TÍTULO

1. Sets S3 Sets S2 Sets S1 Scanning sequence * SPIHT JPEG2000 SPHFB SPIHT JPEG2000 SPHFB a) b) c) a) b) c) Set is quadrisected into sets of type S2 Set of type S3 is significant Send the significance map [0 0 0 1] and update LSS and LIS. • 0.01 bpp, 17.63 dB • 0.39 bpp, 29.55 dB • 0.58 bpp, 31.42 dB • 0.01 bpp, 18.99 dB • 0.39 bpp, 28.93 dB • 0.58 bpp, 30.48 dB • 0.01 bpp, 14.48 dB • 0.39 bpp, 28.99 dB • 0.58 bpp, 31.37 dB • 0.014 bpp, 18.95 dB • 0.26 bpp, 22.74 dB • 0.60 bpp, 25.84 dB • 0.014 bpp, 19.17 dB • 0.26 bpp, 22.75 dB • 0.60 bpp, 24.82 dB • 0.014 bpp, 14.47 dB • 0.26 bpp, 22.61 dB • 0.60 bpp, 25.63 dB * * Significant sets are quadrisected into sets of type S1 ) ) dB dB PSNR ( PSNR ( Send the significance and sign bits [1 1 0 0 0] and update LSS and LIS. Bit Bit Rate Rate ( ( bpp bpp ) ) XV SEMANA DE INGENIERÍA III CONGRESO INTERNACIONAL DE INGENIERÍA Y TECNOLOGÍA21 – 25 DE SEPTIEMBRE 2009 CIUDAD JUÁREZ , CHIHUAHUA TÍTULO ALUMNO (1)a, ALUMNO(2)b, ALUMNO(3)c a Sistemas Digitales y Comunicaciones, Departamento de Ingeniería Eléctrica y Computación, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez, Chihuahua, México, Nombre del a materia bSistemas Computacionales, Departamento de Ingeniería Eléctrica y Computación,, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez, Chihuahua, México, Nombre del a materia cIngeniería Eléctrica, Departamento de Ingeniería Eléctrica y Computación,, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez, Chihuahua, México, Nombre del a materia xxxx@ieee.org, vvvv@edu.mx, grosiles@hotmail, jvega@alumnos.uacj.mx A novel algorithm for very low bit rate based on hierarchical partition of subbands in the wavelet domain is proposed. The algorithm uses the set partitioning technique to sort the transformed coefficients. The threshold of each subband is calculated and the subbands scanning sequence is determined by the magnitude of the thresholds which establish a hierarchical scanning not only for the set of coefficients with large magnitude, but also for the subbands. Results show that SPHFB provides good image quality for very low bit rates. Resúmen Introducción Metodología Thresholds calculation The transformed image X has a hierarchical pyramidal structure. The threshold of each subband is calculated. The subbands are partitioned into sets of type Sq (where q = I,2,… L+1) of mxn adjacent coefficients, according to the subband they belong to. The subbands scanning sequence is established by the magnitude of the thresholds (subbands with larger threshold are scanned first). • New techniques based on wavelet transforms have emerged in recent years. These techniques achieve a hierarchical subband decomposition [1-5]. • The resulting transformed coefficients are coded and transmitted using a progressive transmission scheme [2-5], which consists on sending first the coefficients with higher magnitude. • Encoders like EZW [4], SPIHT [2], and SPECK [5] make use of the progressive transmission. • Partial ordering is a result of comparing transformed coefficient’s magnitudes with a set of octave decreasing thresholds. • EZW arranges the coefficients by magnitude order. A lossless encoder is used after coefficient ordering to compress the ordering information. • SPIHT and SPECK maintain lists of significant coefficients so that they can be transmitted in decreasing bit plane order. • The bit stream is embedded [2], [5]. • The algorithm proposed is a method to decrease the number of zeros to signal the insignificance of a subband. The number of thresholds in the trans- formed image is: Number of bits per threshold (kn) Where: Input image X Flexible scanning sequence The frequency subbands are partitioned into sets according to their resolution and scanned hierarchicallyaccording to their threshold. T2 Image transformation Low frequencysubband High frequency subband The significance of a set inside a subband is veryfied by Significant sets are split into sets of ¼ the resolution. Hierarchical pyramidal structure after image transformation using two levels of DWT decomposition (L=2). Significant sets of type SL+1 are coded along with a sign bit. Resultados Baboon A set inside a subband is tested for significance against a threshold, if it is significant, its position is added to a list of significant sets (LSS) and a ‘1’ is sent to the decoder, otherwise its position is added to a list of insignificant sets (LIS) and a ‘0’ is sent to the decoder. Then, the set is quadrisected into four sets of one-fourth the resolution of the original set. If a subset is not significant its position is added to the LIS. If the subset is significant its position added to LSS. The significant subset is treated as a set of one quarter the resolution of the original set. The process is repeated recursively until the set being tested is of type SL+1. Barbara Refinement is performed on significant SL+1sets from previous passes Comparison of the coding method with SPIHT and JPEG 2000 for Baboon image. Comparison of the coding method with SPIHT and JPEG 2000 for Barbara image. SPIHT: MATLAB implementation of SPIHT (no entropy coding used) by Tian Jing. JPEG 2000: JasPer version 1.900.1 by Michael D. Adams. Conclusiones Threshold calculation avoids sending extra zeros at very low bit rates. The significance tests allow partitioning the sets into subsets to group high energy areas. Flexibility of scanning allows to recover very good image quality at very low bit rates. The code is completely embedded and the computational complexity is low. The algorithm is fast and can be implemented as in SPIHT, maintaining directional lists. [1] M. Antonini, M. Barlaud, P. Mathieu, and I Daubechies, “Image coding using wavelet transform,” IEEE Trans. Image Processing, vol. 1, pp. 205-220, Apr. 1992. [2] A. Said and W.A. Pearlman, “A new, fast and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circuits Syst. Video Technology, vol 6, pp. 243-250, June 1996. [3] J. Andrew, “A simple and efficient hierarchical image coder,” Proc. IEEE Intl. Conf. Image Proc. (ICIP), vol. 3, Oct. 1997, pp. 658-661. [4] J. M. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Processing, vol. 41, pp. 3445-3462, Dec. 1993. [5] W. A. Pearlman, A. Islam, N. Nagaraj, and A. Said “Efficient, Low-Complexity Image Coding With a Set-Partitioning Embedded Block Coder,” IEEE Trans. Circuits Syst. Video Technology, vol. 14, pp. 1219-1235, Nov. 2004.