US RE42186 E1 Abstract A data transform processing apparatus comprising a first lossless transform circuit to perform two step ladder operation processings of receiving unweighted normalized data then outputting weighted nonnormalized rotation-transformed data, and a second lossless transform circuit to perform two step ladder operation processings of receiving the weighted nonnormalized rotation-transformed data from the first lossless transform circuit then performing inverse weighting and outputting unweighted normalized rotation-transformed data, wherein the outputs from the first lossless transform circuit are interchanged and supplied to the second lossless transform circuit.
Claims(9) 1. A data transform apparatus for converting four items of input data X
0, X1, X2 and X3 into four items of data in a frequency space, wherein the input data X0, X1, X2 and X3 are integers, the apparatus comprising:
a first multiplier configured to multiply the input data X
1 by a first coefficient; a second multiplier configured to multiply the input data X
2 by a second coefficient; a first rounding processor configured to perform rounding processing on an output of said first multiplier;
a second rounding processor configured to perform rounding processing on an output of said second multiplier;
a first calculator configured to add an output of said first rounding processor to the input data X
0; a second calculator configured to add an output of said second rounding processor to the input data X
3; a third rounding processor configured to obtain difference data between an output of said first calculator and an output of said second calculator, to multiply the difference data by a third coefficient and to perform rounding processing on the result of multiplication of the difference data by the third coefficient;
a third calculator configured to add an output of said third rounding processor to the input data X
1; a fourth calculator configured to add an output of said third rounding processor to the input data X
2; a fourth multiplier configured to multiply an output of said third calculator by the second coefficient;
a fifth multiplier configured to multiply an output of said fourth calculator by the first coefficient;
a fourth rounding processor configured to perform rounding processing on an output of said fourth multiplier;
a fifth rounding processor configured to perform rounding processing on an output of said fifth multiplier;
a fifth calculator configured to add an output of said fourth rounding processor to an output of said second calculator; and
a sixth calculator configured to add an output of said fifth rounding processor to an output of said first calculator,
wherein the outputs of said third, fourth, fifth and sixth calculators are output as the four items of data in the frequency space.
2. A data transform method of converting four items of input data X
0, X1, X2 and X3 into four items of data in a frequency space, wherein the input data X0, X1, X2 and X3 are integers, the method comprising:
a first multiplying step of multiplying the input data X
1 by a first coefficient; a second multiplying step of multiplying the input data X
2 by a second coefficient; a first rounding step of performing rounding processing on an output obtained in said first multiplying step;
a second rounding step of performing rounding processing on an output obtained in said second multiplying step;
a first calculating step of adding an output obtained in said first rounding step to the input data X
0; a second calculating step of adding an output obtained in said second rounding step to the input data X
3; a third rounding step of obtaining difference data between an output obtained in said first calculating step and an output obtained in said second calculating step, multiplying the difference data by a third coefficient and performing rounding processing on the result of multiplication of the difference data by the third coefficient;
a third calculating step of adding an output obtained in said third rounding step to the input data X
1; a fourth calculating step of adding an output obtained in said third rounding step to the input data X
2; a fourth multiplying step of multiplying an output obtained in said third calculating step by the second coefficient;
a fifth multiplying step of multiplying an output obtained in said fourth calculating step by the first coefficient;
a fourth rounding step of performing rounding processing on an output obtained in said fourth multiplying step;
a fifth rounding step of performing rounding processing on an output obtained in said fifth multiplying step;
a fifth calculating step of adding an output obtained in said fourth rounding step to an output obtained in said second calculating step; and
a sixth calculating step of adding an output obtained in said fifth rounding step to an output obtained in said first calculating step,
wherein the outputs obtained in said third, fourth, fifth and sixth calculating steps are output as the four items of data in the frequency space.
3. A data transform apparatus for converting four items of input data X
0, X1, X2 and X3 into four items of data in a frequency space, wherein the input data X0, X1, X2 and X3 are integers, the apparatus comprising:
a first calculator configured to add the input data X
3 to the input data X2; a second calculator configured to subtract the input data X
1 from the input data X0; a rounding processor configured to obtain difference data between an output of said first calculator and an output of said second calculator, to multiply the difference data by a coefficient and to perform rounding processing on the result of multiplication of the difference data by the coefficient;
a third calculator configured to add the input data X
1 to an output of said rounding processor; a fourth calculator configured to add the input data X
2 to the output of said rounding processor; a fifth calculator configured to subtract an output of said fourth calculator from an output of said second calculator; and
a sixth calculator configured to add an output of said first calculator to an output of said third calculator,
wherein the outputs of said third, fourth, fifth and sixth calculators are output as the four items of data in a frequency space.
4. An apparatus according to
5. A data transform method of converting four items of input data X
0, X1, X2 and X3 into four items of data in a frequency space, wherein the input data X0, X1, X2 and X3 are integers, the method comprising:
a first calculating step of adding the input data X 3 to the input data X2; a second calculating step of subtracting the input data X 1 from the input data X0; a rounding step of obtaining difference data between an output of the first calculating step and an output of the second calculating step, to multiply the difference data by a coefficient and performing rounding processing on the result of multiplication of the difference data by the coefficient; a third calculating step of adding the input data X 1 to an output of the rounding step; a fourth calculating step of adding the input data X 2 to the output of the rounding step; a fifth calculating step of subtracting an output of the fourth calculating step from an output of the second calculating step; and a sixth calculating step of adding an output of the first calculating step to an output of the third calculating step; wherein calculation results in the third, fourth, fifth and sixth calculating steps are output as the four items of data in a frequency space. 6. A data transform apparatus for converting four items of input data X
0, X1, X2 and X3 into four items of data in a frequency space, wherein the input data X0, X1, X2 and X3 are integers, the apparatus comprising:
a first calculator configured to add the input data X 3 to the input data X2; a second calculator configured to subtract the input data X 1 from the input data X0; a rounding processor configured to obtain difference data between an output of said first calculator and an output of the second calculator to multiply the difference data by a coefficient and to perform rounding processing on the result of multiplication of the difference data by the coefficient; a third calculator configured to at least one of add and subtract the input data X 1 and an output of the rounding processor; a fourth calculator configured to at least one of add and subtract the input data X 2 and the output of said rounding processor; a fifth calculator configured to at least one of add and subtract an output of the fourth calculator and an output of the second calculator; and a sixth calculator configured to at least one of add and subtract an output of the first calculator and an output of the third calculator; wherein the outputs of the third, fourth, fifth and sixth calculators are output as the four items of data in a frequency space. 7. A data transform method of converting four items of input data X
0, X1, X2 and X3 into four items of data in a frequency space, wherein the input data X0, X1, X2 and X3 are integers, the method comprising:
a first calculation step of adding the input data X 3 to the input data X2; a second calculation step of subtracting the input data X 1 from the input data X0; a rounding step of obtaining difference data between an output of the first calculation step and an output of the second calculation step to multiply the difference data by a coefficient and performing rounding processing on the result of multiplication of the difference data by the coefficient; a third calculation step of calculating the input data X 1 and an output of the rounding step; a fourth calculation step of calculating the input data X 2 and the output of the rounding step; a fifth calculation step of calculating an output of the fourth calculation step and an output of the second calculation step; and a sixth calculation step of calculating an output of the first calculation step and an output of the third calculation step; wherein each step of calculating in the third, fourth, fifth and sixth calculation steps includes at least one of adding and subtracting, and wherein the calculation results in the third, fourth, fifth and sixth calculation steps are output as the four items of data in a frequency space. 8. A data transform apparatus for converting four items of input data X
0, X1 X2 and X3 into four items of data in a frequency space, wherein the input data X0, X1, X2 and X3 are integers, the apparatus comprising:
a first calculator configured to add the input data X 3 to the input data X2; a second calculator configured to subtract the input data X 1 from the input data X0; a rounding processor configured to obtain difference data between an output of the first calculator and an output of the second calculator, and output an integer value corresponding to a value that is obtained by multiplying the difference data by 1/2; a third calculator configured to at least one of add and subtract using the input data X 1 and an output of the rounding processor; a fourth calculator configured to at least one of add and subtract using the input data X 2 and the output of the rounding processor; a fifth calculator configured to at least one of add and subtract using an output of the fourth calculator and an output of the second calculator; and a sixth calculator configured to at least one of add and subtract using an output of the first calculator and an output of the third calculator; 9. A data transform method of converting four items of input data X
0, X1, X2 and X3 into four items of data in a frequency space, wherein the input data X0, X1, X2 and X3 are integers, the method comprising:
a first calculating step of adding the input data X 3 to the input data X2; a second calculating step of subtracting the input data X 1 from the input data X0; a rounding step of obtaining difference data between an output of the first calculating step and an output of the second calculating step, and outputting an integer value corresponding to a value that is obtained by multiplying the difference data by 1/2; a third calculating step of calculating using the input data X 1 and an output of the rounding processor; a fourth calculating step of calculating using the input data X 2 and the output of the rounding processor; a fifth calculating step of calculating using an output of the fourth calculator and an output of the second calculator; and a sixth calculating step of calculating using an output of the first calculator and an output of the third calculator; Description This application is a reissue of U.S. Pat. No. 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. 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. In 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. In a case where the rotational angle is (−2θ), in the multiplication processor 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 Conventionally, nothing has been obtained in the analysis of the content of rotation processing in FIG. Modifications as shown in FIG. In In In 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 Similarly, Although 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. In The four input data (X Note that the results of transform processing in a case where rounding processings are ignored, for example, linear transforms are performed, are as follows.
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 Further, in a case where the structure in In Further, the rounding processing in the second step ladder operation in the transform Next, the integrated rounding processing is shifted to a position after the third addition processing in the ladder operation. 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 The structure in 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 Further, in Generally, upon Hadamard transform, input data are rearranged (for example, a butterfly operation is performed between X 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 X More specifically, the rotation processing at (3π/8) is performed on two pairs of data, (X 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 In the above-described second embodiment, the structure in 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 d In the above expression, the components x 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, x In The horizontal or vertical lossless rotational transforms First, a lossless two-dimensional DCT transform processing 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. Patent Citations
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