Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 405919, 7 pages

http://dx.doi.org/10.1155/2015/405919

## Block-Matching Based Multifocus Image Fusion

^{1}School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China^{2}School of Information Science and Technology, Taishan University, Tai’an, Shandong 271021, China

Received 12 November 2014; Revised 18 March 2015; Accepted 7 April 2015

Academic Editor: Tarak Ben Zineb

Copyright © 2015 Feng Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A new multifocus image fusion method is proposed. Two image blocks are selected by sliding the window from the two source images at the same position, discrete cosine transform (DCT) is implemented, respectively, on these two blocks, and the alternating component (AC) energy of these blocks is then calculated to decide which is the well-focused one. In addition, block matching is used to determine a group of image blocks that are all similar to the well-focused reference block. Finally, all the blocks are returned to their original positions through weighted average. The weight is decided with the AC energy of the well-focused block. Experimental results demonstrate that, unlike other spatial methods, the proposed method effectively avoids block artifacts. The proposed method also significantly improves the objective evaluation results, which are obtained by some transform domain methods.

#### 1. Introduction

In many cases, defocused parts often exist in the acquired image because interesting sceneries are highlighted or these defocused parts are restricted by environmental factors when the images are acquired. Fusing two or multiple images is an effective method to remove the defocusing phenomenon and to obtain a totally well-focused image. That is, fusing involves using the well-focused parts of the images to compose a new image, in which no defocusing phenomenon exists.

Image fusion has two types: spatial and transform domain. Transform-based image fusion algorithm has received many favorable results, such as pyramid decomposition transform domain fusion [1] and wavelet transform [2–5]. Wavelet transform is one of the most commonly used methods. However, the conventional wavelet transform can well represent only the point singularity and therefore cannot well represent the linear singularity that largely exists in many images, such as line or curve edges in an image. A series of super-wavelets has been proposed and applied to image fusion techniques, including ridgelet [6], curvelet [7], contourlet [8], bandlet [9], and shearlet [10], to effectively represent linear singularity.

Although the image fusion techniques based on wavelet transform and super-wavelet transforms have obtained significant achievements, all of these transformations are local transformations that inevitably bring artifacts into the resulting images. Wavelet transform often introduces the ringing effects, whereas super-wavelet transform often introduces linear artifacts. A nonlocal method has been initially developed for image denoising [11–13] in the recent years. This method has largely relieved the phenomenon of artifacts in the resulting images. As a successful nonlocal method, the block-matching 3D (BM3D) transform in [14, 15] has achieved significant progress in various image processing applications, such as image denoising, image enhancement, and image super-resolution analysis.

An effective multifocus image fusion algorithm is proposed in this paper by utilizing the superiority of the enhanced sparse representation of BM3D. The experimental results show that the proposed algorithm can effectively avoid all kinds of artifacts; that is, the proposed algorithm can obtain excellent subjective visual quality, and we call it BM3D fusion (BM3DF). However, the objective evaluation of the BM3D-based method is not ideal. We remove the 3D transform in BM3D algorithm to improve further the objective evaluation result. However, the block-matching and image aggregating operators are preserved. This simple method is just a spatial one since the transform is removed; however, achieving ideal image fusion results, it is called block-matching spatial fusion (BMSF). The experimental results show that the multifocus image fusion results on both subjective visual quality and objective evaluation of this method are better than those of some existing state-of-the-art image fusion algorithms.

#### 2. Image Fusion Algorithm Based on BM3D

The different purposes between the image fusion and the image denoising are considered when the first stage of BM3D [14] is conducted in this paper; in other words, we need not implement the second stage of BM3D. The image fusion algorithm is as follows.

*Step 1. *Given two images, A and B, which have been well registered with different focus, the input images A and B are divided into several overlapping blocks, and , respectively, where is the set of the coordinates of each block and and are both called reference blocks. Grouping operations are implemented on blocks and according to the method in [14]; that is, those image blocks similar to and are stacked and two 3D matrices are formed:

*Step 2. *Two 3D matrices grouped in Formula (1) are implemented with separable 3D transform to obtain their sparse representation:

*Step 3. *Let and be the low-frequency coefficients of and , respectively. and are the high-frequency coefficients of and , respectively.

The defocused patches do not have enough detailed information, such as texture and contour. After the 3D transform, the bigger magnitude high-frequency coefficients are usually from the well-focused patches. The purpose of image fusion is just to recover these pieces of detailed information. So we select the bigger magnitude coefficients as the fusion result high-frequency coefficients. On the other hand, there are very similar low-frequency transformed coefficients between the well-focused patches and the defocused ones, so we simply average the low-frequency coefficients which are from both the well-focused and defocused patches, respectively, as the fusion result low-frequency coefficients.

*Step 4. *The following coefficient fusion rules are presented in this algorithm:*Note*. Only one low-frequency coefficient exists after the 3D transform of each 3D transform, whereas the rest are all high-frequency coefficients. The high-frequency coefficients to be fused are from the same location in each 3D transform.

*Step 5. *3D inverse transform is implemented on 3D coefficients matrix that consists of as low-frequency coefficients and as high-frequency coefficients:

*Step 6. *Fusion image is obtained by aggregating all the image blocks in each group . The particular aggregation formula is as follows:where is the fused image, is the characteristic function, and is a set of coordinates constituted of all blocks. Figure 1 illustrates the algorithm flow chart.

The flowchart presents a kind of direct BM3D-based algorithm for image fusion. In this paper, this algorithm is called BM3DF.

The experimental results show that the fused result of BM3DF is not ideal on objective evaluation, although the subjective visual quality remains better than some existing algorithms. There may be some following reasons. Firstly, the high-frequency coefficients selection strategy of BM3DF is a little rough. Secondly, the image details from the well-focused image patches are always inevitably smoothed in some degree since the inverse 3D transform after the coefficients fusion and the final aggregation procedure. Thus, the fused result is not ideal on objective evaluation. If we use a good strategy to judge which image blocks are from the well-focused parts in advance, we only implement the block matching on those well-focused image blocks, and if we remove the 3D transform, we may obtain better objective evaluation. Therefore, a simpler but more effective image fusion algorithm than BM3DF is proposed, namely, block-matching spatial fusion (BMSF).