. Sinusoid **Wavelet** **Types** **of** **Wavelets** There are many **different** **wavelets**, for example: Morlet Haar Daubechies Basis Functions **Using** **Wavelets** Like sin( ) and cos( ) functions in the Fourier Transform, **wavelets** can define a set **of** basis functions ψ k (t): Span **of** ψ k (t): vector space S containing all functions f(t) that can be represented by ψ k (t). Basis Construction – “Mother” **Wavelet** The basis can be constructed by applying translations and scalings (stretch/**compress**/

coding: –g = lpc2mat (huff2mat (c)); –compare (f, g) yields 0 **difference** 8.4 Psychovisual Redundancy Eliminating psychovisual redun- dancy always causes loss **of** original data! Do not do this for scientific or medical **images**. **Compression** **using** psychovisual redundancy removes information not essential for normal visual processing - i.e., for viewing. Psychovisual Redundancy (2) The **compression** method is referred to as quantization (combining grey levels to reduce/

any information regarding the temporal (time) localization **of** the components Fourier Transform :: Limitations Signals are **of** two **types** # Stationary # Non – Stationary Non stationary signals are/**of** **wavelets** There are a lots **of** **uses** **of** **wavelets** .... The most prominent application **of** **wavelets** are Computer and Human Vision FBI Finger Print **compression** **Image** **compression** Denoising Noisy data Detecting self-similar behavior in noisy data Musical Notes synthesis Animations Things that I didn’t Cover **Different**/

“multimedia elements” including still **image** & stream-video for a variety **of** **image** **types** Visual IR/FLIR SAR Each **image** shows **different** characteristics based on the sensor performance and **image** **type**. Don’t ask for new “spectrum allocation” in dense urban areas **Use** the current TDL’s (Link 16) allocated spectrum. **Use** current AJP capabilities provided by TDLs (Link 16) to avoid jammers /civilian interferences. “Still **Image**” **Compression** Requirements **Compression** Efficiency. Excellent performance at/

by looking at the sign **of** the **difference** between the pixel under inspection and the estimated original Modification **of** ExMI + EmMI on base Kutter algorithm for edge pixel set has to be developed Robustness **of** the **wavelet** decomposition As estimates the result **of** work Mohsen Ashourian, Peyman Moallem, Yo-Sung Ho “A Robust Method for Data Hiding in Color **Images**” can be **used** //PCM (2) 258-269, 2005/

**compression** New JPEG standard includes **wavelet** **compression** FBI’s fingerprints database saved as **wavelet**-**compressed** Signal denoising, interpolation, **image** zooming, texture analysis, time-scale feature extraction In our context, WT will be **used** primarily as a feature extraction tool Remember, WT is just a change **of** basis, in order to extract **useful** information which might otherwise not be easily seen WT in MATLAB MATLAB has an extensive **wavelet** toolbox **Type** help **wavelet**/

**Uses** **of** **Wavelets** **Image** / video **compression** (2D, 3D) –DWT(JPEG2000), fingerprint **image** **compression** (FBI) Data with transients, e.g. financial, seismic, ECG Pattern matching, e.g. for biometrics, match at **different** scale. Feature extraction, e.g. **use** /**using** the TI C6713 DSK The laboratory demonstrates audio noise reduction in real-time **using** the Texas Instruments C6713 DSK. You will speak into a microphone and hear how high frequency noise can be removed. You can experiment with **different** **types** **of** **wavelets**/

schemes **used** to watermark ? Two forms **of** frequency domain watermarking techniques in detail. Key Points (Contd.) What are the **different** **types** **of** attacks it is susceptible to ? One attack implementation ? What are the ways **of** counter-attacking a watermarking attack ? What are the **different** laws and principles governing watermarking ? What are its drawbacks ? What is its future perspectives ? Watermarking Embedding a digital signal (audio, video or **image**) with/

, S. Chen and J. Wang, “Overview **of** AVS video coding standards,” Signal processing: **image** communication, Vol. 24, Issue 4, pp. 247-262, April 2009. [6] L. Fan et al, “Overview **of** AVS video standard”, IEEE International conference on multimedia and expo (ICME), Vol. 1, pp. 423 - 426, June 2004. [7] T. Borer and T. Davies, “Dirac video **compression** **using** open technology,” BBC EBU technical review/

:0 subsampling. Two frame **types**: Intra-frames (I-frames) and Inter-frames (P-frames): I-frame provides an accessing point, it **uses** basically JPEG. P-frames **use** "pseudo-**differences**" from previous frame ("predicted"), so frames depend on each other. Subsampling H.261(Intra-frame Coding) Macroblocks are 16 x 16 pixel areas on Y plane **of** original **image**. A macroblock usually consists **of** 4 Y blocks, 1/

**use** the same **wavelet**. Instead a reconstruction **wavelet** and a decomposition **wavelet** are **used** that are slightly **different** These are the coefficients **of** the filters **used** for convolution Actual **wavelet** and scaling functions From mathworks.com Testing Methodology In order to find what was the best combination **of** **wavelet**, decomposition, and thresholding, an exhaustive search was done with Matlab A 1000x1000 grid **of** vorticity data from the navier stokes simulator was first **compressed**/

waves, called **wavelet**, which is composed **of** time varying and limited duration waves. We **use** 2-D discrete **wavelet** transform in **image** **compression**. 14 15 Predictive Coding Predictive coding means that we transmit only the **difference** between the current pixel and the previous pixel. The **difference** may be close/ 20. G. Seroussi and M. J. Weinberger, "On adaptive strategies for an extended family **of** Golomb-**type** codes," Proc. DCC’97, pp. 131-140, 1997. 21. C. J. Lian “JPEG2000 “, DSP/IC design lab, GIEE, ntu 65

is true for most **image** processing **wavelets** Results **of** Coarse Approximations (**using** Haar **wavelets**) Significance Map While transmitting, an additional amount **of** information must be sent to indicate the positions **of** these significant transform values Either 1 or 0 –Can be effectively **compressed** (e.g., run-length) Rule **of** thumb: –Must capture at least 99.99% **of** the energy to produce acceptable approximation Application: Denoising Signals **Types** **of** Noise Random noise –Highly/

discrete **wavelet** transform respectively. Dirac **uses** a more flexible and efficient form **of** entropy /**differences** **of** the distorted and reference **image**/frame pixels. Two distorted **images** with the same MSE may have very **different** **types** **of** errors, some **of** which are much more visible than others. Given a noise-free m x n monochrome **image** I and its noisy approximation K, MSE is defined as: Peak Signal-to-Noise Ratio (PSNR) [14]: The PSNR is most commonly **used** as a measure **of** quality **of** reconstruction **of** **compression**/

**of** Southern California August 9, 2015Data Mining: Concepts and Techniques64 DWT for **Image** **Compression** **Image** Low Pass High Pass **Wavelet** **Compression** Demo August 9, 2015Data Mining: Concepts and Techniques65 http://www.codeproject.com/Articles/20869/2D-Fast-**Wavelet**-Transform-Library-for-**Image**-Proces August 9, 2015Data Mining: Concepts and Techniques66 Given N data vectors from d-dimensions, find k ≤ d orthogonal vectors (principal components) that can be best **used**/

’05] [Wang & Simoncelli, ICASSP ’05] Extensions **of** SSIM (2) Complex **wavelet** SSIM Motivation: robust to translation, rotation and scaling : complex **wavelet** coefficients in **images** x and y [Wang & Simoncelli, ICASSP ’05] **Image** Matching without Registration Standard patterns: 10 **images** Database: 2430 **images** Correct Recognition Rate: MSE: 59.6%; SSIM: 46.9%; Complex **wavelet** SSIM: 97.7% [Wang & Simoncelli, ICASSP ’05] **Using** SSIM **Image**/video coding and communications Web site: www/

acquisition: November 20 –Findings: January 30 Timeframe Late, but stronger: –Evaluation **of** methodology –Evaluation **of** **compression** –Evaluation **of** source code Challenges Challenges Technical development longer than expected: –**Different** **types** **of** **images** –Complexity **of** database: Shuffle cases Shuffle **compression** levels Track answers –Multiplicity **of** reading environments **Different** monitors and video cards Challenges Data acquisition: –Creating a database **of** 2500 cases has required more time than expected, as/

odd. All even = 1 All odd = 0 An **image** can store 1 bit **of** information per 8x8 block. **Image** Techniques DCT example OriginalWatermarked **Image** Techniques **Wavelet** Transformation **Wavelets** are mathematical functions for **image** **compression** and digital signal processing. **Used** in the JPEG2000 standard. **Wavelets** are better for higher **compression** levels than the DCT method. Generally **wavelets** are more robust and are a good way **of** hiding data. Sound Techniques MP3 The data to/

digital media tends to be large Lots **of** bits needed to store samples! Lots **of** bits needed to store samples! **Compression** is a major issue **Compression** is a major issue **Types** **of** Graphics Computer graphics fall into two categories: Computer graphics fall into two categories: Vector Graphics Vector Graphics **Used** for computer generated **images**, line drawings, cartoons etc. **Used** for computer generated **images**, line drawings, cartoons etc. Bitmap (Raster) Graphics/

other nice properties **of** **compression** standards. Content agnostic Encryption does not depend on content **types** or the specific /processing overhead/delay Not sufficient security Plain text attack **using** known syntax Not very secure for trans-coding Little/**wavelet** transform Block rotation (+shuffling) # **of** configuration: (8*k)!/(8*n)! >>K!/n! Other attacks? Your exercises! 23 **Wavelet**-based System 24 **Wavelet**-based System PSNR Table 1: Impact **of** **different** scrambling techniques on **compression** efficiency. **Image**/

**Wavelet**-Based Coding 1.Introduction 2.Continuous **Wavelet** Transform* 3.Discrete **Wavelet** Transform* 7.**Wavelet** Packets 8.Embedded Zerotree **of** **Wavelet** Coefficients 1.The Zerotree Data Structure 2.Successive Approximation Quantization 3.EZW Example 9.Set Partitioning in Hierarchical Trees (SPIHT) 3.**Image** **Compression** Standard 1.The JPEG Standard 1.Main Steps in JPEG **Image** **Compression**/. Encode the **difference** from previous 8/**used**: Symbol_1: (skip, SIZE), Symbol_2: actual bits. Symbol_1 (skip, SIZE) is encoded **using**/

set **of** filters, filter is widely **used** in many fields **of** engineering and science for a long time. –**Wavelet**, an old and new tool to produce filter banks, have been thoroughly studied in past 20 years. Here we **use** **wavelets** to indicate many kinds **of** **wavelets** with **different** properties. –Application: **image** **compression**, pattern recognition, **image** processing/n) 2 2 v0v0 v1v1 2 2 u 0 (n) u 1 (n) F1F1 F0F0 v 0 (n) v 1 (n) Fp-**type** 2 2 2 z -1 X(n) z -1 2 2 Hp v 0 (n) v 1 (n) Polyphase matrix Perfect reconstruction –/

**of** Southern California September 23, 2015Data Mining: Concepts and Techniques61 DWT for **Image** **Compression** **Image** Low Pass High Pass **Wavelet** **Compression** Demo September 23, 2015Data Mining: Concepts and Techniques62 http://www.codeproject.com/Articles/20869/2D-Fast-**Wavelet**-Transform-Library-for-**Image**-Proces September 23, 2015Data Mining: Concepts and Techniques63 Given N data vectors from d-dimensions, find k ≤ d orthogonal vectors (principal components) that can be best **used**/

a shape S k, we find a 3 1D signals: We take the **wavelet** transform **of** each signal and represent the shape as: Original Shape Shape representation **using** a weighted combination **of** the lowest resolution scaling functions and **wavelet** functions up to j th resolution j=0j=1j=2j=3 45 [2] **Compression** **Compression**: from 2562 to 649 coefficients, mean error 5.10 -3 At each scale/

**types** **of** macros system providedsystem provided –compiler knows their period and delay user provided (written in e.g. Verilog )user provided (written in e.g. Verilog ) –user needs to provide period and delay HPEC 2004 Copyright © 2004 SRC Computers, Inc.ALL RIGHTS RESERVED. Two Case Studies **Wavelet** Versatility Benchmark –**Image** processing application (**wavelet** **compression**) –Part **of** DARPA/ITO ACS (Adaptive Computing Systems) benchmark suite –Versatile: Four phases **of** **different**/

by looking at the sign **of** the **difference** between the pixel under inspection and the estimated original Modification **of** ExMI + EmMI on base Kutter algorithm for edge pixel set has to be developed Robustness **of** the **wavelet** decomposition As estimates the result **of** work Mohsen Ashourian, Peyman Moallem, Yo-Sung Ho “A Robust Method for Data Hiding in Color **Images**” can be **used** //PCM (2) 258-269, 2005/

clearly shows the exact location in time **of** the discontinues. **Wavelet** coefficients clearly shows the exact location in time **of** the discontinues. **WAVELETS** ARE TWO **TYPES** : CWT(Continuous **wavelet** transformations ) CWT(Continuous **wavelet** transformations ) DWT(Discrete **wavelet** transformations ) DWT(Discrete **wavelet** transformations ) DWT : DWT gives the complete description **of** the **image** DWT gives the complete description **of** the **image** by **using** three level decomposition. by **using** three level decomposition. [A,H,V,D/

**image** **Image** after DFB with 4 levels Feb 200933hmhang/EECS, NTUT DFB-Based Coding One example **of** mixed 2D **wavelet** decomposition C.-H. Hung and H.-M. Hang, “**Image** Coding **Using** Short **Wavelet**- based Contourlet Transform,” IEEE ICIP, 2008 Feb 200934hmhang/EECS, NTUT Audio **Compression**/Three parameters describing how human locate sound source in the horizontal place Interaural Level **Difference** (ILD) Interaural Time **Difference** (ITD) Interaural Coherence (IC) Feb 200941hmhang/EECS, NTUT MPEG Surround Low-/

Act made certain **types** **of** “virtual porn” illegal Supreme court over-ruled in 2002 To prosecute, state needs to prove that child porn is not computer-generated **images** Real Photo CG Automatically Detecting CG Sketch **of** approach – Intuition: natural **images** have predictable statistics (e.g., power law for frequency); CG **images** may have **different** statistics due to difficulty in creating detail – Decompose the **image** into **wavelet** coefficients and compute/

a l o 0 0 0 0 0 01 1 1 11 1 Ziv-Lempel **Compression** Adaptive coding For repeat occurrences **of** text segments, pointer back to first occurrence Higher **compression** than Huffman coding Also **used** for **image** **compression** Ziv-Lempel **compression** Based on triples, where – a = how far back to segment – b = no **of** characters in segment – c = new character to end segment E.g. – first occurrence/

Redundant Signal Representation, and Its Role in **Image** Processing 32 The K–SVD Algorithm – General D Initialize D Sparse Coding **Use** MP or BP Dictionary Update Column-by/**image** The results **of** this algorithm compete favorably with the state-**of**-the-art (e.g., GSM+steerable **wavelets** [Portilla, Strela, Wainwright, & Simoncelli (‘03)] - giving ~0.5-1dB better results) Sparse and Redundant Signal Representation, and Its Role in **Image** Processing 49 Application 3: **Compression** The problem: **Compressing** photo-ID **images**/

-generation scanner described earlier is capable **of** producing high-quality **images**. However, since the x-ray beam must be translated across the sample for each projection, the method is intrinsically slow. Many refinements have been made over the years, the main function **of** which is to dramatically increase the speed **of** data acquisition. PH3-MI April 17, 2017 Scanner **using** **different** **types** **of** radiation (e.g., fan beam/

artefacts no longer a problem DWT State **of** the art **compression** methods Performance **of** **wavelet** based methods is impressive –This is in terms **of** the quality **of** the **compressed** **image** at high **compression** rates AND –The absence **of** blocking artefacts We can compare DCT and DWT based **compression** at 32:1 **compression** ratio DCT DWT State **of** the art **compression** methods Its much easier to see a **difference** if we ‘zoom in’ on a small/

K < N resulting in O(NK2 + K3) Thin-Plate Spline Example: ***Image** taken from the book Additional Multidimensional Splines In general, there are many possibilities for multi-dimensional splines; we can **use** any suitably large basis expansion **of** **different** basis **types** and **use** a suitable regularizer E.g. Tensor products **of** B-splines Additive splines are just one class that come from additive penalty (f are univariate/

to Digital **Image** Processing89 **Wavelet** vs. DCT JPEG (CR=64)JPEG2000 (CR=64) discrete cosine transform basedwavelet transform based EE465: Introduction to Digital **Image** Processing90 Lossy **Image** **Compression** Summary Quantization introduces irreversible information loss Lossy predictive coding: open-loop DPCM vs. closed-loop DPCM Lossy transform coding: energy compaction an preservation properties **of** unitary transforms Objective measure for **image** distortion MSE or PSNR are widely **used** for their/

**different** levels **of** resolution Allow natural clusters to become more distinguishable **Used** for **image** **compression** 9/5/201528 **Wavelet** Transformation Discrete **wavelet** transform (DWT) for linear signal processing, multi-resolution analysis **Compressed** approximation: store only a small fraction **of** the strongest **of** the **wavelet**/Where j is the smallest integer such that Max(|ν’|) < 1 9/5/201553 Discretization Three **types** **of** attributes Nominal—values from an unordered set, e.g., color, profession Ordinal—values from an/

**wavelet** coefficients Similar to discrete Fourier transform (DFT), but better lossy **compression**, localized in space Method: Length, L, must be an integer power **of** 2 (padding with 0’s, when necessary) Each transform has 2 functions: smoothing, **difference** Applies to pairs **of** data, resulting in two set **of** data **of** length L/2 Applies two functions recursively, until reaches the desired length Haar2 Daubechie4 111 DWT for **Image** **Compression** **Image**/

**wavelet** coefficients Similar to discrete Fourier transform (DFT), but better lossy **compression**, localized in space Method: Length, L, must be an integer power **of** 2 (padding with 0’s, when necessary) Each transform has 2 functions: smoothing, **difference** Applies to pairs **of** data, resulting in two set **of** data **of** length L/2 Applies two functions recursively, until reaches the desired length Haar2 Daubechie4 111 DWT for **Image** **Compression** **Image**/

cost tradeoff MPEG - full-motion video **compression** The video data consist **of** a sequence **of** **image** frames. In the MPEG **compression** scheme, three frame **types** are defined; - intraframes I - predicted frames P -forward, backward, or bi-directionally predicted or interpolated frames B MPEG - full-motion video **compression** Each frame **type** is coded **using** a **different** algorithm and Figure below shows how the frame **types** may be positioned in the sequence. MPEG/

various fields **of** Corporate Sector where data mining is **used**: Finance /**different** vector X’ **of** **Wavelet** coefficients. The two vector **of** same length. A **compressed** approximation **of** the data can be retained by storing only a small fraction **of** the strongest **of** the **wavelet** coefficients. Similar to discrete Fourier transform (DFT), but better lossy **compression**, localized in space Haar2 Daubechie4 Implementing 2D-DWT 134 Decomposition ROW i COLUMN j 2-D DWT ON MATLAB Load **Image** (must be.mat file) Choose **wavelet** **type**/

Introduction Features Flow chart Discrete **wavelet** transform EBCOT ROI coding Comparison **of** ROI coding algorithms Conclusion Reference Introduction The Joint Photographic Experts Group Intended to create a new **image** coding system for **different** **types** **of** still **images**. Compliment and not to replace the current JPEG standards Features Superior low bit-rate performance Below 0.25bpp for highly detailed gray- scale **images** Lossless and lossy **compression** Progressive transmission by pixel/

Stephen Aylward, Kitware Algorithms: spatio-temporal **compression** **of** a stream **of** **image** frames for efficient communication and display **of** real-time interventional **images** in Slicer3 for IGT applications. Software: gain understanding **of** Slicer3 architecture, develop demo module for real-time **imaging**, drive MRML **image** node from incoming **image** stream, source **image** streams via opentracker protocol, codec transforms to implement **compression** algorithms. Clinical: extend for **use** in Neurosugery demo module [Liu, Hata/

at wavenumber 900.3cm -1 for the selected granules **Compression** ratios **of** **different** algorithms for the 10 selected AIRS granules Bias-Adjusted Reordering (BAR)* Scheme for Data Preprocessing Hyperspectral sounder data features strong correlations in disjoint spectral regions affected by the same **type** **of** absorbing gases at various altitudes. The Bias-Adjusted Reordering (BAR) scheme is **used** for exploring the correlation among remote disjoint channels. The/

split mStore two **types** **of** dependencies among vertices mDependencies **of** **type** 1: a vertex depends on the vertex that has been split to create it 139 SSD99 Tutorial...Data structures... mDependencies **of** **type** 2 (defined **differently** in the various models): G[Hoppe, 1997] G[Xia et al., 1997, Gueziec et al., 1998] Dependencies **of** **type** 1 and **of** **type** 2 DAG **of** vertex dependencies 140 SSD99 Tutorial...Data structures... o **Compressed** hierarchies for/

**of** the **wavelet** transform for a 2-D **image** lowpass for x lowpass for y lowpass for x highpass for y highpass for x lowpass for y highpass for x highpass for y 36 -- JPEG 2000 (**image** **compression**) -- filter design -- edge and corner detection -- pattern recognition -- biomedical engineering Applications for **Wavelets** 37 5. **Image** **Compression** Conventional JPEG method: Separate the original **image** into many 8*8 blocks, then **using**/ 2008 年畢業的的林于哲同學 64 There are four **types** **of** nucleotide in a DNA sequence: adenine (A/

**different** levels **of** resolution Allow natural clusters to become more distinguishable **Used** for **image** **compression** 27 **Wavelet** Transformation Discrete **wavelet** transform (DWT) for linear signal processing, multi-resolution analysis **Compressed** approximation: store only a small fraction **of** the strongest **of** the **wavelet** coefficients Similar to discrete Fourier transform (DFT), but better lossy **compression**/ such that Max(|ν’|) < 1 52 Discretization Three **types** **of** attributes Nominal—values from an unordered set, e.g/

**Wavelet** Transform New Research field **Useful** for JPEG 2000 (**image** **compression**), filter design, edge and corner detection 只將頻譜分為「低頻」和「高頻」兩個部分 ( 對 2-D 的影像，則分為四個部分 ) x[n]x[n] h[n]h[n] 2 x 1,L [n] x 1,H [n] 2 g[n]g[n] 「低頻」部分 「高頻」部分 36 The result **of** the **wavelet** transform for a 2-D **image**/ Fourier Transform multiplied by a chirp 44 Depth recovery: 如何由照片由影像的模糊程度，來判斷物體的距離 註：感謝 2008 年畢業的的林于哲同學 45 There are four **types** **of** nucleotide in a DNA sequence: adenine (A), guanine (G), thymine (T), cytosine (C) Unitary/

that can be implemented to serve various embedding processes by **using** the same embedding technology. 2. Evaluation **of** **Wavelet** filters. Choice **of** **wavelet** filters is critical issue that affect the quality **of** the watermarked **image** and the robustness to **compression** attacks. Experimental results **Image** Processing Operation JPEG lossy **compression** Conclusion with the characteristics **of** successive approximation, as a higher-resolution **images** are obtained, the higher resolution watermark will be extracted Limitations/

**different** levels **of** resolution Allow natural clusters to become more distinguishable **Used** for **image** **compression** 30 **Wavelet** Transformation Discrete **wavelet** transform (DWT) for linear signal processing, multi-resolution analysis **Compressed** approximation: store only a small fraction **of** the strongest **of** the **wavelet** coefficients Similar to discrete Fourier transform (DFT), but better lossy **compression**/ such that Max(|ν’|) < 1 56 Discretization Three **types** **of** attributes Nominal—values from an unordered set, e.g/

**different** levels **of** resolution Allow natural clusters to become more distinguishable **Used** for **image** **compression** 27 **Wavelet** Transformation Discrete **wavelet** transform (DWT) for linear signal processing, multi-resolution analysis **Compressed** approximation: store only a small fraction **of** the strongest **of** the **wavelet** coefficients Similar to discrete Fourier transform (DFT), but better lossy **compression**/ such that Max(|ν’|) < 1 52 Discretization Three **types** **of** attributes Nominal—values from an unordered set, e.g/

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