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• ID : Q2877

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1. The discrete cosine transform (DCT) represents an image as a sum of sinusoids of varying magnitudes and frequencies.
2. The dct2 function computes the two-dimensional discrete cosine transform (DCT) of an image.
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.
4. For this reason, the DCT is often used in image compression applications.
5. In JPEG decompression, the Inverse Discrete Cosine Transform (IDCT) is applied to the 8×8 DCT coefficient blocks.
6. I know that the DCT can be > performed by a DFT with a post-rotation.
7. But what are the advantages of > the DCT compared to the DFT?
8. Intuitively, the DCT of a finite section of an infinite signal has less discontinuity at the boundaries compared to the DFT, I think.
9. The idea is applied to the DCT-II matrix to derive invertible integer DCT-II.
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.
11. The fast algorithm being already implemented for the DCT-II can be directly applied.
12. Now consider the discrete trigonometric transforms where DCT/DST matrices are obviously orthogonal.
13. Since all present applications involve only even DCT and DST, this chapter considers only four types of even DCT and DST.
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.
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.
16. This chapter discusses the fast rotation-based DCT/DST algorithms.
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.
18. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression.
19. In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers.
20. The most common variant of discrete cosine transform is the type-II DCT, which is often called simply "the DCT".
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.
22. The values as simply calculated from the DCT formula.
23. The 64 (8 x 8) DCT basis functions are illustrated in Fig 7.9.
24. Columns apply 1D DCT (Horizontally) to resultant Vertical DCT above.
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.
26. Many encoders perform a DCT on an eight-by-eight block of image data as the first step in the image compression process.
27. The DCT converts the video data from the time domain into the frequency domain.
28. The DCT takes each block, which is a 64-point discrete signal, and breaks it into 64 basis signals.
29. Models of DCT basis function visibility can be used to design quantization matrices for arbitrary viewing conditions and images.
30. We measured contrast detection thresholds for DCT basis functions at viewing distances yielding 16, 32, and 64 pixels/degree.
31. We find considerable masking between nearby DCT frequencies.
32. The topic of this post is the Discrete Cosine Transformation, abbreviated pretty universally as DCT .
33. The JPEG (Joint Photographic Experts Group) format uses DCT to compress images (we’ll describe how later).
34. By using a DCT transform, the image is shifted into the frequency domain.
35. This is an artifact of how the DCT compression is calculated.
36. The discrete cosine transform (DCT) is used in many areas, the most prominent one probably being lossy compresion of audio and images.
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).
38. type {1, 2, 3, 4}, optional Type of the DCT (see Notes).
39. axis int, optional Axis along which the dct is computed; the default is over the last axis (i.e., axis=-1 ).
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.
41. There are, theoretically, 8 types of the DCT, only the first 4 types are implemented in SciPy.
42. They compute the dct , or its inverse, by treating the matrix as one argument.
43. An extensive bibliography covers both the theory and applications of the DCT.
44. Tables describing ASIC VLSI chips for implementing DCT, and motion estimation and details on image compression boards are also provided.
45. An in-place algorithm for the fast, direct computation of the forward and inverse discrete cosine transform is presented and evaluated.
46. Compute the discrete cosine transform of x .
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.
48. For more information on DCT and the algorithms used here, see Wikipedia and the paper by J. Makhoul.
49. idct ( X ) # scaled DCT-III done through the last dimension assert ( torch .
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.
51. In practice, the DCT is normally implemented using the same basic efficiency techniques as in FFT algorithms.
52. The transformation the Joint Photographic Experts Group chose for the task was the Discrete Cosine Transformation (DCT).
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.
54. We can gain some insight as to how the DCT works if we have a closer look at the images above.
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.
56. In this paper an efficient two-dimensional discrete cosine transform (DCT) operator is proposed for multimedia applications.
57. It is based on the DCT operator proposed in Kovac and Ranganathan, 1995.
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.
59. Discrete cosine transform (DCT) is the most widely used operation in video/image compression.