Application of Wavelet Transform on Multiresolution Image Mosaicing

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1 Application of Wavelet Transform on Multiresolution Image Mosaicing Ms. Snehal J. Banarase Prof. M.R.Banwaskar Abstract Image mosaicing is an effective technique for combination of two or more images, by using mosaicing we can form a new image with the help of different images. In this paper, we present use of wavelet transform for multiresolution image mosaicing. For image mosaicing, multiresolution representation is an effective technique for analyzing information contents of the images, as it processes the images individually at each finer level, to give more accurate results that contains much less distortion. An image mosaicing requires two stages for its implementation. In first stage two images to-be combined are identified and registered. In second stage the corresponding pixels of the images are blended to get proper information about each pixels intensity level. Blending technique overcomes an edge; it combines images such that no obstructive boundary exists around overlapped regions. It forms a new mosaic image without losing original appearance of images. Here the work is focused on designing a model with variable mask instead of using a predefined mask (fixed mask) for various features of images or combinations of images. Here we can select the mask according to our own choice by selecting a proper region with the help of pointer. Index Terms Image processing, Gaussian method, laplacian method, multiresolution mosaicing. I. INTRODUCTION Image mosaic technique is nothing but a combination of two or more image. An image mosaic is typically completed in two stages. First stage is usually referred to as image registration. In the second stage, the intensities of the images are blended after the corresponding points have been registered. It is too difficult to form an ideal mosaic image without any obstructive boundary, but an image mosaic processing technique can be applied greatly to reduce this difficulty. When two or more images are overlapped to form a single mixed ideal image there may be chances of appearance of edges in the images. To mosaic an image is to combine overlapped images so that the mixed image contains no obstructive boundaries in the transition region while care is taken to preserve the general appearance of the original images. Figure 1.1: Example of Image Mosaicing The figure 1.1 shows an example of image mosaicing. By using such mosaicing technique special effects can be given to movies. And this is one of the applications of mosaicing. An image mosaic is typically completed in two stages. In the first stage, the corresponding points in the two, to-be-combined images are identified and registered [3]. This stage is usually referred to as image registration. In the second stage, the intensities of the images are blended after the corresponding points have been registered. Here a novel approach is given to the blending energy minimization model which balances the smoothness of images. It uses weighting average to blend two overlapped region to evaluate pixel values within transition zone. Here different weighted average function are applied for different resolution levels such as wrinkles, skin colour etc. to blend all features properly we have used multiresolution analysis. Multiresolution analysis effectively decomposes the images and smoothly blends those images. After these two stages a new single mosaic mixed image will get formed without losing its original appearance. This paper is organized as follows: Section II present the review of literature related to different techniques of image mosaicing. Section III describes multiresolution image mosaicing. Section IV describes pyramidal representation. In section V our method of wavelet transform i.e. laplacian pyramid using Gaussian is explained in detail. Section VI & VII gives idea about masking & image blending respectively. Finally in section VIII we discuss the results. II. LITERATURE SURVEY For the combination of two or more images various techniques are found in Burt and Adelson method for multiresolution analysis is popular which uses spline functions for blending sub band coefficient based on multiresolution pyramidal representation [2]. This representation requires two steps, in first step two to-be-combined images are decomposed into sub band coefficient by means of pyramidal laplacian operator and in 64

2 second step spline function are applied to combine sub-band coefficient. It is easily computed and yields satisfactory result. It uses weighting average to blend two overlapped region to evaluate pixel values within transition zone. And to blend all features properly multiresolution analysis is used. Mosaic techniques have been used to combine two or more images into a new one with an invisible seam, and with as little distortion of each signal as possible. Multiresolution representation is an effective method for analyzing the information content of signals and it also fits a wide spectrum of visual signal processing and visual communication application. Wavelet transform is one kind of multiresolution representations, and has found a wide variety of application in many aspects, including signal analysis, image coding, image processing, computer vision and etc. Due to its characteristic of multiresolution signal decomposition, wavelet transform is used here to do the image mosaic by choosing the width of mosaic transition zone proportional to the frequency represented band. Both 1-D and 2-D signal mosaics is described, and some factors which affect the mosaics is discussed [5]. In a multiresolution spline technique for combining two or more images into a larger image mosaic, the images to be splined are first decomposed into a set of bandpass filtered component images. Next, the component images in each spatial frequency band are assembled into a corresponding band pass mosaic. In this step, component images are joined using a weighted average within a transition zone which is proportional in size to the wave lengths represented in the band. Finally, these bandpass mosaic images are summed to obtain the desired image mosaic. In this way, the spline is matched to the scale of features within the images themselves. When coarse features occur near borders, these are blended gradually over a relatively large distance without blurring or otherwise degrading finer image details in the neighbourhods of the border [1]. By referring Laplacian pyramid function the encoded data is get converted into the reduced form and by using Gaussian pyramid function it is get decoded into the expanded form. Here weighting average function is used to calculate average pixel value for multiple levels [2][4]. In the proposed technique, the to-be-combined images are first projected into wavelet subspaces. The images projected into the same wavelet space are then blended. Here blending function is derived from an energy minimization model which balances the smoothness around the overlapped region and the fidelity of the blended image to the original images [3]. An image mosaicing algorithm can be achieved by the Laganiere method for corner detection and so called at function for image blending is presented in this dissertation. Good results have been obtained within the mosaics created, clearing the way for a few considerations about the most important topics for an image mosaicing algorithm. The work presented follows 3 steps for Image Mosaicing i.e. Image Registration, Image Warping, Image Composition [6]. In strip mosaicing, a novel mosaic technique based on strip search algorithm is proposed that improves non-linearity, accuracy and vertical distortions possibly found in mosaic image. Strip Search algorithm based on novel measure of Relative Sum of the Squared Difference (R-SSD) is proposed to search particular strip of frame within its specified portion and it is used for normalization and simplification of some important steps of image mosaic [7]. The earlier work also exist on puzzle mosaicing, in puzzle mosaicing, they present a new technique to produce composite images called Puzzle Image Mosaic (PIM). The method is inspired by Jigsaw Image Mosaic (JIM), where image tiles of arbitrary shape are used to compose the final picture. The JIM approach leads to impressive results, but the required computation time is high. They propose an algorithm that produces good results in lower time. The technique takes advantage from recent results about data structures aimed to optimize proximity queries [8]. In image mosaicing for tele reality application they used the fundamental technique i.e. the automatic alignment of multiple images into larger aggregates which are then used to represent portions of a 3-D scene [9]. III. MULTIRESOLUTION IMAGE MOSAICING The frequency and time information content of a signal at some certain point in the time-frequency plane cannot be known. In other words, we cannot know what spectral component exists at any given time instant. The best we can do is to investigate what spectral components exist at any given interval of time. This is a problem of resolution, and it is the main reason why WT is popular than STFT. Since the previously used transforms like short time Fourier transform (STFT), Wigner distributions were not able to give good time and frequency resolution. Instead they were giving fixed resolution. To be simpler, every spectral component is not resolved equally in STFT. Thus the information provided by them was highly redundant in nature as far as reconstruction of the signal is considered. Figure 3.1 Block Diagram for Image Mosaicing The Figure 3.1clearly shows how actually two images are combining to form mosaic image. It shows N level decomposition of image. First image (consider it as A) is taken, then it is decomposed up to N level as per requirement of user. Similarly we have taken second image (consider it as B). Now we need to design mask with same size as that of the image size. Mask is nothing but binary representation of image in to- be combine images. This dummy image is used as mask for hiding appropriate part of image, i.e. Mask is a outer part of image A & inner part of image B. To get multiresolved format mask for each level of decomposition we have used low-pass filter and then sub-sampled [5]. Image is nothing but matrix of values, hence direct multiplication of mask with image is taken. Then two masked images are obtained, which are then combined to form the resultant image at each level of resolution. Here dynamic masking is done with region of interest i.e. we can select the region according to our own choice. Now using 65

3 these entire components, original image is reconstructed. After reconstruction we get the final resultant mosaic image. IV. PYRAMIDAL REPRESENTATION Following are the two important pyramid structures. In this section we present a highly efficient ''pyramid'' algorithm for performing the required filtering operations and also we show that the pyramid structure is ideally suited for performing the splining steps as well. masked image for finer resolution. In case of pyramidal blending we can mosaic different part of various images i.e. we can combine right part of one image to the left part of another image. Due to this pyramidal blending, the obstructive boundaries get converted into smooth transition region. Figure 4.1 A one-dimensional graphical representation of the iterative REDUCE operation used in pyramid construction. Figure 4.1 is a one-dimensional graphic representation of the process which generates a Gaussian pyramid. Each row of dots represents nodes within a level of the pyramid. The value of each node in the zero level is just the gray level of a corresponding image pixel. The value of each node in a high level is the weighted average of node values in the next lower level. Note that node spacing doubles from level to level, while the same weighting pattern or generating kernel" is used to generate all levels. The level-to-level averaging process is performed by the function REDUCE.[6] A sequence of low-pass filtered images G0, G1,...GN can be obtained by repeatedly convolving a small weighting function with an image. With this technique, image sample density is also decreased with each iteration so that the bandwidth is reduced in uniform one-octave steps. Sample reduction also means that the cost of computation is held to a minimum. Figure 4.1 is a graphical representation of the iterative filtering procedure in one dimension. Each row of dots represents the samples, or pixels, of one of the filtered images. The lowest row, G0, is the original image. The value of each node in the next row, G1, is computed as a weighted average of a sub array of G0 nodes, as shown Nodes of array G2 are then computed from G1 using the same pattern of weights. The process is iterated to obtain G2 from G1, G3 from G2 and so on. The sample distance is doubled with each iteration so that successive arrays are half as large in each dimension as their predecessors. If we imagine these arrays stacked one above the other, the result is the tapering data structure known as a pyramid. If the original image measures 2N + 1 by 2N + 1, then the pyramid will have N + 1 levels. Both sample density and resolution are decreased from level to level of the pyramid. For this reason, we shall call the local averaging process which generates each pyramid level from its predecessor a REDUCE operation [6]. In case of image mosaicing generally two types of pyramidal operations are used, i.e. Laplacian pyramid and Gaussian pyramid. In this paper we are applying Laplacian function on two input images and Gaussian function on Figure 4.2 Pyramidal Blending model Figure 4.2 shows pyramidal blending model. In this blending left part of one image is get blend with the right part of another image. In case of blending, the pixel values of images are mixed in each other in such a way that, the image view should be clear so that the boundary should be invisible. In pyramidal blending mixing of images are done with new appearance but without loss of original image appearance. The Figure 4.3 shows the blending model of an apple at a different Laplacian levels. laplacian level 4 laplacian level 2 laplacian level 0 left pyramid right pyramid blended pyramid Figure 4.3: Blending model of an apple V. THE LAPLACIAN PYRAMID USING GAUSSIAN The Gaussian pyramid is a set of low-pass filtered images. In order to obtain the band-pass images required for the multiresolution spline we subtract each level of the pyramid from the next lowest level. Because these arrays differ in sample density, it is necessary to interpolate new samples between those of a given array before it is subtracted from the next lowest array. Interpolation can be achieved by reversing the REDUCE process. We shall call this an EXPAND operation. Let G image obtained by expanding G l K times. Then, (1) 66

4 And for K>0, By EXPAND we mean, Here, only terms for which (2i + m)/2 and (2j + n)/2 are integers contribute to the sum. Note that G l,1 is the same size as G l-1, and that G l,1 is the same size as the original image[4]. We now define a sequence of band-pass images L 0, L 1. L N. For,0<1<N, (2) (3) (4 ) Because there is no higher level array to subtract from G N, We define L N = G N. Just as the value of each node in the Gaussian pyramid could have been obtained directly by convolving the weighting function W l with the image, each node of L l can be obtained directly by convolving W l - W l+1 with the image. This difference of Gaussian-like functions resembles the Laplacian operators commonly used in the image processing, so we refer to the sequence L0, L1,.. LN as the Laplacian pyramid [5]. VI. MASKING In psychophysics and the physiology of human vision, evidence has been gathered showing that the retinal image is decomposed into several partially oriented frequency channels. This explains why multiresolution decomposition methods are so popular in computer vision and image processing research and why Multiresolution Spline approach works well for image mosaic. Our work was also motivated by the above fact originally. Since the low-frequency content of a signal are often sufficient in many instances (such as the content of an image), and the detail information resembles the high frequency components (such as edge of an image), thus, the width of the transition zone T is chosen according to the wave length represented in each band. That is, for lower frequency components, the width of transition zone T is chosen to be larger than that of higher frequency components. This implies that low-frequency components "bleed" across the boundary of mosaic region further than high-frequency components do. using the same width of transition zone between detail component of resolution m and its down-sampled components in resolution m+l means the actual transition zone of the low-frequency components is larger than that of the high-frequency. To simplify and generalize arbitrary shape mosaic both for 1-D and 2-D signals, the transition zone T and the weighting function are not explicitly expressed, instead, another multiresolution structure of mask signal is introduced. The mask signal is a binary representation which describes how two signals will be combined. For example, two signals A and B will be combined to form a mosaic signal, and the mask signal S is a binary signal in which all points inside the mosaic region are set to 1 and those outside the mosaic region are set to 0. As the way to generate a sequence of lower resolution signal (not the detail signal) describe in the above section, the mask signal S is low-pass filter and subsampled to construct its multiresolution structure c Mn (S) c 1n (S) c 2n (S) and then each smoothed version of the mask signal will be used as the weighting function in its corresponding resolution level. Note that the low-pass filter used to construct multiresolution structure of the mask signal need not be the same as the DWT used, that is why here we use c Mn (S) instead of c Mn (S). VII. IMAGE BLENDING In case of blending, the images to be combined are overlapped so that no boundary should exist. It is possible by computing the gray level pixel value within a transition zone as a weighted average of the corresponding points in each image [3]. Suppose that one image Fl(i) is on the left and the other Fr(i) is on the right, and that the images are to be blended at a point (expressed in one dimension to simplify notation). Let Hl (i) be a weighting function which decreases monotonically from left to right and let Hr (i) = 1 Hl (i). Then, the blended image F is given by F(i) = Hl (i ȋ ) Fl(i) + Hr(i ȋ ) Fr(i) [3]. Figure 7.1: Typical Blending model Figure 6.1.The weighted average function W(x). Actually as described in the above section, the signal c m+l,n at resolution m+l is a smoothed down-sampled approximation of c m,n at resolution m, and d m+l,n is just the detail (or difference) information between c m,n and c m+1,n. Therefore, It is clear that with an appropriate choice of H, the weighted average technique will result in a transition which is smooth. However, this alone does not ensure that the location of the boundary will be invisible. Let T be the width of a transition zone over which Hl changes from 1 to 0. If T is small compared to image features, then the boundary may still 67

5 appear as a step in image gray level, albeit a somewhat blurred step. If, on the other hand, T is large compared to image features, features from both images may appear superimposed within the transition zone, as in a photographic double exposure. The size of the transition Zone, relative to the size of image features, plays a critical role in image blending. To eliminate a visible edge the transition width should be at least comparable in size to the largest prominent features in the image [4]. To minimize the image value variation, we impose a constraint that allows the pixel values of a blended image to be as close as possible to the corresponding pixel values of the to-be-combined images. To minimize the first derivative variation we impose the constraint that requires the first derivative of the mosaic images to consistently agree with that of the to-be-combined image. We formulate our energy functional at scale 2j as, In second step, create the mask to form a new image as shown in figure 8.2. This step is called as dynamic masking because we can do the masking according to region of interest. (5) In general, the left side of a mosaic image should be similar to the left to-be-combined image and the right side to the right To-be-combined image and is define as [1]. VIII. RESULTS AND DISCUSSION After performing image mosaicing on two input images we got the results as shown in following figure. 8.1, 8.2, 8.3. Here we can mosaic any input combinations of images by following three simple steps as mentioned. In first step, take two input images, subpanel 11 & subpanel 12 shows two different input images. After taking input images do the selective masking according to region of interest as shown in figure 8.1. Subpanel 13 shows selective masking region. Figure 8.2 Step2: Selective masking of an image In third step we got the final result as shown in figure 8.3. Here Subpanel 11 & Subpanel 12 shows two input images for mosaicing purpose. After execution, subpanel 14 shows direct insertion of images & subpanel 13 shows resultant mosaic image. Figure 8.3 Step3: Resultant mosaic images Figure 8.1 Step1: Insertion of input images & masking (selective) IX. CONCLUSION Subjective comparison has shown that the image quality achieved by the proposed technique is better than any other 68

6 method. In our work we have proposed three main tools for image mosaicing; those are Laplacian pyramid, Gaussian pyramid and Wavelet transform. Smooth transitions of images are occurred without losing original appearances of images. Special mosaic effects can be achieved by combining components with specific frequency. We can select different input images for image mosaicing along with multiple mashing. To simplify shape mosaic, we have used dynamic masking technique instead of using fixed binary mask. Here, there is no edging problem in feature mosaicing as well as in to-be combined image mosaicing. One of the major limitations of this method is that we cannot take more than two input images. It is expected in future that the technique of image mosaicing can be applied to video mosaicing as well as 3D image mosaicing. [14] A. K. Jain, Fundamental of Digital Image Processing. Prentice-Hall publication, Snehal J. Banarase received the B.E. degree in Electronics & Telecommunication in 2009 from Amravati University, Maharashtra, India. She is persuing her M.E. from M.G.M. s College of Engineering.,.under S.R.T.M. University Nanded, Maharashtra, India M. R. Banwaskar is persuing doctorate from M. G. M. s College of Engineering.,.under S. R.T.M. University Nanded, Maharashtra, India Presently she is a H.O.D. of Department of Electronics and Telecommunication at M.G.M.C.O.E., Nanded. ACKNOWLEDGMENT We wish to thank all the authors whose paper we have referred for our research. REFERENCES [1] P. J. Burt and E. H. Adelson, A Multiresolution Spine with application to Image Mosaics, ACM Transactions on graphics, vol. 2, pp , October [2] P. J. Burt and E. H. Adelson, The laplacian pyramid as a compact image code, IEEE Transactions on Communications, vol. 31, April [3] M. S. Su, W. L. Hwang, and K. Y. Cheng, Analysis of Image Mosaics, IEEE Transactions on Image Processing, vol. 13, July [4] Burt and Adelson, Laplacian pyramid, IEEE Transactions on Communications, vol. 31, April [5] C. T. Hsu and J. L. Wu, Multiresolution Mosaic, IEEE Transactions on Consumer Electronics, vol. 42, November [6] A. Rocha, R. Ferreira, and A. Campeche, Image mosaicing using corner detection, Tech. Rep , Institute de Engenharia Biomedica INEB2 Faculdade de Engenharia da Universidad do Portugal FEUP Praca Coronel Pacheco,, Porto PORTUGAL. [7] K. P. Rane and S. G. Bhirud, Image mosaicing with strip search algorithm based on a novel similarity measure, tech. rep., Godavari COE Jalgaon (India); VJTI, Mumbai (India). [8] J. Kim, F. Pellacini, Jigsaw Image Mosaics. Proc SIGGRAPH, San Antonio, TX, 2002, [9] R. Szeliski, Image mosaicing for tele-reality applications, tech. rep., Digital Equipment Corporation Cambridge Research Lab. [10] C. K. Chui, Wavelet analysis and its application, tech. rep. Texas A and M University, college station Texas. [11] G. Woods, Digital Image Processing. Prentice Hall publication, [12] N. Nakanza, Image registration and its application to computer Vision: Mosaicing and independent motion detection, Cape Town, June [13] X. Fang, Registration of blurred images for image mosaic, IEEE Transactions, pp , September