FAST EDGE-GUIDED INTERPOLATION OF COLOR IMAGES

Amin Behnad and Konstantinos N. Plataniotis

The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto

10 King’s College Road, Toronto, Ontario, M5S 3G4, Canada

Keywords:

Color images, Interpolation, Real-time applications.

Abstract:

We propose a fast adaptive image interpolation method for still color images which is suitable for real-time

applications. The proposed interpolation scheme combines the speed of fast linear image interpolators with

advantages of an edge-guided interpolator. A fast and high performance image interpolation technique is

proposed to interpolate the luminance channel of low-resolution color images. Since the human visual system

is less sensitive to the chrominance channels than the luminance channel, we interpolate the former with the

fast method of bicubic interpolation. This hybrid technique achieves high PSNR and superior visual quality

by preserving edge structures well while maintaining a low computational complexity. As veriﬁed by the

simulation results, interpolation artifacts (e.g. blurring, ringing and jaggies) plaguing linear interpolators are

noticeably reduced with our method.

1 INTRODUCTION

Image interpolation has been an active research topic

since early days of image processing, due to a wide

range of its applications, including resolution upcon-

version, resizing, video deinterlacing, video frame

rate upconversion, subpixel motion estimation, im-

age compression, etc. Many of these applications

have real-time requirements, for examples, video de-

interlacing and resolution or/and frame rate upcon-

version. The common solutions for real-time image

interpolation are simple image-independent linear ﬁl-

ters, such as bilinear interpolator and bicubic inter-

polator (Keys, 1981). But these simple linear ﬁlters

are isotropic and ill suited for directional image wave-

forms and also cannot cope with the nonlinearities of

the image formation model (Plataniotis et al., 1999).

Hence they tend to produce severe interpolation arti-

facts in areas of edges and ﬁne image details.

To overcome the above said weaknesses of signal-

independent isotropic interpolators, adaptive nonlin-

ear interpolators were introduced (Li and Orchard,

2001), (Muresan, 2005), (Zhang and Wu, 2006) and

(Li and Nguyen, 2008) . Among these algorithms,

edge preserving interpolators are of great interest.

The ultimate goal of an edge-guided image inter-

polation technique is to avoid interpolation against

the existing edge directions for each missing high-

resolution (HR) pixel. This achieves clean and sharp

reproduced edges in the HR output image. How-

ever in practice there is a major issue with most of

the developed edge-guided interpolators. The edge-

guided interpolators achieve better perceptual quality

than linear ﬁlters at cost of higher computationalcom-

plexity. Therefore most of these algorithms are not

suitable for real-time applications.

In this work, we address this issue and devise

an algorithm to reduce the computational cost of di-

rectional image interpolation for color images. In

the proposed algorithm, low-resolution (LR) color

images are converted to the luminance-chrominance

space, from the RGB counterpart and the interpola-

tion process is carried out in the new space. The rea-

son for this mapping is twofold. First, the human vi-

sual system is much more sensitive to the luminance

component than the chrominance. Hence, we apply

a sophisticated interpolation technique to interpolate

the luminance channel and for computational savings,

a simple linear ﬁlter e.g. bicubic is applied for the

chrominance channels. Second, the luminance chan-

nel captures the variations in the image and magni-

ﬁes the edges and other high-frequency components.

This achieves more reliability on the extracted edge

information from the LR image, which is crucial for

directional image interpolation.

To interpolate the luminance channel, we also pro-

pose a fusion-based image interpolation method. As

veriﬁed by the simulations, this technique achieves

superior performance than the competing methods, at

lower computational complexity.

103

Behnad A. and N. Plataniotis K. (2010).

FAST EDGE-GUIDED INTERPOLATION OF COLOR IMAGES.

In Proceedings of the International Conference on Signal Processing and Multimedia Applications, pages 103-107

DOI: 10.5220/0002933401030107

 SciTePress

The presentation of this paper is as follows. The

proposed interpolation scheme for color images is de-

scribed in section. 2. Proposed edge-guided interpo-

lation algorithm for gray-scaled images is presented

in section.3. Section.4 presents the simulation results

and section.5 concludes.

2 PROPOSED ALGORITHM FOR

COLOR IMAGE

INTERPOLATION

As in the existing literature, we assume that each

pixel in the input color image has three color val-

ues: red (R), green (G) and blue (B). In pursuit of

low computational cost, we interpolate color images

in a new space which must include smooth (low-pass)

components. As such, we can effectively interpolate

the smooth components with fast linear interpolators,

without sacriﬁcing the perceptual quality. The conve-

nient RGB to YCbCr conversion faithfully satisfy the

above condition. The equations for this mapping in

the JPEG JFIF format (Hamilton, 1992) are:

Y = 0.299R + 0.587G+ 0.114B

Cb = − 0.1687R− 0.3313G+ 0.5B

Cr = 0.5R− 0.4187G− 0.0813B (1)

and the reverse equations are given as:

R = Y + 1.402Cr

G = Y − 0.34414Cb− 0.71414Cr

B = Y + 1.772Cb (2)

However, the applied coefﬁcients in (1) and (2) are

real numbers which incurs error for hardware imple-

mentations. This issue can be addressed by applying

a reversible transformation such as RGB to YCoCg

with corresponding conversion formula:

Y = 0.25R+ 0.5G+ 0.25B

Co = 0.5R− 0.5B

Cg = − 0.25R+ 0.5G− 0.25B (3)

and reverse formula

R = Y +Co− Cg

G = Y +Cg

B = Y −Co− Cg. (4)

For more details about developing of (3) and (4)

please refer to (Malvar et al., 2008). The advan-

tage of YCoCg transform over YCbCr is that the in-

verse formula, mapping YCoCg into RGB only re-

quires additions and subtractions. To be more pre-

cise, the inversion can be performed with four ad-

ditions: G = Y + Cg, t = Y − Cg, R = t + Co and

B = t − Co (Malvar et al., 2008). We use this re-

versible transformation for the proposed interpolation

technique. Color images are converted from RGB

to YCoCg space, then the chrominance channels (Co

and Cg) are interpolated with bicubic interpolator.

By now, we have described the interpolation pro-

cess of the chrominance channels. Human visual sys-

tem is more sensitive to the luminance (Y) channel.

Hence in our design a high-performance edge-guided

interpolation algorithm is utilized for interpolation of

the luminance channel. In the next section the pro-

posed image interpolation algorithm for the Y chan-

nel is presented.

3 FAST ADAPTIVE

INTERPOLATION OF

GRAY-SCALED IMAGES

In this section we reexamine the problem of resolution

upconversion of gray-scaled images. Formation of an

HR image from original LR samples is depicted in

ﬁgures. 1(a). The missing pixels are recovered in two

batches. First missing pixels with coordinates (2i, 2j)

are recovered and in the second batch, pixels with co-

ordinates (2i−1, 2j) and (2i, 2j− 1) are interpolated.

As illustrated in ﬁgures. 1(b) and (c), the problem of

interpolation of the second batch becomes the same

as the ﬁrst bacth by 45

◦

rotation. Therefore, we only

describe the algorithm for the ﬁrst batch in detail.

Figure 1: (a) Formation of a high-resolution (HR) image

from low-resolution (LR) samples (empty circles) and miss-

ing HR pixels (black circles). (b),(c) Interpolation of HR

missing pixels with different coordinates. Two estimates

are made from the LR samples (hatches circles) for each

missing pixel.

Two estimates for each missing pixel are obtained

by cubic convolution (Keys, 1981) in two orthogo-

nal directions (ﬁgures. 1(b) and (c)): d

and d

In (Zhang and Wu, 2006) a linear minimum mean-

squares method of fusing these two directional esti-

mates is proposed. For low complexity and ease of

implementation, we also adopt afﬁne weights to lin-

early fuse d

and d

to interpolate the HR pixel Y

namely:

SIGMAP 2010 - International Conference on Signal Processing and Multimedia Applications

104

0 5 10 15

30.75

30.8

30.85

30.9

30.95

31.05

31.1

31.15

31.2

|γ|

PSNR

Figure 2: Average PSNR result over a set of training images

for different values of γ.

= αd

+ (1− α)d

, α ∈ [0, 1]. (5)

The value of α is computed as follows. First, the

smoothness along directions 1 and 2 are measured by

computing the sum of the absolute differences (SAD)

of the available LR pixels in the locality of the miss-

ing HR pixel Y

(2i, 2j) as:

SAD

(2i, 2j) =

∑

(m,n)∈W

2i,2 j



(m, n) −Y

(m+ 1, n+1)



(6)

and

SAD

(2i, 2j) =

∑

(m,n)∈W

2i,2 j



(m, n) −Y

(m− 1, n+1)



(7)

where W

2i,2j

is a 7× 7 spatial template in the HR lat-

tice centered at the position (2i, 2j). As described in

the section.1, edge-guided interpolators perform the

interpolation ﬁltering along the directions of smooth-

ness. Hence, it is expected that more wight be as-

signed to the direction with less corresponding value

of SAD

, which means:

α ∝ SAD

, γ < 0 in our de-

sign. Once γ is given,

α is computed as:

α =

SAD

+ SAD

. (8)

The following subsection concerns with evaluating

the global optimum value of γ for the proposed al-

gorithm.

3.1 Calculation of γ

In our design, the value of γ is determined by train-

ing. A large set of HR images is selected and down-

sampled by the factor of two and then reconstructed

by the proposed method. The training is accom-

plished on the activity regions of the aforementioned

HR images. The average PSNR over the all training

images for different values of γ is plotted in ﬁgures 2.

We choose γ = −4 that achieves the highest objective

performance for the proposed method.

Figure 3: Six sample images in the test set: (a) Lena, (b)

Parrots, (c) Flight, (d) Window, (e) Flower and (f) Fruits.

4 SIMULATION RESULTS

The proposed interpolation method was implemented

and tested on a variety of scenes. A brief objec-

tive comparison between the proposed method in

section.3 and some existing interpolation algorithms

is presented by Table 1. Please note that the reported

PSNR results are for the luminance channel of the

pictures depicted in ﬁgures. 3. As veriﬁed by the re-

sults, the proposed method outperforms the competi-

tion with NEDI (Li and Orchard, 2001) and method

of (Zhang and Wu, 2006) which are among the best

edge-guided image interpolation algorithms in the lit-

erature. The reported execution time also veriﬁes the

simplicity of the proposed algorithm. The major pa-

rameters of the exploited server for the simulations

are: CPU: Intel



Core 2 Duo E8400 (3 GHz), RAM:

4 GB, 6 MB of L2 cache and 1333 MHz front side bus

(FSB). The proposed algorithm is highly paralleliz-

able, since it recovers each missing pixel in isolation.

Therefore the proposed algorithm is also suitable for

hardware implementations.

Table 1: PSNR (decibels) results of reconstructed images

and the average execution time for NEDI (Li and Orchard,

2001), LMMSE INTR (Zhang and Wu, 2006) and the pro-

posed method.

Image NEDI LMMSE INTR Proposed

Lena 33.36 33.38 33.93

Parrot 34.52 34.15 35.21

Flight 29.95 29.92 30.36

Window 34.68 34.92 35.88

Flower 27.96 28.12 28.77

Fruits 36.35 36.81 38.92

Average 32.80 32.88 34.01

Time(s) 21.03 10.52 0.92

FAST EDGE-GUIDED INTERPOLATION OF COLOR IMAGES

105

Table 2: PSNR (decibels) results of reconstructed color images in ﬁgures. 3 in YCoCg color space with three different

methods. bicubic: all channels are interpolated with bicubic. bicubic+proposed: Y channel is interpolated by the proposed

method in section. 3 and chrominance channels are interpolated with bicubic. proposed: all channels are recovered with the

proposed algorithm in section. 3.

Image Lena Parrot Flight

channels R G B R G B R G B

bicubic 35.47 32.19 30.72 34.13 34.09 34.04 29.69 29.54 29.33

bicubic+proposed 35.53 32.70 31.07 34.99 34.96 34.89 30.55 30.43 30.20

proposed 35.89 32.70 31.18 34.98 34.92 34.85 30.54 30.43 30.19

Image Window Flower Fruits

channels R G B R G B R G B

bicubic 34.94 34.92 34.75 28.10 27.10 30.15 36.79 37.20 38.51

bicubic+proposed 35.61 35.63 35.44 28.15 27.25 29.92 37.45 37.88 38.70

proposed 35.62 35.62 35.37 28.13 27.19 30.25 37.48 37.91 38.87

Figure 4: Interpolation results of a portion of the image

Fruits with three different methods: (a) bicubic, (b) bicu-

bic+proposed, (c) proposed. (a) is the original image.

To evaluate the performance of the proposed inter-

polation scheme for color images we conduct the fol-

lowing test. The color images listed in the ﬁgures.3

are ﬁrst down-sampled by a factor of two, and recov-

ered by three different schemes:

1. Bicubic: the R,G and B channels are interpolated

with bicubic interpolator.

2. Bicubic+Proposed: images are ﬁrst converted to

the YCoCg space and the Y channel is upcon-

verted by the proposed edge-guided interpolator

while the Co and Cg channels are interpolated by

bicubic.

3. Proposed: images are ﬁrst converted to the

YCoCg space and the Y,Co and Cg channels are

Figure 5: Interpolation results of a portion of the image

Flight with three different methods: (a) bicubic, (b) bicu-

bic+proposed, (c) proposed. (a) is the original image.

interpolated with the proposed edge-guided inter-

polator.

The results are tabulated in Table.2. It can be veriﬁed

that the combinatory algorithm (bicubic+proposed)

achievessimilar results to those of the third algorithm.

The perceptual quality of the recovered image by the

three algorithms are compared in ﬁgures. 4,5 and 6.

The outputs of the schemes 2 and 3 are visually sim-

ilar which manifests the efﬁcacy of the proposed al-

gorithm for reducing the complexity of color image

interpolation without loss of visual quality. The re-

constructed images by the proposed simpliﬁed image

interpolation method are in turn greatly sharper and

cleaner than those of bicubic interpolation.

SIGMAP 2010 - International Conference on Signal Processing and Multimedia Applications

106

Figure 6: Interpolation results of a portion of the image

Bush with three different methods: (a) bicubic, (b) bicu-

bic+proposed, (c) proposed. (a) is the original image.

5 CONCLUDING REMARKS

A fast interpolation algorithm for color images is pro-

posed. Color images are ﬁrst converted from RGB to

luminance-Chrominance format, then the luminance

channel is interpolated with a proposed edge-guided

interpolation technique and the luminance channels

are interpolated with simple bicubic interpolation.

Since chrominance channels have low-pass 2D wave-

forms, we can effectively interpolate them without de-

grading the perceptual quality of the recovered im-

ages. Simulation results verify that the proposed in-

terpolation technique is fast and also removes com-

mon interpolation artifacts.

REFERENCES

Hamilton (1992). Jpeg ﬁle interchange format, version 1.02.

Keys, R. G. (1981). Cubic convolution interpolation for

digital image processing. In IEEE Trans. on Acous-

tic, Speech, Signal Processing, vol. 29, no.6, pp.1153–

1160.

Li, M. and Nguyen, T. Q. (2008). Markov random ﬁeld

model-based edge-directed image interpolation. In

IEEE Trans. on Image Processing, vol. 17, no. 7, pp.

1121–1128.

Li, X. and Orchard, M. T. (2001). New edge-directed in-

terpolation. In IEEE Trans. on Image Processing, vol.

10, pp. 1521–1527.

Malvar, H. S., Sullivan, G. J., and Srinivasan, S. (2008).

Lifting based reversible color transformations for im-

age compression. In SPIE Applications of Digital Im-

age Processing, vol. 7073, pp. 707307–707307-10.

Muresan, D. D. (2005). Fast edge directed polynomial inter-

polation. In IEEE International Conference on Image

Processing, vol. 2, pp. II-990-3.

Plataniotis, K. N., Androutsos, D., and Venetsanopoulos,

A. N. (1999). Adaptive fuzzy systems for multichan-

nel signal processing. In Proceedings of the IEEE, vol.

87, no. 9, pp. 1601-1622.

Zhang, L. and Wu, X. (2006). An edge-guided image in-

terpolation algorithm via directional ﬁltering and data

fusion. In IEEE Trans. on Image Processing, vol. 15,

no. 8, pp. 2226–2238.

FAST EDGE-GUIDED INTERPOLATION OF COLOR IMAGES

107