Representation of Primary Color Tone Reproduction Curves their Stabilization

This paper proposes and compares different methods of representing the primary color tone reproduction curves (TRC) for the stabilization control in a color xerographic printing process. TRC stabilization is vital in maintaining high consistency in color printout. Colors are typically represented by a 3-dimensional representation such as the CIELAB or CIEXYZ colorspaces. For stabilization control, the 3-dimensional representation is redundant due to the fact that limited actuators authority would not account for all the degree of freedom in the data representation. In this respect it is more meaningful to represent color as a 1-dimensional parameterization of the 3dimensional representation. The proposed parameterization methods involved projection of the 3-dimensional representation onto a parameterization curve to minimize the effect of measurement noise. An empirical-based and a Neugenbauer model-based approach was used to describe this curve. Simulation and experimental results are presented to demonstrate the performance of the different parameterization methods subject to measurement noise. Introduction In color printing, color reproduction with high consistency and fidelity is very important. Unlike typical black and white printers, image defects in color image composition is highly noticeable. In term of the color reproduction, the xerographic color printer is well represented by the color reproduction function, CRC : C → C, desired-color 7→ output-color, where C is a 3-dimensional color space. It is desirable to have CRC to be an identity map. A CMYK xerographic color printer generates color by printing and overlaying the Cyan, Magenta, Yellow and blacK color separations. The different CMYK tones subtract unwanted spectral components from ”white” light while transmitting the required wavelengths to produce the desired color. The printing process of a particular color separation is characterized by the tone reproduction curve, TRC : [0,1] → C, desired tone 7→ output-color, where a solid colorant is represented by 1, and 0 represent the background without any colorant. In xerographic printing, there exist different disturbance sources such as temperature, humidity, material age etc.. There are also several xerographic actuators such as laser power, corotron voltage and development/bias voltages that can be used to compensate the disturbances. The objective of the TRC stabilization controller is to maintain a constant and stable process throughout the print cycles of the printer. To stabilize the xerographic printing process, there are several issues to be addressed. First of all, the high dimensionality of CRC and TRC mapping pose significant problem for sensing and control. This results in a control formulation that is under-actuated. A solution to this problem has been previously addressed for the TRC stabilization using a curve-fitting approach [1][2]. Secondly, the limited sensing capability pose significant problem for feedback control. The sensing of the TRC or CRC is typically limited to sensing 3 to 5 patches printed on an unused area of the photoreceptor for every few photoreceptor belt cycles. A solution to this problem was proposed in [3, 2] using time-sequential sampling. Current concepts of sensing the xerographic process generally involve printing a small number of small patches of single primary color tone images which are subsequently read. The reading can be performed using a toner area coverage sensor (TAC) which monitor the development of the color tones on the organic photoconductor belt. With the advances of spectrophotometers and calorimeters, we expect that these patches can be similarly read to give the 3-dimensional color measurement data. Such sensing concept allows sensing of the entire color gamut. This represents a critical step in achieving color printout with high fidelity. Our work on TRC stabilizing control center around this sensing concept. This bring about the third issue to be addressed – the 3-dimensional color representation is redundant for TRC stabilization control. The limited actuation authority would not account for all the degree of freedom in the 3-dimensional color representation. This paper addressed the issue of representing the 3-dimensional colorspace as a 1-dimensional representation such that the TRC map can be effectively stabilized. Different parameterization methods are proposed and their effectiveness in the presence of measurement noise evaluated. In our perspective, the most effective parameterization method would be the one that is least sensitive to the measurement noise. The rest of this paper is organized as follows. First of all we present a general framework for the colorspace reparameterization. This is followed by description of the empirical and physical model (Neugenbauer) based parameterization methods. We then present simulation and experimental results that compared the effectiveness of the proposed parameterization methods. Colorspace Parameterization Lets X be the 3-dimensional color space with a color difference function dX : X×X → R such that dX(C1, C2) ∈ R. The colorspace reparameterization gives a 1-dimensional representation defined on a space, Y . Then the colorspace parameterization function, π : X → Y assigns each 3dimensional colorspace measurement C ∈ X an element π(C) = κ ∈ Y . κ denotes the 1-dimensional parameterization. π can be any function that maps X into Y, πX = {π(C)|C ∈ X} ⊂ Y . Figure 1 shows the mapping of different parameterization functions.