Special Issue - 2021 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 NTASU - 2020 Conference Proceedings Analysis of Ringing Artifact in Image Fusion Using Directional Wavelet Transforms y z x Ashish V. Vanmali Tushar Kataria , Samrudhha G. Kelkar , Vikram M. Gadre Dept. of Information Technology Dept. of Electrical Engineering Vidyavardhini’s C.O.E. & Tech. Indian Institute of Technology, Bombay Vasai, Mumbai, India – 401202 Powai, Mumbai, India – 400076 Abstract—In the field of multi-data analysis and fusion, image • Images taken from multiple sensors. Examples include fusion plays a vital role for many applications. With inventions near infrared (NIR) images, IR images, CT, MRI, PET, of new sensors, the demand of high quality image fusion fMRI etc. algorithms has seen tremendous growth. Wavelet based fusion is a popular choice for many image fusion algorithms, because of its We can broadly classify the image fusion techniques into four ability to decouple different features of information. However, categories: it suffers from ringing artifacts generated in the output. This 1) Component substitution based fusion algorithms [1]–[5] paper presents an analysis of ringing artifacts in application of 2) Optimization based fusion algorithms [6]–[10] image fusion using directional wavelets (curvelets, contourlets, non-subsampled contourlets etc.). We compare the performance 3) Multi-resolution (wavelets and others) based fusion algo- of various fusion rules for directional wavelets available in rithms [11]–[15] and literature. The experimental results suggest that the ringing 4) Neural network based fusion algorithms [16]–[19]. artifacts are present in all types of wavelets with the extent of Wavelet based multi-resolution analysis decouples data into artifact varying with type of the wavelet, fusion rule used and levels of decomposition. low frequency (LF) and high frequency (HF) components at Index Terms—Directional Wavelets, Image Fusion, Modified various scales. This allows for separate processing of LF and Structural Dissimilarity, Ringing Artifacts HF components, and gives more flexibility and freedom in designing better fusion algorithms. Also, the computational I. INTRODUCTION complexity is very low for wavelet analysis-synthesis filter banks. These advantages make wavelets popular for the image Fusion of complementary information from different source fusion applications. The wavelet based image fusion algo- images is known as image fusion. In this digital age, there is rithms follow three simple steps: a huge influx of data captured from multiple camera setting 1) Decompose source images into LF and HF coefficients and/or sensors of the same object or scene being imaged. Each to form wavelet pyramids. image captured, thus exhibits different features of data, with 2) Fuse LF and HF coefficients using the prescribed fusion varying amounts of details of the objects. Combining these rule to form a fused wavelet pyramid. shreds of information from different images becomes imper- 3) Take inverse transform of the fused coefficients to get the ative, as it helps in defining the big picture. For example, in fused image. medical applications, fusing Computerized Tomography (CT), One of the simplest fusion rule in wavelet base fusion is Magnetic Resonance Imaging (MRI), Functional Magnetic mean-max fusion. In mean-max fusion, the detail coefficient Resonance Imaging (fMRI), Positron Emission Tomography with the highest magnitude among two images is chosen (PET) etc., helps in the diagnosis of a disease in a reliable, as the detail wavelet coefficient of the fused image. This efficient and quick manner. In surveillance, use of visible and ensures maximum detail preservation in the fused image. infrared (IR) images is a common practice. High dynamic The approximate wavelet coefficients are generated by av- range (HDR) imaging involves fusion of differently exposed eraging individual approximate wavelet coefficients. In more low dynamic range (LDR) images. sophisticated algorithms, LF and HF coefficients are weighted The objective of image fusion is find one image which has based on the certain features like local energy, local entropy, more information about the scene than any of the source im- matching degree, and so on. A study of such fusion rules is ages. The input data for image fusion algorithms is generally presented by B. Zhang in [20]. of two types: Along with separable wavelet transform, use of non- • Images taken from a single sensor but with differ- separable wavelet transforms and other variants of wavelet ent parameters of the imaging apparatus. Examples in- transform is also a common practice in many image fusion clude multi-focus images, multi-exposure images, multi- applications. Singh and Khare [13] used Daubechies’ complex temporal images etc. wavelet transform for multi-modal medical image fusion. At Volume 9, Issue 3 Published by, www.ijert.org 495 Special Issue - 2021 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 NTASU - 2020 Conference Proceedings traditional mean-max fusion algorithm. It can be observed that the ringing artifacts are more prominent across the strong edges and not so visible around the weak edges. Also, the ringing artifacts are not perceivable around textures (hair’s in the image) as textures themselves are oscillatory in nature. Even though ringing artifacts will be present in such areas, they will not be perceivable to the naked human eye because of smaller magnitude perturbations than background textures. Ringing artifacts intrinsically occur because the loss in HF information of a signal. In wavelet based image fusion, it is (a) Multi-focus image 1 (b) Multi-focus image 2 because of loss of the original HF coefficients of an image and subsequently substitution with other coefficients in that place. Preliminary analysis of ringing artifacts in wavelet based fusion is given by Dippel et al. in [22]. According to Dippel et al., in case of wavelet pyramid, there is a strong parent- child relationship among the coefficients termed as inter-scale correlation . In the fusion process, this relationship is altered, giving rise to the ringing artifacts. Also, the reconstruction pro- cess involves frequency sensitive high pass filtering operation, which further amplifies these ringing artifacts. These ringing (c) Fused image (d) Zoomed part of (c) artifacts are dominant for strong edges than weak edges. Fig. 1. Example of ringing artifacts In our previous work, Vanmali et al. [24] and Kelkar [25] investigated more on this problem with thorough experimen- tation for separable wavelets to draw following observations: the same time, non-subsampled contourlet transform (NSCT) • The ringing artifact increases with the number of levels is used by Bhatnagar et al. [12] for the fusion of multi- of decomposition, and then remains constant after a modal images. Wang et al. [14] used shearlet transform for particular level of decomposition. decomposition of medical images. Upla et al. [15] used con- • Ringing artifacts are more abrupt for smaller lengths of tourlet transform for fusion of panchromatic (PAN) and multi- the filters. spectral (MS) images in remote sensing applications. Malik et • Ringing artifacts are smoother for higher lengths of the al. [21] has proposed a weight map based wavelet based multi- filters. resolution fusion for the application of the multi-exposure We now extend this work for the directional wavelets. image fusion. A general introduction of multi-resolution image III. EXPERIMENTAL SETUP fusion is provided by Piella in [11]. For the analysis of artifacts in case of the directional However, the main drawback of wavelet based techniques wavelets, we use similar experimental setup as used in Vanmali is that, they suffer from ringing artifacts in the fused image et al. [24] and Kelkar [25]. We start with a standard test image, [22], [23]. The analysis for the separable wavelets is presented and form two multi-focus images, first with increasing blur in our previous work, Vanmali et al. [24] and Kelkar [25]. from bottom to top and the second with increasing blur from Two possible methods to compensate ringing artifacts for top to bottom. An example of the input images so generated separable wavelets are also presented in our previous work, is shown in Figure 2. These multi-focus images are then Vanmali et al. [24]. In this paper, we focus on the analysis of fused using different fusion algorithms with varying levels of ringing artifacts in case of directional wavelets like curvelets, decomposition and the corresponding outputs are observed. contourlets, non-subsampled contourlets, shearlets. Analysis of Since, we are forming multi-focus images from the standard ringing artifacts at different levels of decomposition, using test image, it makes ground truth available, which can be different fusion algorithms and for a variety of images is used to compare the quality of fusion. The experiments were presented in this work. carried out for standard test images of ‘Phantom’, ‘Peppers’, II. RINGING ARTIFACTS IN WAVELET BASED FUSION ‘Girlface’, ‘Lena’, and ‘Baboon’, all of size 512 × 512 pixels. The ‘Phantom’ images has constant gray level areas without In digital image processing and signal processing ringing any shading and texture. The ‘Peppers’ images has variation artifacts appear close to strong edges (high gradient value) or in the shading with very low amount of texture. The images high transitions of a signal. Because of the oscillatory