1.

Introduction

In digital image processing, image resolution enhancement is in great demand. Medical images, surveillance images, and old photographs require an accurate image enlargement scheme for reconstructing missing information. Interpolation is such a process of estimating the missing pixels of high-resolution images from low-resolution images.

Linear interpolation is simple and fast, but not suitable for high-quality image restoration. For sophisticated applications, nonlinear interpolation methods such as edge-directed interpolation (EDI) are preferable. The human vision system is particularly responsive to a sudden change of pixel intensities. Hence, the quality of the entire image can be improved by restoring edges with less degradation. New EDI (NEDI)¹ is a representative EDI that uses Wiener filter theory. NEDI restores high-quality images; however, it suffers from blocking artifacts because of the deficiency of edge directionality information and the geometric duality assumption.¹ While various modifications of NEDI in Refs. 2 and 3 show some improvements, restored images are still degraded easily.

In this letter, we present a multidirectional EDI method. A new interpolation algorithm uses 12 directional neighboring pixels to restore various directional edges. To reduce high computational complexity, a method for dividing the interpolation region is also proposed.

2.

Proposed Algorithm

2.1.

Multidirectional Interpolation Model

Consider an interpolation of a low-resolution image $X$ with a size of $H\times W$ into a high-resolution image $Y$ with a size of $2H\times 2W$, that is, $Y_{2i,2j}=X_{i,j}$. For unknown pixel $Y_{2i+1,2j+1}$, a new interpolation model is proposed:

Eq. (1)

$$Y_{2i+1,2j+1}=\sum _{k=0}^3\sum _{l=0}^3{\alpha }_{4k+l}{Y}_{2(i+k-1),2(j+l-1)},$$

where $\alpha$ indicates an interpolation coefficient and ${\alpha }_{0,3,12,15}=0$. Figure 1(a) shows the visual concept of Eq. (1). Twelve neighboring pixels participate in the interpolation of $Y_{2i+1,2j+1}$. Unlike NEDI, the proposed model uses a sufficiently large number of directional pixels for precise estimation. Since this new interpolation model is expanded to all directions for an estimation window at Sec. 2.3, the geometric duality mismatch problem of NEDI is also solved.

Fig. 1

(a) Interpolation model for $Y_{2i+1,2j+1}$ (Ref. 4). (b) Step 3 of interpolation region division method. Black pixels are edge pixels and white pixels are non-edge pixels. The upper red pixels are marked with 1 if there are other edge pixels around the eight neighborhoods. Starting from the leftmost edge pixel, red pixels are marked from a to d in sequence. The lower blue pixels are marked with 2 from a to c in the same manner.

With the proposed interpolation model, the computational complexity of the algorithm increases dramatically because of the large dimensional matrix multiplications in the coefficient estimation process. Also, using additional neighboring pixels may duplicate details in the short- and random-edge regions. These difficulties can be resolved by the interpolation region division method proposed below.

3.

Simulation Results

The proposed algorithm has been implemented with MATLAB 7.1. ${\mathrm{TH}}_e$ is set to be 8, and ${\mathrm{TH}}_{\text{edge}}$ is set to be 3, the default. Twenty-four color images from a Kodak PhotoCD are used for the tests. Each image is downsampled directly from an original image and interpolated with three methods: bilinear, NEDI, and the proposed. Since other modifications of NEDI can be applied to the proposed method in the same way, only NEDI is selected for representative comparison.

Zoomed-in portions of interpolated images are presented in Figs. 2 and 3. Interpolated images from bilinear (b) and NEDI (c) show blocking artifacts along edges. On the other hand, the interpolated image from the proposed method (d) shows clear edges just like the original figure. In Fig. 3, the fine wood grain is restored in the right direction in (d), but not in (b) and (c). In Table 1, the peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM) index⁶ are compared. SSIM quantifies the degradation of the structural information in an image. Our algorithm also shows competitive performance in the objective tests.

Fig. 2

Zoomed-in portions of the (a) original kodim20 image and the interpolated images from (b) bilinear, (c) NEDI, and (d) proposed method.

Fig. 3

Zoomed-in portions of the (a) original kodim03 image and the interpolated images from (b) bilinear, (c) NEDI, and (d) proposed method.

Table 1

(a) PSNR(dB) values of interpolated images. (b) SSIM values of interpolated images.

The proposed algorithm has disadvantages in computational time. A user can adjust threshold values for reducing computational complexity at the expense of performance. However, process time is not a critical issue when restored image quality is a major concern.

4.

Conclusion

This letter presents a new idea for EDI. Twelve neighboring pixels are used for interpolation in order to reflect 12 directionalities. Also proposed is an interpolation region division method that resolves concerns related to the computational complexity and performance. Depending on the edge continuity, an image can be divided into three regions: even (non-edge) region, short-edge region, and long-edge region. Only long-edge regions are interpolated by the proposed model. Simulation results show that our method restores multidirectional edges clearly with fair performance in objective tests.