR, K., SOLER, C., AND DURAND, F. 2009. Edge-preservingmultiscale image decomposition based on local extrema. ACMTrans. Graph. 28, 5, 147:1–9.