Fast 2D to 3D Conversion Using Wavelet Analysis

Fast 2D to 3D Conversion Using Wavelet Analysis

CHAPTER 1

INTRODUCTIONThere are several technologies regarding the conversion of 2-D contents for 3-D TV systems, for example, Philips WOWVX system. In the system, a 3-D data representation which includes the traditional 2-D images and their associated per-pixel depth maps is adopted. The depth maps associated with X-Y information can be used to describe the spatial location of each point in the images. These data are processed by customized DSP and optical devices to emit rays into our eyes as stereoscopic images.The key problem rest in the above system is how to obtain the depth information from the 2D data. Recently a new technology called Depth Image-Based Rendering (OlBR) has been applied to the advanced 3-D TV system. One method to obtain a relative depth map from a single image using wavelet analysis and edge defocus estimation based on Lipschitz exponents was proposed in. Images were handled as series of 1-0 row signals, with the resulting horizontal stripes in the depth map.

The depth map is further optimized and smoothed based on color segmentation to obtain much more accurate and reliable results. In this paper, a more simple approach is proposed to obtain the depth map of an image. In our approach, each image is first transformed to the grayscale imaging color .Afterwards; the high-frequency area of an image can be obtained from analyzing the high-frequency wavelet sub bands of the image. Finally, binarization and smoothing techniques are applied to find the position of the focused objects on the image.CHAPTER 2

LITERATURE SURVEYTe-Wei Chiang

Department of Accounting Information Systems

Chihlee Institute of Technology

Banciao City,Taiwan, R.O.C.

ctw@mail.chihlee.edu.tw2.1 ABSTRACTThis paper proposes a depth estimation method which converts two-dimensional images of limited depth of field (DOF) into three-dimensional data. The goal is to separate the focused foreground objects from the blurred background objects in an image. Our approach is based on two observations: (1) the focused objects on an image of limited DOF correspond to the objects with high frequency; (2) the high-frequency area of an image appears high energy on its high-frequency waveletsubbands. In our approach, each image is first transformed to the grayscale, and then Y component of the image is further transformed to the wavelet domain. Afterwards, the high frequency area of an image can be obtained from analyzing the high-frequency wavelet sub bands of the image. Finally, binarization and smoothing techniques are applied to find the position of the focused objects on the image. The experimental Result demonstrates the effectiveness of our approach. There are several technologies regarding the conversion of 2-D contents for 3-D TV systems, for example, Philips WOWVX system.

In the system, a 3-D data representation which includes the traditional 2-D images and their associated per-pixel depth maps is adopted. The depth maps associated with X-Y information can be used to describe the spatial location of each point in the images. These data are processed by customized DSP and optical devices to emit rays into our eyes as stereoscopic images.1. Mathematics Discipline,

Khulna University, Khulna-9208, Bangladesh

2. Department of Mathematics,

Comilla University, Comilla-3500, Bangladesh

Email: saif_math_ku@yahoo.com2.2 ABSTRACTWavelet analysis is an exciting new method for solving difficult problems in mathematics, physics, and engineering, with modern applications as diverse as wave propagation, data compression, signal processing, image processing, pattern recognition, computer graphics, the detection of aircraft and submarines and other medical image technology. Wavelets allow complex information such as music, speech, images and patterns to be decomposed into elementary forms at different positions and scales and subsequently reconstructed with high precision. Signal transmission is based on transmission of a series of numbers. The series representation of a function is important in all types of signal transmission. The wavelet representation of a function is a new technique. Wavelet transform of a function is the improved version of Fourier transform. 2.3. INTRODUCTIONIn 1982 Jean Morlet a French geophysicist, introduced the concept of a `wavelet'. The wavelet means small wave and the study of wavelet transform is a new tool for seismic signal analysis. Immediately, Alex Grossmann theoretical physicists studied inverse formula for the wavelet transform. The joint collaboration of Morlet and Grossmann yielded a detailed mathematical study of the continuous Wavelet transforms and their various applications, of course without the realization that similar results had already been obtained in 1950's by Calderon, Littlewood, Paley and Franklin. However, the rediscovery of the old concepts provided a new method for decomposing a function or a signal. Wavelet analysis is originally introduced in order to improve seismic signal analysis by switching from shortime Fourier analysis to new better algorithms to detect and analyze abrupt changes in signals Daubechies [2,3], Mallat [6]. Intime-frequency analysis of a signal, the classical Fourier transform analysis is inadequate because Fourier transform of a signal does not contain any local information. This is the major drawback of the Fourier transform. To overcome this drawback, Dennis Gabor in 1946, first introduced the windowed-Fourier transform, i.e. short-time Fourier transform known later as Gabor transform. Meyer [7] found the existing literature of wavelets. Later many eminent mathematicians e.g. I. Daubechies, A. Grossmann, S. Mallat, Y. Meyer, R. A. deVore, Coifman, V. Wickerhauser made a remarkable contribution to the wavelet theory. The modern applications of wavelet theory diverse mainly as wave propagation, data compression, signal processing, image processing, pattern recognition, computer graphics, the detection of aircraft and submarines, improvement of CAT scans and some other medical image technology etc. In this study, our main goal is to find out the advantages of wavelet transform compared to Fourier transform.CHAPTER 3IMAGE CLASSIFICATION AND DIGITIZATIONIn general images can be defined as any two dimensional function f(x, y) where x, y are spatial coordinates, and amplitude of f at any pair of coordinates(x,y) is called intensity or gray level of the image at that point.3.1 DIGITAL IMAGE

When x, y and the amplitude values of f are all finite, discrete quantities, we call the image a digital image.

Fig 3.1 A Digital Image

3.1.1 PIXEL:A pixel is a single point in a graphic image. Graphics monitors display pictures by dividing the display screen into thousands (or millions) of pixels, arranged in rows and columns. The pixels are so close together that they appear connected. The number of bits used to represent each pixel determines how many colors or shades of gray can be displayed. For example, in 8-bit color mode, the color monitor uses 8 bits for each pixel, making it possible to display 2 to the 8th power (256) different colors or shades of gray.

3.2 IMAGE TYPES

The different types of images are 1. Binary Images2. Indexed Images3. Intensity Images4. Multi-frame Images5. RGB Images.3.2.1 BINARY IMAGE:An image contains only black and white pixels. In MATLAB, a binary image is represented by a uint8 or double logical matrix containing 0's and 1's (which usually represent black and white, respectively). A matrix is logical when its "logical flag" is turned "on." We often use the variable name BW to represent a binary image in memory. Fig 3.2 (a) Binary Image (b) Intensity image (c) RGB image3.2.2 INDEXED IMAGE:An image pixel values are direct indices into an RGB color map. In MATLAB, an indexed image is represented by an array of class uint8, uint16, or double. The color map is always an m-by-3 array of class double. We often use the variable name X to represent an indexed image in memory, and map to represent the color map.3.2.3 INTENSITY IMAGE:An image consists of intensity (grayscale) values. In MATLAB, intensity images are represented by an array of class uint8, uint16, or double. While intensity images are not stored with color maps, MATLAB uses a system color map to display them. We often use the variable name I to represent an intensity image in memory. This term is synonymous with the term "grayscale."

3.2.4 MULTI-FRAME IMAGE:

An image file contains more than one image, or frame. When in MATLAB memory, a multiframe image is a 4-Darray where the fourth dimension specifies the frame number. This term is synonymous with the term "multipage image."3.2.5 RGB IMAGE:In an image each pixel is specified by three values -- one each for the red, blue, and green components of the pixel's color. In MATLAB, an RGB image is represented by an m-by-n-by-3 array of class uint8, uint16, or double. We often use the variable name RGB to represent an RGB image in memory.

3.3 IMAGE DIGITIZATION

An image captured by a sensor is expressed as a continuous function f(x, y) of two coordinates in the plane. Image digitization means that the function f(x, y) is sampled into a matrix with m rows and n columns. The image quantization assigns to each continuous sample an integer value. The continuous range of image functions f(x, y) is split into k intervals. The finer the sampling (i.e. the larger m and n) and quantization (larger k) the better the approximation of the continuous image f(x, y).3.4 SAMPLING AND QUANTIZATION

To be suitable for computer processing an image function must be digitized both spatially and in amplitude. Digitization of spatial coordinates is called image sampling and amplitude digitization is called gray level quantization.

CHAPTER 4

IMAGE PROCESSING

The field of digital image processing refers to processing of digital image by means of a digital computer. A digital image is an image f(x, y) that has been discretized both in spatial coordinates and brightness. A digital image can be considered as a matrix whose row and column indices identifies a point in the image and corresponding matrix element value identifies the gray level at that point. The elements of such a digital array are called image elements, picture elements, pixels or pels. The last two being commonly used abbreviations of pictures elements.

The term digital processing generally refers to a two dimensional picture by a digital computer. In a broader context it implies digital processing of any two dimensional data.

In the form in which they usually occur, images are not directly amenable to computer analysis. Since computers work with numerical rather than pictorial data, an image must be converted to numerical form before processing. This conversion process is called digitization. The image is divided into small regions called picture elements or pixels . At each pixel location the image brightness is sample and quantized. This step generates an integer at each pixel representing the brightness or darkness of the image at that point.When this has been done for all pixels the image is represented by rectangular array of integers. Each location has allocation or address, and an integer value called gray level. This array digital data is now candidate for computer processing.

4.1 APPLICATIONS OF DIGITAL IMAGE PROCESSING

1. Office automation: optical character recognition; document processing cursive script recognition; logo and icon recognition; etc.

2. Industrial automation: automation inspection system; non destructive testing; automatic assembling; process related to VLSI manufacturing; PCB checking; etc.

3. Robotics: Oil and natural gas exploration; etc4. Bio-medical: ECG, EEG, EMG analysis; cytological, histological and stereological applications; automated radiology and pathology; x-ray image analysis; etc5. Remote sensing: natural resources survey and management; estimation related to agriculture, hydrology forestry, mineralogy; urban planning; environment control and pollution control; etc6. Criminology: finger print identification; human face registration and matching; forensic investigation; etc.7. Astronomy and space applications: restoration of images suffering from geometric and photometric distortions; etc.8. Information technology: facsimiles image transmission, video text; Video conferencing and video phones; etc.9. Entertainment and consumer electronics: HDVT; multimedia and video editing.10. Military applications: missile guidance and detection; target identification; navigation of pilot less vehicle; reconnaissance; and range finding; etc.11. Printing and graphics art: color fidelity in desktop publishing; art conservation and dissemination; etc.

CHAPTER 5

WAVELET ANALYSIS

A wavelet is a waveform of effectively limited duration that has an average value of zero. Compare wavelets with sine waves, which are the basis of Fourier analysis. Sinusoids do not have limited duration they extend from minus to plus infinity. And where sinusoids are smooth and predictable, wavelets tend to be irregular and asymmetric.

Fourier analysis consists of breaking up a signal into sine waves of various frequencies. Similarly, wavelet analysis is the breaking up of a signal into shifted and scaled versions of the original (or mother) wavelet.

Just looking at pictures of wavelets and sine waves, you can see intuitively that signals with sharp changes might be better analyzed with an irregular wavelet than with a smooth sinusoid, just as some foods are better handled with a fork than a spoon. It also makes sense that local features can be described better with wavelets that have local extent.

5.1. WHAT CAN WAVELET ANALYSIS DO?One major advantage afforded by wavelets is the ability to perform local analysis that is to analyze a localized area of a larger signal.

Consider a sinusoidal signal with a small discontinuity one so tiny as to be barely visible. Such a signal easily could be generated in the real world, perhaps by a power fluctuation or a noisy switch.

Wavelet analysis is capable of revealing aspects of data that other signal analysis techniques miss aspects like trends, breakdown points, discontinuities in higher derivatives, and self-similarity. Furthermore, because it affords a different view of data than those presented by traditional techniques, wavelet analysis can often compress or de-noise a signal without appreciable degradation.

Indeed, in their brief history within the signal processing field, wavelets have already proven themselves to be an indispensable addition to the analyst's collection of tools and continue to enjoy a burgeoning popularity today.

5.2. CONTINUOUS WAVELET TRANSFORMLike the Fourier transform, the continuous wavelet transform (CWT) uses inner products to measure the similarity between a signal and an analyzing function. In the Fourier transform, the analyzing functions are complex exponentials. The resulting transform is a function of a single variable, . In the short-time Fourier transform, the analyzing functions are windowed complex exponentials and the result in a function of two variables. The STFT coefficients represent the match between the signal and a sinusoid with angular frequency in an interval of a specified length centered at .In the CWT, the analyzing function is a wavelet, . The CWT compares the signal to shifted and compressed or stretched versions of a wavelet. Stretching or compressing a function is collectively referred to as dilation or scaling and corresponds to the physical notion of scale. By comparing the signal to the wavelet at various scales and positions, you obtain a function of two variables. The two-dimensional representation of a one-dimensional signal is redundant. If the wavelet is complex-valued, the CWT is a complex-valued function of scale and position. If the signal is real-valued, the CWT is a real-valued function of scale and position. For a scale parameter, a>0, and position, b, the CWT is:

Where * denotes the complex conjugate. Not only do the values of scale and position affect the CWT coefficients, the choice of wavelet also affects the values of the coefficients.

By continuously varying the values of the scale parameter, a, and the position parameter, b, you obtain the cwt coefficients C (a, b). Note that for convenience, the dependence of the CWT coefficients on the function and analyzing wavelet has been suppressed.

Multiplying each coefficient by the appropriately scaled and shifted wavelet yields the constituent wavelets of the original signal.

There are many different admissible wavelets that can be used in the CWT. While it may seem confusing that there are so many choices for the analyzing wavelet, it is actually strength of wavelet analysis. Depending on what signal features you are trying to detect, you are free to select a wavelet that facilitates your detection of that feature. For example, if you are trying to detect abrupt discontinuities in your signal, you may choose one wavelet. On the other hand, if you are interesting in finding oscillations with smooth onsets and offsets, you are free to choose a wavelet that more closely matches that behavior.5.3. DISCRETE WAVELET TRANSFORM

If we choose scales and positions based on powers of two so-called dyadic scales and positions then our analysis will be much more efficient and just as accurate. We obtain such an analysis from the discrete wavelet transform (DWT).

An efficient way to implement this scheme using filters was developed in 1988 by Mallat. The Mallat algorithm is in fact a classical scheme known in the signal processing community as a two-channel subband coder. This very practical filtering algorithm yields a fast wavelet transform which is a box into which a signal passes, and out of which wavelet coefficients quickly emerge.5.3.1. ONE-STAGE FILTERING: APPROXIMATIONS AND DETAILSFor many signals, the low-frequency content is the most important part. It is what gives the signal its identity. The high-frequency content, on the other hand, imparts flavor or nuance. Consider the human voice. If you remove the high-frequency components, the voice sounds different, but you can still tell what's being said. However, if you remove enough of the low-frequency components, you hear gibberish.

In wavelet analysis, the approximations are the high-scale, low-frequency components of the signal and the details are the low-scale, high-frequency components. The filtering process at its most basic level looks as shown in figure below:

The original signal S passes through two complementary filters and emerges as 2 signals.5.3.2. MULTIPLE-LEVEL DECOMPOSITIONThe decomposition process can be iterated, with successive approximations being decomposed in turn, so that one signal is broken down into many lower resolution components. This is called the wavelet decomposition tree.

5.3.3. NUMBER OF LEVELSSince the analysis process is iterative, in theory it can be continued indefinitely. In reality, the decomposition can proceed only until the individual details consist of a single sample or pixel.

5.3.4. WAVELET RECONSTRUCTION

We have seen how the discrete wavelet transform can be used to analyze or decompose signals and images. This process is called decomposition or analysis. The other half of the story is how those components can be assembled back into the original signal without loss of information. This process is called reconstruction or synthesis. The mathematical manipulation that effects synthesis is called the inverse discrete wavelet transforms (IDWT).

To synthesize a signal using Wavelet Toolbox software, we reconstruct it from the wavelet coefficients.

The downsampling of the signal components performed during the decomposition phase introduces a distortion called aliasing. It turns out that by carefully choosing filters for the decomposition and reconstruction phases that are closely related (but not identical); we can "cancel out" the effects of aliasing.

The low- and high-pass decomposition filters (L and H), together with their associated reconstruction filters (L' and H'), form a system of what is called quadrature mirror filters:

The reconstructed details and approximations are true constituents of the original signal. In fact, we find when we combine them that

A1 + D1 = S

5.3.5. MULTISTEP DECOMPOSITION AND RECONSTRUCTION

A multistep analysis-synthesis process can be represented as shown in figure below:

This process involves two aspects: breaking up a signal to obtain the wavelet coefficients, and reassembling the signal from the coefficients.CHAPTER 6

BACKGROUND AND RELATED WORK

6.1. YUV COLOR SPACEThere are some existing color models to describe images, known as color spaces, such as ROB, HSV, HIS, YUV, etc. ROB is perhaps the simplest color space for people to understand because it corresponds to the three colors that the human eyes can detect. However, the ROB color model is unsuitable for similarity comparison. The luminance and saturation information are implicitly contained in the R, G, and B values. The YUV (brightness, blue chrominance, and red chrominance) model defines a color space in terms of one luminance and two chrominance components, which are created from an original ROB (red, green and blue) source. The weighted values of R, G and B are added together to produce a single Y signal, representing the overall brightness, or luminance, of that spot. The U signal is then created by subtracting the Y from the blue signal of the original ROB, and then scaling; and V by subtracting the Y from the red, and then scaling by a different factor. There are many slightly different formulas to convert between YUV and ROB. The only major difference is a few decimal places. The equations used to convert from RGB to YUV spaces can be found inY(x, y) =O.299R(x, y) +O. 587G(x, y) +O.114B(x, y),U(x, y) = 0.492(B(x, y)-Y(x, y)),V(x, y) = O.877(R(x, y)-Y(x, y)).6.2 WAVELET ANALYSISThe multi resolution wavelet transform has been shown to be an effective technique and achieved very good performance for texture analysis. An image can be decomposed into its wavelet coefficients by using Mallat's pyramid algorithm. After wavelet decomposition, the object image energy is distributed in different sub bands, each of which keeps a specific frequency component. In other words, each sub band image contains one directional feature. The wavelet decomposition is illustrated in Fig. 6.1. Given an image (see Fig. 6.1 (a)), four sub images (see Fig. 6.2(b)), i.e. DC-component (upper left), H-component (upper right), V-component (lower left), and D-component (lower right), of the image can be obtained after the wavelet decomposition. Here H, V and 0 are used to indicate horizontal, vertical and diagonal, respectively. From Fig. 6.1 (b), it can be found that horizontal edges, vertical edges and diagonal edges of the image can be obtained from the wavelet decomposition of the image.

Fig 6.1(a) A test image and (b) its wavelet decomposed image (or sub images)

Fig 6.2 Illustration of the proposed wavelet-based edge detection method:

(a) The horizontal component,(b) The vertical component,(c) The diagonal component, and(d) The combined result of the image given in Fig 6.1.6.3 RELATED WORKFor images of limited depth of field (DOF), the main foreground objects are focused with sharp edges and the objects in the background are blurred. In other words, the high frequencies are retained in the focused foreground, but greatly attenuated in the background. This suggests that the spatial frequency is directly related with the degree of blurring, and thus the relative distance of the object from the camera. The high frequencies can be described by the coefficients of the wavelet transform of the image. If there is larger energy in the wavelet bands of high frequency, it suggests that there are more details and less blurring in this region, where the 3-D location is nearer. The elementary relative depth can be estimated based on the values of wavelet coefficients in the high frequency bands. Based on this, divide the images into macro blocks of size are 16-pixel by 16-pixel. A macro block wavelet transforms which generated 256 wavelet coefficients was performed. Relative depth was estimated by counting the number of non-zero wavelet coefficients. A method to obtain a relative depth map from a single image using wavelet analysis and edge defocus estimation based on Lipschitz exponents was proposed in. Images were handled as series of 1-0 row signals, with the resulting horizontal stripes in the depth map.To overcome this issue, an incremental algorithm based on wavelet transform and edge focus analysis in two-dimensions was proposed in, taking into account the direction of edges and the two-dimensional characteristics of images. The depth map is further optimized and smoothed based on color segmentation to obtain much more accurate and reliable results.CHAPTER 7

METHODOLOGY

The proposed depth map estimation algorithm is introduced in this section, which can be summarized as the following steps.

Fig 7: Steps Involved in Depth map Estimation

7.1 Y COMPONENT EXTRACTIONSSince the focused object on an image is the object with high-frequency (or fine texture), the simplest way to distinguish the focused object from others is to analyze the texture of the image. Moreover, the Y component of an image represents the overall brightness (or luminance) of the image; the texture of the Y component of the image is similar to that of the original color image. Therefore, in our approach, each image is first transformed from the standard RGB color space to the YUV space; then Y component of the image is further transformed to the wavelet domain.7.2 WAVELET-BASED EDGE DETECTIONAs discussed before the depth of limited-DOF images can be measured by their frequencies. In this step, we analyze the frequency energy based on the wavelet transforms. Basically, the edges of the focused object appear high frequency energy. Each pixel of the wavelet sub-band image corresponds to a wavelet coefficient. The larger the value of a wavelet coefficient, larger is the energy within the corresponding pixel. The values of the coefficients in the high frequency wavelet sub-bands (the H-component, V-component, and D-component) show how much the details are not blurred, and therefore give a relative depth value. The range of depth is adjusted from 0 to 255 (0 denotes black and 255 denotes white in the depth map). Larger depth value indicates nearer in distance.

Since the wavelet analysis can extract the directional edges of an image easily, we can obtain the overall edges of the image by merging its directional edges. Given the test image shown in Fig. 6.1(a), three sub-images with different directional edges, i.e. H-component (see Fig. 6.2(a)), V-component (see Fig. 6.2(b)) and D-component (see Fig. 6.3(c)), of the image can be obtained after the wavelet decomposition. By merging the three sub-images, we can obtain the overall edges of the original image, which results in our initial depth map, as shown in Fig. 6.2(d).

Fig 7.1 (a) Input Image (b) its Y component (c) edges detected by wavelet-based approach7.3 EDGE ENHANCEMENT BY BINARIZATIONImage binarization converts an image of up to 256 gray levels to a black and white image. Frequently, binarization is used as a pre-processor before optical character recognition (OCR). The simplest way to use image binarization is to choose a threshold value, and classify all pixels with values above this threshold as white, and all other pixels as black.

In our study, each pixel of the wavelet sub-band image corresponds to a wavelet coefficient. The larger the value of the corresponding wavelet coefficient, larger is the energy within the pixel. After the previous steps, the edges of the focused object appear high-frequency energy and the values of the corresponding wavelet coefficients range from 0 to 255. For the purpose of enhancing the important edges, we re-assign the value of a wavelet coefficient to 255 if its original is larger than a particular threshold; and re-assign it to 0, otherwise. Therefore, the pixels with high-frequency energy over the threshold will be enhanced.

Fig 7.2 the initial depth map after binarization using varying threshold value: (a) T=10, (b) T=15 and (c) T=20.7.4 NOISE DEFOCUSING BY SMOOTHINGSmoothing algorithms are often applied in order to reduce noise and/or to prepare images for further processing such as segmentation. They can be broadly categorized into linear and non- linear algorithms where the former are amenable to analysis in the Fourier domain and the latter are not. For the implementation of the linear algorithm, the filter can be based on a rectangular support or a circular support.

In order to remove the noises on the initial depth map, smoothing techniques are used to defocus them. Here noise refers to a high-energy pixel whose neighboring pixels consist of low energy. In our study, a uniform rectangular filter is adopted for smoothing where the output image is based on a local averaging of the input filter and all of the values within the filter support have the same weight. To do so, for each pixel of the depth map, its value is re-assigned to the average of the values of the GxG pixels whose center is the pixel. Note that the noises on the depth map can be further removed by the subsequent binarization step.

Fig 7.3 the depth map after smoothing: (a) G=l, (b) G=2 and (c) G=3.7.5 NOISE REMOVING BY BINARIZATIONAfter applying smoothing techniques on the depth map, the energy of the noisy pixels can be reduced significantly. Therefore, the noises can be removed by the binarization method, i.e. setting a threshold and remove those below the threshold. The problem is how to select the correct threshold. In many cases, finding one threshold compatible to the entire image is very difficult, and in many cases even impossible. In our study, an optimal threshold will be examined through a series of experiments for the illustrative image.

Fig 7.4 the depth map after smoothing and binarization: (a) G=1, T=0 (best), (b) G=2, T=20 (best) and (c) G=3, T=50 (best)CHAPTER 8 ADVANTAGES AND DISADAVNTAGES8.1 ADVANTAGES OF DWT OVER DCT

1. No need to divide the input coding into non-overlapping 2-D blocks, it has higher compression ratios avoid blocking artifacts.2. Allows good localization both in time and spatial frequency domain.3. Transformation of the whole image( introduces inherent scaling.4. Better identification of which data is relevant to human perception( higher compression ratio5. Higher flexibility: Wavelet function can be freely chosen6. No need to divide the input coding into non-overlapping 2-D blocks, it has higher compression ratios avoid blocking artifacts.7. Transformation of the whole image( introduces inherent scaling8. Better identification of which data is relevant to human perception( higher compression ratio (64:1 vs. 500:1)

8.2 DISADVANTAGES OF DWT1. The cost of computing DWT as compared to DCT may be higher. 2. The use of larger DWT basis functions or wavelet filters produces blurring and ringing noise near edge regions in images or video frames3. Longer compression time4. Lower quality than JPEG at low compression rates8.3 FUTURE ENHANCEMENT OF WAVELET ANALYSIS1. The combined use ofwavelet transformsand Singular value decomposition (SVD) gives the promising applications in finger print reading, mine detection.etc.2. The application of wavelet transform to determine the type of fault and its automation incorporating PNN could achieve an accuracy of 100% for all type of faults. Back propagation algorithm could not distinguish all ofphase-ground and double-line to ground faults.3. The application of wavelets as a possible vehicle for investigating the issue of market efficiency in futures markets for oil.4. The application of wavelet theory in modeling and analyzing economic data (and phenomena) is still in its infancy and many properties of these models are not explored yet in economic and finance literature.8.4 APPLICATIONS OF WAVELET ANALYSIS

Wavelets are a powerful statistical tool which can be used for a wide range of applications, namely Signal processing Data compression Smoothing and image denoising Fingerprint verification Biology for cell membrane recognition, to distinguish the normal from the pathological membranes DNA analysis, protein analysis Blood-pressure, heart-rate and ECG analyses Finance (which is more surprising), for detecting the properties of quick variation of values In Internet traffic description, for designing the services size Industrial supervision of gear-wheel Speech recognition Computer graphics and multifractal analysis Many areas of physics have seen this paradigm shift, including molecular dynamics, astrophysics, optics, turbulence and quantum mechanics.

CHAPTER 9EXPERIMENTAL RESULT

In this preliminary experiment, a focused red flower with obscure background is used as the illustrative example (see Fig. 7.1(a)). Fig. 7.1(b) shows the Y component of the image. Since Y component is the luminance of the image, it looks like a gray level image. Then the edges of the flower can be detected using wavelet analysis, as shown in Fig. 7.1(c). The sensitivity of varying the values of threshold for binarization is next investigated. Fig. 7.2 shows the initial depth map using varying threshold value, T, for binarization. It can be found that the best result occurs when T=15 (see Fig. 7.2(b)). Although the focused flower is separated from the background, some noises appear in the contour of the flower. In what follows, we examine the impact of smoothing to the depth map. Fig. 7.3 gives the depth map after smoothing. It can be found that the noise in the depth map is defocused. Fig. 7.4(a) gives the depth map after smoothing and binarization, using G=1 and varying threshold value T=0. Fig. 7.4(b) gives the depth map after smoothing and binarization, using G=2 and varying threshold value T=20. Fig. 7.4(c) gives the depth map after smoothing and binarization, using G=3 and varying threshold value T=50. Fig.8.1 summarizes the best one out of each depth map, which results from one value of 0 (in our case, G = 1, 2, or 3) and different values of threshold T. It is observed that Fig. 8.1(c) gives the best performance. In other words, the optimal parameter combination is G=3 and T=50, in an attempt to achieve the depth map for Fig. 3(a).Fig 8.1 the resulting depth map: (a) G=1 and T=O, (b) G=2 and T=20, and (c) G=3 and T=50(best).CONCLUSIONThis paper proposes a depth estimation method which converts two-dimensional images of limited depth of field (DOF) into three-dimensional data. The experimental result shows that we can get simple depth maps easily through the wavelet analysis, binarization and smoothing techniques. However, our approach has difficulty in face of the DOF images with smoothed focused object. In such a situation, high-frequency energy only lies in the edge of the focused object. To overcome this drawback, our future work is to incorporate the color features. In addition, user-assisted workflow associated with visual cues might be used to solve the problems.REFERENCE

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First binarization for edge enhancement

(a)

Smoothing for edge defocusing

3d Depth map

Wavelet-based edge detection

Y component extraction

2d Input Image

Second binarization for noise Removing

(b)

(C)

(C)

(b)

(a)

(C)

(b)

(a)

(C)

(b)

(a)

(C)

(b)

(a)

Dept of DECS, VTU-RC, Mysore 27