This invention relates to an image processing method and apparatus thereof, and more particularly, to an image processing method and apparatus which performs a rounding processing.
When a conversion processing is performed on k input data having an arbitrary bit length, if a conventional processing circuit shown in FIG. 8 is used, output data includes some amount having a positive deviation or negative deviation from a mathematical or theoretical value (hereinafter referred to as a "true value"). In such errors, there is an error element which can be canceled out when statistically meaningful data are added or data including an error are integrated over a predetermined period of time (hereinafter referred to as a "symmetric error"). There is also an error element in which the error cannot be canceled out by the above operation (hereinafter referred to as an "asymmetric error").
In the conventional processing circuit shown in FIG. 8, when k input data x.sub.1, x.sub.2, . . . , x.sub.k (whose data lengths are n.sub.1, n.sub.2, . . . , n.sub.k bits respectively) are inputted from an input terminal 1010 in parallel, each of the data is respectively multiplied in conversion units (T.sub.1) 1020, (T.sub.2) 1030, . . . , (T.sub.k) 1040 and a rounding processing is performed. The k output data x'.sub.1, x'.sub.2, . . . , x'.sub.k (whose data lengths are m.sub.1, m.sub.2, . . . , m.sub.k bits respectively) obtained from these conversion units are added together by an adder 1050 and a single data whose data length is m' bits is obtained. The rounding processing is performed on this data by a rounding processing circuit 1060 and the result is outputted as a rounded output X whose data length is P bits.
In the above processing, when a predetermined number of data having statistical meaning or data over the predetermined period of time are considered, maximum errors .+-..DELTA.x.sub.1, .+-..DELTA.x.sub.2, . . . , .+-..DELTA.x.sub.k are respectively generated in the output data x'.sub.1, x'.sub.2, . . . , x'.sub.k by the rounding processing in the conversion units (T.sub.1, . . . T.sub.k). If an asymmetric error with respect to the true value is .alpha., and a symmetric error is .beta. (where .alpha. and .beta. are both positive or both negative), the maximum errors generated by the rounding processing of the rounding processing circuit 1060 are as follows: ##STR1##
Accordingly, the maximum error generated in the output X is a sum of errors generated by the rounding processing in the conversion units (T.sub.1 . . . T.sub.k) and errors generated by the rounding processing circuit 1060, and expressed by the formula (2): ##STR2##
When the processing is performed in accordance with the above conventional approach, as indicated by the formula (2), the maximum error having positive deviation from the true value in the output X is not equal to the maximum error having negative deviation. Accordingly, when the output X is considered on the predetermined number of data or the data over the predetermined period of time, the asymmetric error cannot be canceled and remains contrary to the symmetric error. This remainder appears as a noise component in a signal processing and an S/N ratio of the signal processing is deteriorated as an asymmetric error becomes larger.
For example, the case where the processing circuit shown in FIG. 8 is adapted in a color printer connected to a host computer, color image data such as RGB signals inputted from the host computer are inputted to the color printer. A color conversion processing is performed on the RGB signals for color image formation in the printer and the RGB signals are converted to data represented in the other color space (e.g. YUV, L*a*b*, YMCBk). The processing circuit shown in FIG. 8 is used for this color conversion processing. However, as described above, an asymmetric error is generated by the rounding processing in the color conversion processing and this remains as noise in the output signal (the color data after the conversion). In other words, generation of the asymmetry error causes deterioration of color reproducibility in the color conversion processing.
Furthermore, the color conversion processing is repeated numerous times in the color printer, and the asymmetric errors are accumulated, thus creating a problem in the color reproducibility in the color image data processing.