This website uses cookies to ensure you have the best experience. Learn more

Wavelets And Edge Detection Essay

1794 words - 8 pages

Wavelets and Edge Detection CS698 Final Project

Submitted To: Professor Richard Mann Submitted By: Steve Hanov Course: CS698 Date: April 10, 2006

Wavelets have had a relatively short and troubled history. They seem to be forever confined to footnotes in textbooks on Fourier theory. It seems that there is little that can be done with wavelets that cannot be done with traditional Fourier analysis. Stephane Mallat was not the father of wavelet theory, but he is certainly an evangelist. His textbook on the subject, A Wavelet Tour of Signal Processing [1], contains proofs about the theory of wavelets, and a summation about what is known about them with applications to signal ...view middle of the document...

For most signals, this is not the case. Consider music, which is continuously varying in pitch. Fourier analysis done on the entire song tells you which frequencies exist, but not where they are. The short time Fourier transform (STFT) is often used when the frequencies of the signal vary greatly with time. [3] In the JPEG image encoding standard, for example, the image is first broken up into small windows with similar characteristics. The Fourier transform is not applied to the entire image, but only to these small blocks. The disadvantage of this technique can be seen at high compression ratios, when the outlines of the blocks are clearly visible artifacts. A second disadvantage is in resolution of analysis. When larger windows are used, lower frequencies can be detected, but their position in time is less certain. With a smaller window, the position can be determined with greater accuracy, but lower frequencies will not be detected. The wavelet transform helps solve this problem. Once applied to a function f(t), it provides a set of functions Wsf(t). Each function describes the strength of a wavelet scaled by factor s at time t. The wavelet extends for only a short period, so its effects are limited to the area immediately surrounding t. The wavelet transform will give information about the strengths of the frequencies of a signal at time t. In the first pages of his treatise [1], Mallat defines a wavelet as a function of zero average,

THEORY It is best to describe wavelets by showing how they differ from Fourier methods. A signal in the time domain is described by a function f(t), where t is usually a moment in time. When we apply the Fourier transform to the signal, we obtain a function F(ω) that takes as input a frequency, and outputs a complex number describing the strength of that frequency in the original signal. The real part is the strength of the cosine of that frequency, and the imaginary part is the strength of the sine. One way to obtain the Fourier transform of a signal is to repeatedly correlate the sine and cosine

ψ (t )dt = 0


which is dilated with scale parameter s, and translated by u:

ψ u , s (t ) =

Unlike the sine and cosine functions, wavelets move toward quickly zero as their limits approach to +/-∞. In [2], Mallat notes that the derivative of a smoothing function is a wavelet with good properties. Such a wavelet is shown in Figure 1.
1 0.9 0.8
0.2 0.4 0.3

0.7 0.6 0.5 0.4 0.3
-0.2 0.1 0 -0.1

0.2 0.1 0
-0.3 -0.4











Figure 1: A smoothing function, and its corresponding wavelet.

By correlating the signal with this function at all possible translations and scales, we obtain the continuous wavelet transform. The transformation also increases the dimension of the function by one. Since we have both a scaling and position parameter, a 1-D signal will have a 2D wavelet transform. As an...

Other Papers Like Wavelets and Edge Detection

News Video Indexing Essay

3366 words - 14 pages segmentation, key frame extraction, feature extraction, clustering, indexing and video retrieval-by similarity, probabilistic, transformational, refinement and relevance feedback. A new caption text extraction algorithm that takes full advantage of the temporal information in a video sequence is developed. Keywords—Shot Boundaries Detection, Inserted Caption Detection, Machine Learning, Face Annotation, Edge/Field Detection. I. INTRODUCTION E

Gravitional Waves Essay

3861 words - 16 pages gravitational waves and discusses the current condition of the experimental search for gravitational waves. It deals with the newest techniques that will enable their detection. The focus of the paper is on three experimental groups: LIGO, VIRGO, and LISA. From our research of these groups we believe that the detection of gravitational waves will occur within the next decade. 2 The Detection of Gravitational Waves, How Close Are We

Gravitational Waves

3861 words - 16 pages explanation of gravitational waves and discusses the current condition of the experimental search for gravitational waves. It deals with the newest techniques that will enable their detection. The focus of the paper is on three experimental groups: LIGO, VIRGO, and LISA. From our research of these groups we believe that the detection of gravitational waves will occur within the next decade. 2 The Detection of Gravitational Waves, How

Video Analytics Market by Type (Hardware, Video Analytics Software, and Services), Applications


Performance Enhancing

661 words - 3 pages and they want to look female". Dr Don Caitlin, man who has developed complex tests That have broken the codes to many substances, has brought down many pro athletes like Marion jones and sprinter Kelli white. Caitlin says he does not know how many female athletes may break the rules to gain an unfair competitve edge. But he points out they have an advantage in escaping detection if they chose to do so. Seeking an unfair avantage by taking

Flip-Flops and Related Devices

1566 words - 7 pages Flip-Flops and Related Devices Multiple Choice 1 . A "D" flip-flop utilizing a PGT clock is in the CLEAR state. Which of the following input actions will cause it to change states? [Hint] CLK = NGT, D = 0 CLK = PGT, D = 0 CLOCK NGT, D = 1 CLOCK PGT, D = 1 Both a and c 2 . Which statement BEST describes the operation of a negative-edge-triggered D flip-flop? [Hint] The logic level at the D input is

Flight History

823 words - 4 pages identifying the boundaries of both. This system is proven in day and night condition as well as poor weather and low visibility situations. There are several types of lighting used on an airport, the first type is runway edge lighting these lights are the industry standard located on either side of the runway and are elevated by a short metal pole to help clear the grass or snow the lights are spaced at intervals of 200 feet and out line the full

Business Fraud

933 words - 4 pages number of new leading-edge data security measures. “Epsilon's new security features, along with innovative technologies from Verizon, provide enhanced protection for its information technology (IT) infrastructure. Combining intelligence from Verizon's expansive global-IP network, their insight into Internet traffic, one of the largest databases of breach statistics and frontline experience against the world's most sophisticated hackers, the new


606 words - 3 pages contrast independent and thus can overcome this methodological problem. The gradients earlier were used as the means for different edge detection methods and also for the medical image segmentation [23–28]. In addition, Veenland et al. [20, 29-30] and Pulkkinen et al. have successfully utilized the features of morphological gradient method for the trabecular bone analysis [8, 31]. The trabecular features extracted from digital X-ray image in the evaluation of osteoporosis based analysis has not been well studied so far across the globe. Henceforth, it would serve as an efficient tool for osteoporosis diagnosis.

Htc One Dual Sim vs. Sony Xperia Z1 - Gsmarena

1045 words - 5 pages -Fi 802.11 a/b/g/n/ac, Wi-Fi Direct, DLNA, Wi-Fi hotspot Yes, v4.0 with A2DP Yes (Market dependent) Yes Yes, microUSB v2.0 (MHL) 4 MP, 2688 x 1520 pixels, autofocus, optical image stabilization, LED flash 1/3'' sensor size, 2µm pixel size, simultaneous HD video and image recording, geo-tagging, face and smile detection Yes, 1080p@30fps, 720p@60fps, HDR, stereo sound rec., video stabilization Yes, 2.1 MP, 1080p@30fps, HDR Android OS, v4.1.2 (Jelly

Week 7 Project Paper

3453 words - 14 pages while blocking fake emails. This program will significantly bring down the number of phishing attacks (Network World). Emerging Threats Pro is a great application being designed by Lafayette Industries. Emerging threats pro is a cutting edge intrusion detection system that utilizes open source engine Suricata and is a must have for any layered defense network. Lastly there is a company named Sterling that is located in Toronto and they are

Related Essays

Bio And Electrocardiogram Essay

3302 words - 14 pages DENOISING OF ECG SIGNALS USING WAVELETS AND CLASSIFICATION USING SVM Shivanesan S M. 1, Pradheep M. 1, Sharath K. 1, Aravind Prasad. 1, Manoj M. 1 Ganesan M. 2 Abstract- Electrocardiogram is the recording of the electrical potential of heart versus time. The analysis of ECG signal has great importance in the detection of cardiac abnormalities. In this paper we have dealt about the removal of noises in ECG signals and arrhythmia

Lab 4: Edge Detection In Images

2212 words - 9 pages , edge detection easily shows the outline of the bike, the bricks in the wall, and even the writing on the bike. | | Edge Detection Example: Original Image (left) and Edge Detected Image (right) | So how does edge detection work? The first step in understanding the process is to understand what an edge is in an image. If you were to look at the values of in an image along a single row or column, you would see something that looks like

Advertisement Detection 2 Essay

2191 words - 9 pages . 2008 "A combined corner and edge detector" Proceedings of the 4th Alvey Vision Conference: pp Hong Shan Neoh, Asher Hazanchuk, 2004 “Adaptive Edge Detection for Real-Time Video Processing using FPGAs”, International Signal Processing Conference (ISPC), SantaClara, California, September 27-30. Alberto Albiol Mar , María José , Ch. Fullà , Antonio Albiol, 2004 “Detection of TV Commercials” In Proceedings of the International Conference on Acoustics, Speech and Signal Processing,. C. J. Kaufman, Rocky Mountain Research Lab., Boulder, CO, private communication, May 1995.

How Facial Feature Extraction Works Essay

980 words - 4 pages proposed in the literatures for this purpose and can be mainly classified in four groups: geometric feature-based, template-based, color segmentation-based and appearance-based approaches. In geometric feature-based approaches, the features are extracted using anthropometric relation [7], [8] of the face components [9]. Valley detection filters [10] and analysis of horizontal and vertical edge projections are such examples [11]. Functions