Method for compressing and extending an image by transforming orthogonally and encoding the image

Abstract: Block distortion standards are obtained by considering the non-linearity of the visual sensation on stimulus, the non-linearity of illumination brightness versus voltage in an image display apparatus, the measurement of errors of lightness which is sensed on brightness stimulus by human beings, the discrimination threshold characteristic on lightness of the visual sensation, and brightness ruggedness. The brightness ruggedness is made proximate by brightness dispersion, so that a calculation cost is lowered. Formulas are given for the various kinds of distortion and, in particular, for the distortion at the boundaries between adjacent blocks. The quantization step is controlled in accordance with the desired block distortion.

Description: The invention relates to a method for compressing and extending an image by transforming orthogonally and encoding the image, and more particularly to, and an evaluation method of an image for obtaining an objective standard in regard to block distortion occurring at a block boundary of an image which is transformed orthogonally and encoded. In a conventional facsimile or television-telephone set, transmission data is compressed and encoded so that the data transmission amount is decreased. As a method for compressing image data, an estimate encoding method and a transformation encoding method are utilized conventionally. In the estimate encoding method, a signal to be next supplied is estimated in accordance with a signal which has been known by decoding an encoded signal, so that only a signal component which is different in the estimation from a correct signal is transmitted to decrease the amount of information to be encoded. In the transformation encoding method, only coefficients of components, signal electric power of which converges on a low frequency region, are encoded to decrease the amount of information, because the signal electric power of image signals having high correlation is distributed mainly on the low frequency region. That is, the correlation of the image signals is positively utilized, so that higher compression effect is obtained in the transformation encoding method than in the estimate encoding method. However, the amount of arithmetic logic processes is larger in the transformation encoding method than in the estimate encoding method, so that the practical use of the transformation encoding method has been delayed as compared to the estimate encoding method. In accordance with the development of computer technology, however, the calculation of orthogonal transformation required for the transformation encoding method has been easy in these days, so that the transformation encoding method has been widely used in the encoding of images. As an orthogonal transformation to a frequency region, DCT (discrete cosine transformation) is considered to be most effective for practical uses, because DCT is superior in regard to electric power converging on a low frequency region and the process speed of calculation algorithm. Among other orthogonal transformations than DCT, slant transformation, hurl transformation, etc. can be used in encoding images. According to the conventional image compression methods disclosed in IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 37, no. 11, November 1989, pages 1743-1749, and US Patent No. 4581638, there is a disadvantage in that an optimum compression factor is difficult to be set therein. That is, when coefficients are coarsely quantized, a data compression factor becomes large to deteriorate the quality of image. In other words, the process of the image compression is carried out with high speed, while block distortion which is discontinuity at boundaries of blocks is generated in reproducing images. On the other hand, when the coefficients are finely quantized, the data compression factor becomes small to decrease the block distortion, while a high speed process in hindered, and the process of pictures having fast motion is difficult to be carried out. Considering this disadvantage, a higher order portion corresponding to a high frequency region is coarsely quantized, and a lower order portion corresponding to a low frequency region is finely quantized, because an actual image does not include a substantial amount of the high frequency component. Consequently, the highly effective encoding of images is carried out without lowering quality of the images. It has been reported that block distortion which is one of factors for deteriorating the quality of reproduced images is sensed to be larger than random interference by ten times. In spite of the above coarse and fine quantization dependent on frequencies, a considerable block distortion occurs visually, in cases where an original image includes a large amount of high frequency component. This is applied to image compression methods using transformation other than DCT. According to the present invention, there is provided a method for compressing and extending an image by transforming orthogonally and encoding the image, said method including steps of; compressing said image by a compression factor determined as a result of an image evaluation of a block having predetermined number of pixels which is obtained from the division of said image; providing a block distortion standard using the variation in the error between corresponding blocks in the original image (10) and the reproduced image (20), and; correcting said compression factor in accordance with the result of said calculated block distortion standard; charactarised by calculating block distortion standards of adjacent blocks at a boundary between the blocks in accordance with the following equations: q h ( k , l ) = q h ( k , l ) σ 2 ( k , l ) for 1 ≤ σ 2 ( k , l ) ≤ σ 2 ( k -1, l ) q h ( k , l ) = q h ( k , l ) σ 2 ( k -1, l ) for 1 ≤ σ 2 ( k -1, l ) ≤ σ 2 ( k , l ) q h ( k , l ) = q h ( k , l ) for σ 2 ( k , l ) < 1 or σ 2 ( k - 1, l ) < 1 where d h (m,n) is an error variation amount between horizontal adjacent pixels (m,n) and (m-1,n), N is the number of vertical pixels in the block, M is the number of horizontal pixels in the block, k ≥ 1, l ≥ 0, and q v ( k , l ) = q v ( k , l ) σ 2 ( k , l ) for 1 ≤ σ 2 ( k , l ) ≤ σ 2 ( k , l -1) q v ( k , l ) = q v ( k , l ) σ 2 ( k , l - 1) for 1 ≤ σ 2 ( k , l - 1) ≤ σ 2 ( k , l ) q v ( k , l ) = q v ( k , l ) for σ 2 ( k , l ) < 1 or σ 2 ( k , l - 1)< 1 where d v (m,n) is an error variation amount between vertical adjacent pixels (m,n) and (m,n-1), where k is a horizontal address of a block and the first block of the left side is represented by (k=0) while 1 is a vertical address of the block, and the first block on the upper side is represented by (1=0), wherein a dispersion σ 2 (k,l) of a virtual sensation of brightness in a block (k,l) of a reproduced image is given by the following equation: and an average visual sensation of brightness p(k,l) in said block (k,l) of said reproduced image is given by the following equation: where Y (m,n) is the brightness signal level of a pixel (m,n) of a reproduced image. The invention will be described in more detail in conjunction with the appended drawing, wherein: Fig. 1 is a block diagram showing an image compression apparatus using DCT. The background of the invention will be explained with reference to Fig. 1. An image data compression apparatus using a standard DCT comprises a transmitter (compression circuit)1, a receiver (extension circuit) 2, and a transmission line 3, wherein image data 10 which is divided into blocks each having 8 x 8 pixels (dots) is supplied to the transmitter 1, and reproduced image data 20 is supplied from the receiver 2. In the transmitter 1, the two dimensions DCT transformation is carried out for each block in accordance with the following transformation equation (1). In the above equation (1), x and y are positions of a pixel, and u and v are positions of a DCT coefficient, wherein Cu and Cv are 1 2 , when u and v are zero, Cu and Cv are 1, when u and v are other values, Ls is 128, when a bit precision for a pixel value Pxy is of 8 bits, and Ls is 2048, when the bit precision is of 12 bits. As a result of this transformation, 64 coefficients Suv are obtained in each block, among which a coefficient Soo is called DC coefficient indicating a mean value (direct current component) of 64 pixels in a block, while the remaining coefficients are called AC coefficients. In accordance with this transformation, 8 x 8 pixels of a block are defined by a linear coupling of 64 DCT fundamental vectors. In this DCT transformation, electric power of ordinary images is distributed mainly on a low frequency region. By using this property, image compression is realized to carry out quantization in which a small number of bits are allocated to coefficients of a low frequency component, and a large number of bits are allocated to coefficients of a high frequency component. The coefficient Suv is quantized at each coefficient position in a step size different from others by using a quantization table 4. When the quantization is coarsely carried out by decreasing the number of quantization levels, the amount of data can be decreased. In this case, a data compression factor becomes large, while the deterioration can not be avoided in quality of images, if the coarse quantization is made without any consideration. As a result, discontinuity occurs at boundaries of blocks, and error occurs due to the drop of data. Thus, block distortion is increased in the quantization. On the other hand, when the quantization is finely carried out to result in the decrease of the compression factor, the block distortion is decreased, while the process of motion pictures having a large amount of data is difficult to be carried out. In fact, however, a high frequency component is not included in actual images by a substantial amount. In accordance with this tendency, the coarse quantization is made in the DCT method for higher order coefficients, and the fine quantization is made therein for lower order coefficients. Consequently, the encoding of data can be carried out with a high efficiency, while the quality of images is not lowered. Practically, the decision of a compression factor is made in accordance with the selection of an appropriate compression factor from plural compression factors by an operator. For this purpose, quantization tables corresponding to plural compression factors are accessed in a compression circuit to quantize coefficients of the transformation equation (1). At this time, almost all of the high frequency component is deleted. The quantized coefficients are encoded in accordance with entropy encoding by using an encoding table 5. For this purpose, Hoffman encoding method is often used. Then, encoded data is transmitted from the transmitter 1 via the transmission line 3 to the receiver 2 together with a parameter including information as to which table is used. In the receiver 2, the encoded data is decoded to provide the quantized data by referring to the transmitted encoding table 5. The quantized data is inversely quantized to provide the DCT coefficients by referring to the transmitted quantization table 4. In accordance with the property of the quantization, completely original DCT coefficients are not restored. In this sense, the DCT method is defined as a non-invertible encoding method. Then, the DCT coefficients are inversely transformed to the reproduced image data 20 of blocks each having 8 x 8 pixels. As described above, the original image data 10 is processed in the transmitter 1 to be the compression data 30 in accordance with the orthogonal transformation, the quantization and the variable length encoding, and the compression data 30 is extended in the receiver 2 to provide the reproduced image data 20 in accordance with the decoding, the inverse quantization and the inverse orthogonal transformation. Next, a method for compressing and extending an image by transforming orthogonally and encoding the image of a preferred embodiment according to the invention, in which the evaluation of the image is carried out in the apparatus shown in Fig. 1 in accordance with the following steps. (1) Considering the non-linearity of visual sensation on a stimulus. The characteristic of the visual sensation on the stimulus of brightness is not linear. In order to measure an error in accordance with the sense of human beings (not dependent on the level of brightness), it is necessary to convert the level of brightness to a level proportional to the visual sensation characteristic of human beings. In general, the visual sensation characteristic is approximately represented by the rules of Weber, Fechner and Stevens. According to the rule of Stevens, a brightness E for human beings to sense a stimulus I of brightness is represented by the following equation (2). E = α I β where α and β are constants, and β ranges 0.3 to 0.5. (2) Considering the non-linearity of an image display apparatus. In general, images are displayed on a display apparatus such as CRT, etc. Therefore, the characteristic of the display apparatus is necessary to be considered. An image on the display apparatus becomes bright dependent on a voltage applied to electrodes thereof. A relation of the voltage V of the electrodes and an illumination brightness is represented by the following equation (3). I = c V γ where c and γ are constants. In accordance with the equation (3), the equation (4) is obtained. Vk = Ik c 1 γ where Vk and Ik are values for V and I, respectively. This is referred to as γ correction. A value of γ is 2.2 to 2.8 for general CRT display apparatus. In order to reproduce relative brightness of original images on a CRT display apparatus, the γ correction is necessary to be applied to brightness signals proportional to brightness of the original images. In this preferred embodiment, image signals which are processed in advance by the γ correction are used. (3) Measuring an error of lightness "Lightness" is defined by a sense amount on a brightness stimulus of human beings. An error e(m, n) of a pixel (m, n) of a reproduced image relative to a pixel (m, n) of an original image is defined by the following equation (5). e ( m , n ) = E ( Y ( m , n )) - E ( X ( m , n )) where m is a horizontal address of a pixel and the first pixel on the left side is represented by (m=0), and n is a vertical address of the pixel and the first pixel on the upper side is represented by (n=0). A pixel on the right side of the pixel (m, n) is represented by (m+1, n) and a pixel on the lower side is represented by (m, n+1). X(m, n) is a brightness signal level of a pixel (m, n) of an original image, and Y(m, n) is a brightness signal level of a pixel (m, n) of a reproduced image. In the equation (5), E(v) is a conversion function for converting a brightness signal level V of an image to a brightness. Image signals to be processed are applied in advance with the γ correction relative to an illumination brightness by the equation(3), so that an actual brightness is necessary to be sought by applying the conversion (inverse γ correction) of the equation(3) to the image signal level V. Further, the conversion of the equation(2) is necessary to be carried out to obtain a relative lightness which is sensed to this illumination brightness by human beings. Accordingly, E(v) is obtained from the equations(2) and (3) as represented by the following equation(6). E ( V ) = α c β V γβ As described before, if β is 0.3 to 0.5 and γ is 2.2 to 2.8, γ β is 0.66 to 1.4. By assuming this value to be "1", the equation(5) is replaced by the following equation(7), because E(v) is proportional to V. e ( m , n ) = Y ( m , n ) - X ( m , n ) (4) Defining an error in consideration of the discrimination threshold characteristic relative to a lightness of the visual sensation. The visual sensation of human beings keeps the discrimination threshold characteristic relative to a lightness, and an error less than a threshold value is not sensed. This is necessary to be considered to measure an objective error amount. An error e'(m, n) in consideration of a discrimination threshold relative to a lightness of the visual sensation is defined by the following equation (8). e ' ( m , n ) = t e ( m , n ) where the coefficient t is "1" (t=1), when an error e(m, n) of a lightness of a pixel of a reproduced image relative to a lightness of a pixel of an original image is greater than K th [e(m, n) ≧ K th ], and the coefficient t is 0(t=0), when the error e(m, n) is equal to or less than K th [e(m, n) < K th ]. Here, K th is a discrimination threshold value of human beings relative to a lightness. (5) Defining a standard of block distortion. When the variation of errors between the original image and the reproduced image is continuous before and after a boundary of blocks, no block distortion occurs, even if an absolute value of the errors is large. In other words, block distortion occurs, when the errors are discontinuous at the boundary. The error variation amount d h (m, n) between horizontal adjacent pixels (m, n) and (m-1, n) in an image, and the error variation amount d v (m, n) between vertical adjacent pixels (m, n) and (m, n-1) in the image are defined by the following equations (9a) and (9b). dh ( m , n ) = e' ( m , n ) - e' ( m - 1, n ) ( m ≧ 1 , n ≧ 0) d v ( m , n ) = e ' ( m , n ) - e ' ( m , n - 1) ( m ≧ 0, n ≧ 1) A standard of block distortion at block boundaries is obtained in self-multiplication of the error variation amount at each block boundary and in an average of the self-multiplication values by a side length of the blocks. That is, a block distortion standard q h (k, l) at a boundary of blocks(k, l) and (k-1, l) and a blocks distortion standard q v (k, l) at a boundary of blocks (k, l) and (k, l-1) are defined by the following equations(10a) and (10b). where k is a horizontal address of a block, and the first block on the left side is represented by (k=0), while 1 is a vertical address of the block, and the first block on the upper side is represented by (l=0). A block next on the right side to the block(k, l) is (k, l+1), and a block next on the lower side to the block(k, l) is (k, l+1). M is the number of horizontal pixels in a block, and N is the number of vertical pixels in the block. (6) Obtaining a block distortion standard in consideration of the variation(ruggedness) of brightness. A small error is neglected at a portion having a large variation f brightness by human being eyes. When the variation of brightness is large, a block distortion amount is sensed to be smaller than an actual value. Considering this tendency, it is found that the following equations (11a) to (11c) and (12a) to (12c) are appropriate to provide block distortion standards more proximate to the visual sensation characteristic of human beings. q h ( k , l ) = q h ( k , l ) σ 2 ( k , l ) (1 ≦ σ 2 ( k , l ) ≦ σ 2 ( k - 1, l )) q h ( k , l ) = q h ( k , l ) σ 2 ( k -1, l ) (1 ≦ σ 2 ( k - 1, l ) ≦ σ 2 ( k , l )) q h ( k , l ) = q h ( k , l ) (σ 2 ( k , l ) < 1 or σ 2 ( k - 1, l ) < 1) where k is equal to or more than 1(k≧1) and l is equal to or more than 0(l≥0) in the equations (11a) to (11c). q v ( k , l ) = q v ( k , l ) σ 2 ( k , l ) (1 ≦ σ 2 ( k , l ) ≦ σ 2 ( k , l -1)) q v ( k , l ) = q v ( k , l ) σ 2 ( k , l -1) (1 ≦ σ 2 ( k , l - 1) ≦ σ 2 ( k , l )) q v ( k, l ) = q v ( k , l ) (σ 2 ( k , l ) < 1 or σ 2 ( k , l - 1) < 1) where k is equal to or more than 0 (k≧0) and l is equal to or more than 1(1≧1) in the equations (12a) to (12c). In the equations (11a) to (11c) and (12a) to (12c), dispersion of brightness is used as parameters representing the configuration of the brightness variation. The dispersion σ 2 (k, l) of the visual sensation brightness in a block(k, l) of the reproduced image is defined by the following equation(13). In the equation(13), p(k, l) is a mean value of the visual sensation brightnesses in the block(k, l) in the reproduced image, and is defined by the following equation (14). Using the dispersion of brightness defined in the equations(13) and (14) as parameters for the variation of the brightness makes a calculation cost low. The precision of a calculation result is sufficiently met for a required level. The block distortion standards obtained by the equations (11a) to (11c) and (12a) to (12c) used in the invention fully considers the visual sensation characteristic of human beings to adequately evaluate the image quality relating to the block distortion. Further, the calculation process becomes easy, because the dispersion of a low cost calculation is used. In the apparatus as shown in Fig.1, a quantizatation table 4 is adequately selected by using the block distortion standards represented by the equations (11a) to (11c) and (12a) to (12c), and compression and extension of an image are carried out by the selected quantization table. Consequently, the image compression having high efficiency can be realized. In the block distortion evaluation method as explained above, the visual sensation of human beings on a brightness stimulus, a voltage characteristic of illumination brightness, the discrimination threshold characteristic on lightness of the visual sensation, etc. are considered, so that a standard for correct image evaluation is obtained to select a compression factor as a compression parameter, dependent on which a quantization table is selected. Consequently, the block distortion is decreased, and the compression and extension of images having a high compression factor is carried out. In the conventional method, however, the increase of calculation cost occurs to make the process impossible substantially, where a brightness variation parameter is included therein. On the other hand, the dispersion of brightness is used in the invention in place of a theoretically faithful parameter, so that the cost of calculation is decreased, and a calculated value has a small error. Consequently, a correct evaluation standard is obtained in the invention. Although the invention has been described with respect to specific embodiment for complete and clear disclosure, the appended claims are not to be thus limited but are to be construed as embodying all modification and alternative constructions that may occur to one skilled in the art which fairly fall within the basic teaching herein set forth.

Claims: A method for compressing and extending an image by transforming orthogonally and encoding the image, said method including steps of; compressing said image by a compression factor determined as a result of an image evaluation of a block having predetermined number of pixels which is obtained from the division of said image; providing a block distortion standard using the variation in the error between corresponding blocks in the original image (10) and the reproduced image (20), and; correcting said compression factor in accordance with the result of said calculated block distortion standard; characterised by calculating block distortion standards of adjacent blocks at a boundary between the blocks in accordance with the following equations: q h ( k , l ) = q h ( k , l ) σ 2 ( k , l ) for 1 ≤ σ 2 ( k , l ) ≤ σ 2 ( k - 1, l ) q h ( k , l ) = q h ( k , l ) σ 2 ( k -1, l ) for 1 ≤ σ 2 ( k -1, l ) ≤ σ 2 ( k , l ) q h ( k,l ) = q h ( k , l ) for σ 2 ( k , l ) < 1 or σ 2 ( k - 1, l ) < 1 where d h (m,n) is an error variation amount between horizontal adjacent pixels (m,n) and (m-1,n), N is the number of vertical pixels in the block, M is the number of horizontal pixels in the block, k ≥ 1, l ≥ 0, and q v ( k , l ) = q v ( k , l ) σ 2 ( k , l ) for 1 ≤ σ 2 ( k , l ) ≤ σ 2 ( k , l -1) q v ( k , l ) = q v ( k , l ) σ 2 ( k , l -1) for 1 ≤ σ 2 ( k , l -1) ≤ σ 2 ( k , l ) q v ( k , l ) = q v ( k , l ) for σ 2 ( k , l )< 1 or σ 2 ( k , l - 1)< 1 where d v (m,n) is an error variation amount between vertical adjacent pixels (m,n) and (m,n-1), where k is a horizontal address of a block and the first block of the left side is represented by k=0 while 1 is a vertical address of the block, and the first block on the upper side is represented by l=0, wherein a dispersion σ 2 (k,l) of a virtual sensation of brightness in a block (k,l) of a reproduced image is given by the following equation: and an average visual sensation of brightness p(k,l) in said block (k,l) of said reproduced image is given by the following equation: where Y (m,n) is the brightness signal level of a pixel (m,n) of a reproduced image.

Inventors: ITAGAKI FUMIHIKO, ITAGAKI, FUMIHIKO, Itagaki, Fumihiko, c/o Hudson Soft Co. Ltd.
Applicants: HUDSON SOFT CO LTD, HUDSON SOFT CO., LTD.
Application year: 1993
Main classification: H04N7
IPC codes: H04N7, H04N1, G06T9