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* ID :  [https://www.wikidata.org/wiki/Q2877 Q2877]

2020년 12월 26일 (토) 05:01 판

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  1. The discrete cosine transform (DCT) represents an image as a sum of sinusoids of varying magnitudes and frequencies.[1]
  2. The dct2 function computes the two-dimensional discrete cosine transform (DCT) of an image.[1]
  3. The DCT has the property that, for a typical image, most of the visually significant information about the image is concentrated in just a few coefficients of the DCT.[1]
  4. For this reason, the DCT is often used in image compression applications.[1]
  5. In JPEG decompression, the Inverse Discrete Cosine Transform (IDCT) is applied to the 8×8 DCT coefficient blocks.[2]
  6. I know that the DCT can be > performed by a DFT with a post-rotation.[3]
  7. But what are the advantages of > the DCT compared to the DFT?[3]
  8. Intuitively, the DCT of a finite section of an infinite signal has less discontinuity at the boundaries compared to the DFT, I think.[3]
  9. The idea is applied to the DCT-II matrix to derive invertible integer DCT-II.[4]
  10. N C N II x , , where α N is a relatively small constant depending on the value of N. Finally, each DCT-II coefficient is rounded to the nearest integer.[4]
  11. The fast algorithm being already implemented for the DCT-II can be directly applied.[4]
  12. Now consider the discrete trigonometric transforms where DCT/DST matrices are obviously orthogonal.[4]
  13. Since all present applications involve only even DCT and DST, this chapter considers only four types of even DCT and DST.[5]
  14. The crucial aspect for the applicability of DCT and DST is the existence of fast algorithms that allow their efficient computation compared to the direct matrix–vector multiplication.[5]
  15. Over three decades many fast algorithms for the efficient computation of one-/two-dimensional (1-D/2-D) DCT and DST have been developed.[5]
  16. This chapter discusses the fast rotation-based DCT/DST algorithms.[5]
  17. A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies.[6]
  18. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression.[6]
  19. In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers.[6]
  20. The most common variant of discrete cosine transform is the type-II DCT, which is often called simply "the DCT".[6]
  21. It is computationally easier to implement and more efficient to regard the DCT as a set of basis functions which given a known input array size (8 x 8) can be precomputed and stored.[7]
  22. The values as simply calculated from the DCT formula.[7]
  23. The 64 (8 x 8) DCT basis functions are illustrated in Fig 7.9.[7]
  24. Columns apply 1D DCT (Horizontally) to resultant Vertical DCT above.[7]
  25. a) Used in JPEG and the MPEG, H.261, and H.263 video compression algorithms, DCT techniques allow images to be represented in the frequency rather then time domain.[8]
  26. Many encoders perform a DCT on an eight-by-eight block of image data as the first step in the image compression process.[8]
  27. The DCT converts the video data from the time domain into the frequency domain.[8]
  28. The DCT takes each block, which is a 64-point discrete signal, and breaks it into 64 basis signals.[8]
  29. Models of DCT basis function visibility can be used to design quantization matrices for arbitrary viewing conditions and images.[9]
  30. We measured contrast detection thresholds for DCT basis functions at viewing distances yielding 16, 32, and 64 pixels/degree.[9]
  31. We find considerable masking between nearby DCT frequencies.[9]
  32. The topic of this post is the Discrete Cosine Transformation, abbreviated pretty universally as DCT .[10]
  33. The JPEG (Joint Photographic Experts Group) format uses DCT to compress images (we’ll describe how later).[10]
  34. By using a DCT transform, the image is shifted into the frequency domain.[10]
  35. This is an artifact of how the DCT compression is calculated.[10]
  36. The discrete cosine transform (DCT) is used in many areas, the most prominent one probably being lossy compresion of audio and images.[11]
  37. That's also the reason why most libraries that implemenent the DCT will likely compute coefficients which are different from the ones shown here (for didactical reasons).[11]
  38. type {1, 2, 3, 4}, optional Type of the DCT (see Notes).[12]
  39. axis int, optional Axis along which the dct is computed; the default is over the last axis (i.e., axis=-1 ).[12]
  40. None , there is no scaling on dct and the idct is scaled by 1/N where N is the “logical” size of the DCT.[12]
  41. There are, theoretically, 8 types of the DCT, only the first 4 types are implemented in SciPy.[12]
  42. They compute the dct , or its inverse, by treating the matrix as one argument.[13]
  43. An extensive bibliography covers both the theory and applications of the DCT.[14]
  44. Tables describing ASIC VLSI chips for implementing DCT, and motion estimation and details on image compression boards are also provided.[14]
  45. An in-place algorithm for the fast, direct computation of the forward and inverse discrete cosine transform is presented and evaluated.[15]
  46. Compute the discrete cosine transform of x .[16]
  47. This library implements DCT in terms of the built-in FFT operations in pytorch so that back propagation works through it, on both CPU and GPU.[17]
  48. For more information on DCT and the algorithms used here, see Wikipedia and the paper by J. Makhoul.[17]
  49. idct ( X ) # scaled DCT-III done through the last dimension assert ( torch .[17]
  50. In image coding (such as MPEG and JPEG), and many audio coding algorithms (MPEG), the discrete cosine transform (DCT) is used because of its nearly optimal asymptotic theoretical coding gain.[18]
  51. In practice, the DCT is normally implemented using the same basic efficiency techniques as in FFT algorithms.[18]
  52. The transformation the Joint Photographic Experts Group chose for the task was the Discrete Cosine Transformation (DCT).[19]
  53. Recall that the preprocessing portion of algorithm partitions the image into 8 x 8 blocks, so the DCT is an 8 x 8 matrix.[19]
  54. We can gain some insight as to how the DCT works if we have a closer look at the images above.[19]
  55. Putting this all together, we see that in general, the DCT tends to store information about all 64 input values in a few values and "shoves" them to the upper left-hand corner of the output.[19]
  56. In this paper an efficient two-dimensional discrete cosine transform (DCT) operator is proposed for multimedia applications.[20]
  57. It is based on the DCT operator proposed in Kovac and Ranganathan, 1995.[20]
  58. Rather than using classical subword sizes (8, 16, and 32 bits), multimedia oriented subword sizes (8, 10, 12, and 16 bits) are used in the proposed DCT operator.[20]
  59. Discrete cosine transform (DCT) is the most widely used operation in video/image compression.[20]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Discrete Cosine Transform
  2. ↑ Discrete Cosine Transform (DCT)
  3. ↑ 3.0 3.1 3.2 DCT vs. DFT
  4. ↑ 4.0 4.1 4.2 4.3 Discrete Cosine Transform - an overview
  5. ↑ 5.0 5.1 5.2 5.3 Discrete Cosine Transform - an overview
  6. ↑ 6.0 6.1 6.2 6.3 Discrete cosine transform
  7. ↑ 7.0 7.1 7.2 7.3 The Discrete Cosine Transform (DCT)
  8. ↑ 8.0 8.1 8.2 8.3 What is the discrete cosine transform (DCT) in MPEG?
  9. ↑ 9.0 9.1 9.2 Discrete cosine transform (DCT) basis function visibility: effects of viewing distance and contrast masking
  10. ↑ 10.0 10.1 10.2 10.3 Discrete Cosine Transformations
  11. ↑ 11.0 11.1 Discrete Cosine Transform
  12. ↑ 12.0 12.1 12.2 12.3 scipy.fft.dct — SciPy v1.5.4 Reference Guide
  13. ↑ Discrete Cosine Transform
  14. ↑ 14.0 14.1 Discrete Cosine Transform
  15. ↑ Algorithm 749: fast discrete cosine transform
  16. ↑ Function Reference: dct
  17. ↑ 17.0 17.1 17.2 zh217/torch-dct: DCT (discrete cosine transform) functions for pytorch
  18. ↑ 18.0 18.1 The Discrete Cosine Transform (DCT)
  19. ↑ 19.0 19.1 19.2 19.3 Why Do Math?
  20. ↑ 20.0 20.1 20.2 20.3 High Performance Discrete Cosine Transform Operator Using Multimedia Oriented Subword Parallelism

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