|Publication number||USRE42186 E1|
|Application number||US 12/764,555|
|Publication date||Mar 1, 2011|
|Filing date||Apr 21, 2010|
|Priority date||Jun 23, 2003|
|Also published as||US7460729, US20040258320|
|Publication number||12764555, 764555, US RE42186 E1, US RE42186E1, US-E1-RE42186, USRE42186 E1, USRE42186E1|
|Original Assignee||Canon Kabushiki Kaisha|
|Export Citation||BiBTeX, EndNote, RefMan|
|Patent Citations (25), Non-Patent Citations (2), Referenced by (2), Classifications (19), Legal Events (2)|
|External Links: USPTO, USPTO Assignment, Espacenet|
This application is a reissue of U.S. Pat. No. 7,460,729, which issued from application Ser. No. 10/870,974 filed Jun. 21, 2004.
The present invention relates to a data transform processing apparatus and its method for performing a lossless 4-point orthogonal transform processing capable of, for example reversible transform to output integer data.
Images and particularly multivalue images include a very large amount of information. Upon storage or transmission of such image, the large data amount causes a problem. For this reason, upon storage or transmission of image, employed is high efficiency coding to reduce the amount of image data by eliminating redundancy of image or allowing the degradation of image to a degree that degradation of image quality is not visually recognizable. For example, in the JPEG method recommended by the ISO and the ITU-T as an international standardized still picture coding method, image data is compressed by performing discrete cosine transform (DCT) by block (8 pixels×8 pixels) to obtain DCT coefficients, then quantizing the respective DCT coefficients, and entropy encoding the quantized results. Other compression techniques such as H261 and MPEG 1/2/4 methods also utilize the DCT transform.
In the JPEG method, a lossless coding mode was standardized such that a compressed/decompressed image completely corresponds with its original image, however, at that time, a lossless transform technique was not fully studied and lossless transform using DCT was not realized. Accordingly, the lossless coding was realized by predictive coding in several pixel units using a technique different from a DCT-used block transform coding.
Thereafter, a standard coding technique specialized for lossless coding (JPEG-LS) was standardized, and in the further-standardized JPEG 2000, both lossless transform and general compression with degradation (lossy transform) are realized.
In recent years, a DCT lossless transform has been studied to try to realize JPEG lossless compression based on the currently popularized DCT transform. The DCT used in the JPEG compression is an 8 point DCT transform. As shown in
As shown in
In this method, input/output data are interchanged so as to obtain “1” as determinant values of 2-point transform matrix, then the 2-point transform becomes a rotational transform. It is well known in the field of geometry that a 2-point transform can be realized with three two-dimensional shear transforms. In a 2×2 transform matrix in the two-dimensional shear transform, two diagonal components are “1”, and one of two off-diagonal components is “0”, and the other one is a parameter corresponding to an angle of inclination.
In a signal flow of the shear transform, one shear transform is replaced with a single-step ladder operation including multiplication processing and addition processing. Accordingly, the 2-point rotational transform is realized with three-step ladder operation as shown in FIG. 3. In
Then, rounding processing is performed so as to round the results of multiplication by one step of ladder operation, thereby rounding errors occur unless the results of multiplication are integers, and the rounding errors are included in output data.
Conventionally, the 4-point orthogonal lossless transform including four 2-point rotational transforms is arranged as shown in FIG. 4.
On the other hand, in the above document 1, the lossless transform is realized by dividing a 4-point orthogonal transform into five four-dimensional shear transforms. As a single n-dimensional shear transform corresponds (n−1) ladder operations, in the 4-point orthogonal transform, (4−1)×5=15 ladder operations are required. The number equals the number of multiplication processings. However, by virtue of shear transform, the number of rounding processings can be greatly reduced. In a multidimensional shear transform, as the ends of ladder operations (data as the subjects of addition) are concentrated to one data, these data are added up then rounding processing is performed. Thus the number of rounding processings can become one. In the 4-point orthogonal transform in the above document 1, five rounding processings are performed totally.
In use of results of non-lossless transform, for example results of linear transform, in the above lossless transformed data, the rounding errors increase in proportion to the number of rounding processings and the accuracy of transform is degraded.
Upon decoding of coded data generated by entropy coding after lossless transform, there is no problem if an inverse lossless transform corresponding to the lossless transform is necessarily performed. However, in a case where data JPEG-encoded by using a lossless DCT transform is decoded with a general JPEG decoder, the difference of lossless DCT accuracy appears as a difference of decoded image signal, which influences the image quality. This means that the lossless transform should desirably be close to linear transform as much as possible.
Further, in a case where the same type of transform is used in lossless coding and lossy coding, a lossless transform is required. In consideration of coding efficiency upon lossy coding, the lossless transform should desirably be close to a linear transform as much as possible.
In the conventional lossless 4-point orthogonal transform processing, the number of multiplication processings is 12 or 15. If the number of multiplications is smaller, the number of rounding processings is 12, while if the number of rounding processings is 5, the number of multiplications is 15. To increase the transform accuracy so as to reduce the errors in linear 4-point orthogonal transform, it is necessary to select a method with a smaller number of rounding processings. However, as the number of operations increases, the processing speed is lowered, or the hardware scale increases.
Further, if a high priority is placed on the processing speed and hardware scale, the number of rounding processings is 12, and the transform accuracy is seriously low. In this manner, it has been difficult to improve both the transform accuracy and the processing speed (hardware scale).
The present invention has been made in consideration of the above conventional art, and provides a data transform processing apparatus and its method capable of performing lossless orthogonal transform processing with a small amount of operation or with a small circuit scale.
Further, the present invention provides a data transform processing apparatus and its method for performing lossless orthogonal transform processing with high transform accuracy.
The data transform apparatus according to one aspect of the present invention is a data transform processing apparatus comprising: two first transform means for performing two step ladder operation processings respectively of receiving unweighted normalized data and outputting weighted nonnormalized rotational-transformed data; and two second transform means for performing two step ladder operation processings respectively of receiving the weighted nonnormalized rotational-transformed data from the two first transform means, performing inverse weighting and outputting unweighted normalized lossless rotational-transformed data, wherein the respective two data outputted from the two first transform means are inputted into the two second transform means respectively, and a lossless 4-point orthogonal transform is performed.
Further, the data transform method according to one aspect of the present invention is a data transform processing method comprising: first and second transform steps of performing two step ladder operation processings respectively of receiving unweighted normalized data and outputting weighted nonnormalized rotational-transformed data; and third and fourth transform steps of performing two step ladder operation processings respectively of receiving the weighted nonnormalized rotational-transformed data from the first and second transform steps, performing inverse weighting and outputting unweighted normalized lossless rotational-transformed data, wherein the respective two data outputted in the first and second transform steps are inputted in the third and fourth transform step respectively, and a lossless 4-point orthogonal transform is performed.
Other features and advantages of the present invention will be apparent from the following description taken in conjunction with the accompanying drawings, in which like reference characters designate the same name or similar parts throughout the figures thereof.
The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.
Preferred embodiments of the present invention will now be described in detail in accordance with the accompanying drawings.
As described above, the above document 1 shows a structure to realize a lossless 2-point transform as shown in FIG. 3.
In a case where the rotational angle is (−2θ), in the multiplication processor 311 in the first step ladder operation portion, one data (X1) is multiplied by (−TAN(θ)), then rounding processing is performed by the rounding processor 313 to obtain an integer value from data below decimal point, and the result of the rounding is added to the other data (X0) by the addition processor 315.
Further, similar processing is performed in the second step and third step ladder operation portions on the assumption that a multiplication coefficient in the second step ladder operation portion is SIN(2θ) and that in the third step ladder operation portion is (−TAN (θ)). Note that other documents and the like merely show such three-step ladder operation as examples of 2-point lossless transform.
Assuming that the rotational angle of the transform processing is (−2θ), rotation by (−θ) is performed by the preceding two steps of ladder operation 501, rotation by (−θ) is performed by the subsequent two steps of ladder operation 502, thus rotation by (−2θ) as a whole is performed. In this case, the rotational angle in the preceding two steps of ladder operation 501 and that in the subsequent two steps of ladder operation 502 are the same, however, transformed data is not normalized in the rotational transform by the preceding two steps of ladder operation 501, and the two transformed data are weighted with a scaling coefficient (COS(θ)) depending on the rotational angle (−θ). The scaling coefficient is 1/COS(θ) in the upper output from the ladder operation 501, and is COS(θ) in the lower output. In the subsequent two steps of ladder operation 502, the weighted nonnormalized data are subjected to rotation processing and inverse weighting, and finally normalized rotation-transformed data are generated.
Conventionally, nothing has been obtained in the analysis of the content of rotation processing in FIG. 4. Further, as the multiplication and rounding processings increase, such structure with wastefulness has been worthless. However, the present inventor has found a new analysis and a new lossless 4-point transform structure based on the new analysis. The structure has elements in
Modifications as shown in FIG. 5B and
Next, a supplementary explanation will be made about the above modifications.
There are two methods to inverse the rotational direction of rotation processing. One method is to inverse the signs of multiplication coefficients in ladder operations, and the other method is to inverse the directions of the ladder operations. In
Generally, in respective reports and the like, processings such as DCT and orthogonal transform are not expressed in the form of flowchart but in the form of signal flow as in the case of
Next, 4-point orthogonal transform method and apparatus using a combination of the basic structures in the above-described first embodiment will be described as a second embodiment of the present invention. The basic form of the second embodiment is as shown in FIG. 7. In
The four input data (X0 to X3) are lossless transformed by lossless transforms 501 and 503 and weighted intermediate data are generated. The intermediate data are weighted with 1/COS(θ), COS(θ), COS(θ) and 1/COS(θ). Then the second and third data with the same weight are interchanged and inputted into the next lossless transforms 502 and 504, thereby the weights are removed, and at the same time, lossless rotational transforms are realized.
Note that the results of transform processing in a case where rounding processings are ignored, for example, linear transforms are performed, are as follows.
Y3=(a2X0+aX1+aX2+X3)/(1+a2) [Expression 1]
Assuming that the multiplication coefficients for the input data are vectors, all the four vectors corresponding to the four transform expressions are orthogonal to each other (the inner product is “0”). Further, as the absolute vector value is “1”, a 4-point normal orthogonal transform is realized.
In the conventional 4-point normal orthogonal transform using four rotation processings, even if the four rotation processings have the same rotational angle, the respective rotation processings are replaced with three-step ladder operations, so that the transform is realized by total 12 ladder operations. However, in the present embodiment, the transform can be realized by eight step ladder operations.
In the conventional lossless transform, as rounding processing is performed in each ladder operation, 12 rounding processings are necessary. On the other hand, according to the second embodiment, only 8 rounding processings are performed as shown in
The two lossless 2-point transforms may be those in
The modification means that the lossless 4-point orthogonal transform can be realized with two lossless 2-point transforms having inverse rotational directions.
The transform expressions of the 4-point orthogonal transform obtained by the structure in
Y3=(aX0+X1−a2X2−aX3)/(1+a2) [Expression 2]
Further, in a case where the structure in
Further, the rounding processing in the second step ladder operation in the transform 503 and the rounding processing in the first step ladder operation in the transform 502 in
Next, the integrated rounding processing is shifted to a position after the third addition processing in the ladder operation.
round (R)+N=round (R+N) [Expression 3]
Note that the left side corresponds to the rounding before the shift, and the right side, to the rounding after the shift. The expression 3 indicates that the result of rounding processing performed after addition of a real number to an integer is the same as that of rounding processing performed before addition of rounded result to the integer. The real number corresponds to the sum of the results of multiplications in the second step and third step ladder operation respectively, before the new rounding processors 801 and 803. Note that the rounding processing of the embodiment may be a most general rounding off (to the nearest whole number), or may be rounding up or rounding down.
The structure in
The feature of the structure in
In the case of the modification in
A normal ladder operation is a 1-input 1-output operation, however, in this modification, the structure in
By introducing this expanded ladder operation, it can be said that the structure in
In a case where the rounding processings are removed from the structure in
As the structure in
Generally, upon Hadamard transform, input data are rearranged (for example, a butterfly operation is performed between X0 and X3), however, the input data rearrangement is not performed but the output data are rearranged.
In the structure in
In a case where the multiplication coefficient in the ladder operation is an integer value, as the value below decimal point is “0”, the rounding processing is not necessary, therefore the number of rounding processings is reduced. Further, as the multiplication coefficient (½) can be realized only by bit shift, the multiplier can be omitted.
The structure in
In the structure in
On the other hand, the following document 2 shows the structure of lossless 4-point Hadamard transform. In the document 2, to realize the lossless transform, a 4-point Hadamard matrix is divided into triangular matrices and replaced with ladder operations. In this complicated structure, the number of addition processings is larger than that in the structure in
(Document 2) Shinji Fukuma, Kohichi Ohyama, Masahiro Iwahashi and Nori Kanbayashi, “Lossless 8-Point High-Speed Discrete Cosine Transform Utilizing Lossless Hadamard Transform”, Singaku Gihou, IE99-65, pp. 37-44, October 1999
In the 4-point DCT operation shown in
In the expression 4, components X11, X12, X21, and X22 are data in the middle of operation. If the left side transform matrix is subjected to the horizontal processing, the right side transform matrix corresponds to the vertical processing. Both transform matrices express rotation processing at (3π/8). In a linear transform, any of the transform processings can be performed first (at this time, as rounding processing for lossless transform is not inserted, the transform is not a lossless transform but a linear transform), however, in this example, the left transform matrix is first subjected to processing.
More specifically, the rotation processing at (3π/8) is performed on two pairs of data, (X11, X21) and (X12, X22), then the results of transform is transposed, for example, a part of the data are interchanged and the rotation processing at (3π/8) is performed again. This processing is realized as a lossless transform in the structures in
In this embodiment, orthogonal transform processing capable of selection between the 2-point orthogonal transform and the 4-point orthogonal transform is provided by using the structures in
In this structure, a new constituent element is a data selector 1201. If the data flow is changed by the data selector 1201, the lossless 4-point orthogonal transform is realized, whereas if the data flow is not changed by the data selector 1201, the two lossless 2-point orthogonal transforms are realized.
In the above-described second embodiment, the structure in
In this embodiment, image data or the like is encoded by quantizing and Huffman coding the DCT coefficients, obtained by the lossless two-dimensional DCT transform to which the above-described ladder operation is applied.
Generally, an 8×8 block sized two-dimensional DCT in JPEG compression or the like is used, however, in this example, a 4×4 lossless two-dimensional DCT transform is-used. The 4×4 two-dimensional DCT can be expanded to an 8×8 two-dimensional DCT by a well-known technique.
The 4-point DCT transform matrix Mdct is expressed as follows.
Assuming that the original 4×4 data are represented as d00, d01, d02, . . . , d32 and d33, the 4×4 two-dimensional DCT is expressed as follows.
In the above expression, the components x00x01, x02, . . . , x32 and X33 indicate data obtained by a two-dimensional Hadamard transform on original data.
The horizontal lossless rotational transform and the vertical lossless rotational transform performed on the data resulted from the lossless two-dimensional Hadamard transform equals a lossless two-dimensional DCT transform. The horizontal lossless rotational transform is performed on four pairs of data, x01 and x03, x11 and x13, x21 and x23, and x31 and x33, while the vertical lossless rotational transform is performed on the four pairs of data, x10 and x30, x11 and X31, x12 and x32, and x13 and X33, which are results from horizontal transform.
The horizontal or vertical lossless rotational transforms 1601 to 1604 are realized with a conventional three step ladder operation as shown in
First, a lossless two-dimensional DCT transform processing 1701 as shown in
Accordingly, by setting the quantization steps upon coding processing, the quality of compressed/decompressed image can be continuously controlled by lossless coding to nonlossless (lossy) high-efficiency compression with degradation.
Further, the object of the present invention can also be achieved by providing a storage medium holding software program code for performing the aforesaid processes to a system or an apparatus, reading the program code with a computer (e.g., CPU, MPU) of the system or apparatus from the storage medium, then executing the program. In this case, the program code read from the storage medium realizes the functions according to the embodiments, and the storage medium holding the program code constitutes the invention. Further, the storage medium, such as a floppy disk (registered trademark), a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a CD-R, a DVD, a magnetic tape, a non-volatile type memory card, and ROM can be used for providing the program code.
Furthermore, besides aforesaid functions according to the above embodiments are realized by executing the program code which is read by a computer, the present invention includes a case where an OS (operating system) or the like working on the computer performs a part or entire actual processing in accordance with designations of the program code and realizes functions according to the above embodiments.
Furthermore, the present invention also includes a case where, after the program code read from the storage medium is written in a function expansion card which is inserted into the computer or in a memory provided in a function expansion unit which is connected to the computer, CPU or the like contained in the function expansion card or unit performs a part or entire process in accordance with designations of the program code and realizes functions of the above embodiments.
As described above, the present invention provides lossless 4-point orthogonal transform processing and apparatus capable of transformation with a reduced amount of operation and with high transform accuracy. More particularly, a lossless 4-point orthogonal transform can be realized as five multiplications and five rounding processings with an optimized structure.
Further, the number of multiplications can be reduced to ⅓ of a conventional case where twelve multiplications and twelve rounding processings or fifteen multiplications and five rounding processings are required, even with approximately the same transform accuracy (with the same number of rounding processings).
The present invention is not limited to the above embodiments and various changes and modifications can be made within the spirit and scope of the present invention. Therefore, to appraise the public of the scope of the present invention, the following claims are made.
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|U.S. Classification||382/276, 382/250, 375/240.03, 708/400|
|International Classification||H04N19/625, H04N19/90, H04N19/60, H04N19/91, G06K9/36, G06F17/14, H04B1/66, H04N1/41, H03M7/30|
|Cooperative Classification||G06F17/147, H04N19/42, H04N19/60|
|European Classification||H04N7/30, H04N7/26L, G06F17/14M|
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