Delta E formula matching prediction

Abstract

A method for determining a color formulation for a target color starts by generating a plurality of candidate color formulations to reproduce the target color. For each candidate formulation, a predicted Delta E indicating the difference between the predicted color of the candidate formulation and the target color is determined. Also for each candidate formulation, a confidence value in the predicted Delta E is generated by summing weighted quality factors for each colorant in the candidate formulation. The weighted quality factors represent the proportion of each colorant in the candidate formulation. Then, a formulation is selected based on the predicted Delta E and the confidence value. The target color may be defined according to a multi-dimensional color space.

Description

[0001] Related Applications

[0002] This application claims the benefit of European Application No. 19205482.3, filed Oct. 25, 2019, and PCT / US2020 / 057355, filed Oct. 26, 2020, the disclosures of which are incorporated herein by reference. Background Art

[0003] Developing color recipes for inks, coatings, plastics, etc. typically involves using formulation software that includes a color formulation engine. The color formulation engine uses characterization data for various colorants, ink vehicles, and substrates (in the graphics field) or other colorant / vehicle information (in other fields such as coatings, plastics, textiles). The characterization data provides information on how each ingredient in an ink or other color product "behaves" when combined.

[0004] Generating the characterization data is typically done as follows. The user prepares samples of colorants or colorant mixtures with various concentration levels of vehicle, white, and / or black component ingredients. The user measures the reflectance and / or transmittance properties of each sample to obtain spectra and other measurements. Multiple samples can also be prepared and measured at each concentration to assess colorant and / or process consistency. The reflectance / transmittance measurements are then input into a color formulation engine such as Color iMatch available from X-Rite Inc. The color formulation engine generates characterization data for each colorant and vehicle from the measured samples. The characterization data can include K (absorption) and S (scattering) values or derivatives. This process is repeated for additional colorants, which can be combined at various concentrations to produce a color gamut. A set of such colorants with their characterization data is called an EFX set.

[0005] The target color is identified and then selected or input into a color matching engine. The color formulation engine then generates one or more recipes that attempt to match the target color spectral reflectance curve. Evaluation of the predicted recipes has traditionally been done by calculating the difference between the spectral curve of the desired target color and the theoretical spectral curve of the predicted recipe. This difference is called "Delta E" or ΔE. Methods for calculating ΔE are well known in the art.

[0006] In practice, the actual Delta E of a blended recipe is often different from the predicted Delta E. One reason for inaccurate ΔE calculations is that the characterization data may not have enough data points, such as insufficient colorant density samples (causing interpolation errors) or insufficient samples at a given density (affecting reproducibility).

[0007] Inaccurate ΔE predictions are problematic because users of color matching engines can generate a large number of potential formulations for a given target color, and to process the large number of formulations, users typically sort the formulations by ΔE. The user can then prepare test samples of the formulation with the closest ΔE match, believing that a lower ΔE implies a greater likelihood of a match. However, formulations that rely on poorly characterized data may rank well by ΔE but provide poor results when prepared, resulting in increased costs and delays. Summary of the Invention

[0008] A method for determining a color formulation for a target color begins by generating a plurality of candidate color formulations to reproduce the target color. For each candidate formulation, a predicted delta E is determined that indicates the difference between the predicted color of the candidate formulation and the target color. Also for each candidate formulation, a confidence value in the predicted delta E is generated by summing weighted quality factors for each colorant in the candidate formulation. The weighted representation of the quality factor represents the proportion of each colorant in the candidate formulation. Then, a formulation is selected based on the predicted delta E and the confidence value. The target color can be defined according to a multidimensional color space.

[0009] The quality factor can include the average standard deviation (pSD) of the predicted spectral response of the colorant relative to the spectral measurement of the colorant sample, where the sample is prepared at different colorant concentrations. The pSD for each colorant can be obtained by: obtaining spectral measurements of a plurality of samples made with the colorant at different colorant concentrations; generating a plurality of formulations by generating at least one formulation to match the spectral measurement of each sample; generating a predicted spectral response for each formulation; and determining the average standard deviation between the predicted spectral response of the formulation and the spectral measurement of the sample.

[0010] The confidence value can be generated by: determining the percentage of each colorant in the candidate formulation; multiplying the pSD of each colorant by its percentage in the formulation to obtain the weighted pSD of each colorant; summing the weighted pSDs; and expressing the sum of the weighted pSDs as a percentage confidence.

[0011] In another method, the quality factor includes the average delta E (pΔE) of the predicted color of the colorant relative to the spectral measurement of the colorant sample.

[0012] In another aspect of the present invention, a system for determining a color formulation for a target color is provided. The system includes a computing device having non-volatile instructions that, when executed by a processor, cause the computing device to generate a plurality of candidate color formulations to reproduce the target color. The computing device further performs the following steps: for each candidate formulation, determine the predicted Delta E, which indicates the difference between the predicted color of the candidate formulation and the target color; for each candidate formulation, generate a confidence value in the predicted Delta E by summing the weighted quality factors of each colorant in the candidate formulation, where the weighted representation of the quality factor indicates the proportion of each colorant in the candidate formulation; and select a formulation based on the predicted Delta E and the confidence value. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a system block diagram according to one aspect of the present invention.

[0014] Figure 2 is a method flowchart according to another aspect of the present invention.

[0015] Figure 3 is a table including characterization data of colorants at various concentrations and the calculated quality factors of the colorants according to another aspect of the present invention.

[0016] Figure 4 is a user visual display according to another aspect of the present invention. DETAILED DESCRIPTION

[0017] In the present disclosure, a singular reference may also include a plural. Specifically, unless the context otherwise indicates, the word "a" or "an" may refer to one, or one or more.

[0018] One aspect of visual appearance is color. The "color" of an object is determined by the portion of the incident white light spectrum that is reflected or transmitted to an observer without being absorbed. The color of an object can be described by "color attributes". Generally, color attributes indicate the spectral response of an object when illuminated by incident light. In the context of the present disclosure, the term "color attribute" should be understood broadly to cover any form of data that indicates the spectral response of an object when illuminated by incident light. Color attributes can take the form of color values in any color space, such as in a trichromatic color space like RGB or CIEXYZ, or in any other color space like CIELAB (L*a*b*) or CIE L*C*h, or in the form of spectral data in any format representing the spectral response of a material to incident light. In the context of the present disclosure, color attributes can particularly include the absorption and scattering coefficients of a material at multiple wavelengths.

[0019] The term "colorant" shall be understood as a component of a material that provides the appearance of color when light is reflected from or transmitted through the material. Colorants include inks, pigments, and dyes. A "pigment" is a colorant that is generally insoluble in the base component material. Pigments can be from natural or synthetic sources. Pigments can contain organic and inorganic components. A "dye" is a colorant that is generally soluble in the base component material.

[0020] The term "formulation" shall be understood as related to a collection of information that determines how an ink or other material is to be prepared. The material can include coating materials (such as automotive paints), solid materials (such as plastic materials), semi-solid materials (such as gels), inks for application to a printing substrate, combinations of inks and printing substrates, and combinations thereof. The prescription particularly includes the concentrations of the components (such as the base and colorant) that make up the material. A material that has been prepared according to a formulation can also be referred to as a "preparation".

[0021] The term "database" refers to an organized collection of data that can be electronically accessed by a computer system. In a simple embodiment, a database can be a searchable electronic file in any format. Examples include Microsoft Excel TM spreadsheets or searchable PDF documents. In a more complex embodiment, a database can be a relational database maintained by a relational database management system using a language such as SQL.

[0022] The term "computer" or "computing device" refers to any device that can be instructed via a program to automatically perform a sequence of arithmetic or logical operations. Without limitation, a computer can take the form of a desktop computer, laptop computer, tablet computer, smart phone, programmable digital signal processor, etc. A computer generally includes at least one processor and at least one memory device. A computer can be a sub-unit of another device (such as an image capture device). A computer can be configured to establish a wired or wireless connection to another computer, including a computer for querying a database. A computer can be configured to be coupled via a wired or wireless connection to a data input device, such as a keyboard or computer mouse, or to a data output device, such as a display or printer.

[0023] "Computer system" shall be understood broadly to encompass one or more computers. If a computer system includes more than one computer, these computers do not necessarily need to be in the same location. The computers within a computer system can communicate with each other via a wired or wireless connection.

[0024] A "processor" is an electronic circuit that performs operations on external data sources, particularly memory devices.

[0025] A "memory device", or simply "memory", is a device used to store information for use by a processor. Memory devices can include volatile memory, such as random access memory (RAM), and non-volatile memory, such as read-only memory (ROM). In some embodiments, the memory device can include non-volatile semiconductor memory devices, such as (E)EPROM or flash memory devices, which can take the form of, for example, a memory card or a solid state drive. In some embodiments, the memory device can include a mass storage device having mechanical components, such as a hard disk. The memory device can store programs for execution by the processor. The non-volatile memory device can also be referred to as a non-volatile computer-readable medium.

[0026] A "program" is a set of instructions that can be executed by a processor to perform a specific task.

[0027] Process 30 and system 10 are provided for evaluating the quality of characterization data and generating a confidence level for the predicted ΔE, and for indicating the best candidate formulation for a preparation. Refer to Figure 1 , system 10 includes color formulation software 12 operating on a general-purpose computer or computer server. Color formulation software 12 includes a characterization data engine 14 and a color formulation engine 16. The characterization data 20 of the EFX set is provided to the characterization data engine 14. The characterization data 20 can be obtained as described above. The target color 22 is also provided to the color formulation engine 16.

[0028] Refer to Figure 2 for process 30, in step 32, the characterization data engine 14 uses the characterization data 20 to generate the K and S (absorption and scattering) values for the entire EFX set that will be used in the color formulation engine 16. Then, each calibration level / sample within this EFX set of the characterization data passes through the color formulation engine, and in step 34, the color formulation engine 16 generates a color formulation. System 10 compares the predicted spectral curve of the generated formulation with the actual spectral curve of the individual calibration samples and calculates the predicted delta E in step 36. Examples are provided in Figure 3 Table 1 in. In Table 1, the measurements and characterizations from eleven calibration samples are provided. The concentration ranges from 1.0000% to 18.0000%. As elaborated above, the delta E for each calibration sample is determined along with additional appearance characteristics.

[0029] In steps 34, 36, and 38, the predicted delta E (pΔE) is then calculated for all samples of a given colorant. In step 40, the average pΔE for the colorant is calculated by averaging the pΔE for all individual samples of the colorant. In the example of Table 1, the average pΔE is 0.28. The predicted delta E (the average of all samples of the set) can also be calculated for the entire EFX set. The average pΔE value for each colorant provides an indication of how well the colorant table is characterized (in terms of confidence, it represents how the colorant performs across all concentration ranges and mixtures).

[0030] Although pΔE can be used to indicate the confidence level in a formulation, if the user prepares only a small number of samples to characterize a colorant, the "variation" between the predicted / actual samples may be deceptively small. To compensate for this and provide a more accurate indication of variability, system 10 calculates the average standard deviation (pSD) for each colorant at each wavelength of the calculated calibration data (such as the predicted spectral curves). As used herein, both pΔE and pSD can be referred to as colorant quality factors.

[0031] In use, a target color 22 is provided to the color formulation engine 16. The color formulation engine accesses the characterization data engine 14 and generates one or more candidate formulations to reproduce the target color along with the predicted ΔE. As described in more detail below, the color formulation engine 16 also generates a confidence value for the predicted ΔE.

[0032] In step 44, system 10 uses the colorant quality factors for each colorant (such as the average predicted pSD value, pΔE value, or a combination thereof) to calculate a predicted confidence value "%PC" for a particular formulation. This can be expressed as a percentage from 0 to 100, but typically ranges from 10 - 90. For example, 10% PC would be a very low predicted confidence, and 90% PC would be a very high predicted confidence. In one example, the pSD and pΔE values for each colorant are weighted proportionally to the concentration of the colorant in the color formulation. In this way, the quality of the characterization data for colorants used at low concentrations will not overly affect the predicted confidence.

[0033] For example, the weighted pΔE for a candidate formulation can be calculated by: determining the percentage of each colorant in the formulation, multiplying the pΔE of each colorant by its percentage in the formulation to obtain the weighted pΔE for each colorant, and summing the weighted pΔE. Then, the sum of the weighted pΔE can be divided by the maximum pΔE and multiplied by 100 to obtain the percentage confidence.

[0034] In another example, the weighted pSD of a candidate formulation can be calculated as follows: Determine the percentage of each colorant in the formulation, multiply the pSD of each colorant by its percentage in the formulation to obtain the weighted pSD of each colorant, and sum the weighted pSDs. The sum of the weighted pSDs can then be divided by the maximum pSD and multiplied by 100 to obtain the percentage confidence.

[0035] The color formulation engine can generate a number of formulations with pΔE within a specified tolerance. For example, the user can specify a ΔE tolerance of 2.0. The color formulation engine 16 can generate a number of candidate formulations within this tolerance. By quantifying a confidence metric in the candidate formulations and providing the ability to rank a plurality of predicted formulations according to each formulation based at least in part on the predicted confidence, the user is given a tool to select which candidate formulations to prepare for evaluation. In some embodiments, the system 10 ranks the candidate formulations and displays them on a display.

[0036] According to one aspect of the present invention, therefore, a predicted confidence value %PC is generated and provided to the user, which gives the confidence level (having a range between 10% - 90%) that an actual sample prepared with a given formulation will be close to the pΔE value. As Figure 4 illustrated, example formulations can be displayed to the user on the display 50. In this example, three candidate formulations for beige are shown. Formulation 5 has a predicted color difference of ΔE2000 = 0.07, and in the case of preparing an actual sample using this formulation, the user will be able to obtain a predicted confidence of approximately 70% within 0.07. This provides a relatively high confidence that if formulated, the actual result will be close to a pΔE of 0.07. If %PC is low (less than 50%), it is an indication that the reproducibility of the colorants used to make the formulation as determined by the characterization data of the included colorants is not ideal, or that there are not enough samples to well characterize the work of the colorants.

[0037] For example, Formulation 4 has a predicted ΔE2000 of 0.05, which is closer to the target than Formulation 5 or Formulation 6. However, Formulation 4 also has a %PC of 34, i.e., a low confidence in the predicted ΔE value. Formulation 6 has the highest %PC at 71. However, Formulation 6 has a predicted ΔE2000 of 0.10, which is the furthest from the target color. Therefore, Formulation 5 is indicated as the better formulation, followed by Formulation 6, and then Formulation 4. This is an example of taking both pΔE and %PC into account, since Formulation 5 is ranked at the top, even though it is neither the best pΔE nor the best %PC. Additional predicted appearance attributes can also be taken into account. As Figure 4 shown, the formulation ranking can be indicated by the order in which the system displays the candidate formulations.

[0038] The above examples are made with respect to polymer formulations and preparations. In Figure 4 the example, the base material is general purpose polystyrene (GPPS), and colorants are added as a whole in various proportions relative to the formulation weights. However, the present invention is not limited to polymers or plastics. The present invention can also be applied to the graphic arts (e.g., printing) - whether on paper or other substrates, architectural paints and coatings, tiles, automotive paints, other paints and coatings, durable goods, or any application where a colored product is made from a component colorant and a base material, or an ink / colorant and a printing substrate.

[0039] In the printing example, the color can be produced as a process color (i.e., a combination of cyan, magenta, yellow, and black), an extended gamut process color (CMYK plus orange, green, and violet), or a spot color. Each can have a combination of multiple inks or colorants to produce a desired target color on a given substrate. Printing techniques can be used on a variety of substrates, including paper, plastic film, metal, and textiles (e.g., "dye sublimation printing"). These substrates can also affect pΔE and %PC. The present invention can be used to rank many potential formulations to obtain the best results in matching a target color.

[0040] In the automotive paint example, automotive repair or refurbishment work may require matching the paint coating on a damaged vehicle. The paint formulation engine typically starts with a reference prescription based on a paint code or vehicle identification number. However, even for a given paint code, there are small variations in appearance between batches of paint used during manufacturing and between locations due to base components and colorants from different sources. Over time and exposure to various elements, the paint may also change appearance. In addition, automotive coatings typically have appearance properties that vary with the lighting angle and viewing angle. Therefore, the appearance properties of the target color are typically obtained by measuring the undamaged part of the damaged vehicle with a multi-angle spectrophotometer. The present invention can be extended to determining pΔE and %PC at multiple lighting angles and / or viewing angles.

[0041] Embodiments within the scope of the present disclosure include physical and other computer-readable media for carrying or storing computer-executable instructions and / or data structures. In particular, one or more of the processes or methods described herein can be at least partially implemented as instructions embodied in a non-transitory computer-readable medium and executable by one or more computing devices (e.g., any of the media content access devices described herein). Generally, a processor (e.g., a microprocessor) receives instructions from a non-transitory computer-readable medium (e.g., a memory, etc.) and executes those instructions, thereby performing one or more processes or methods, including one or more of the processes or methods described herein.

[0042] A computer-readable medium can be any available medium that can be accessed by a general-purpose or special-purpose computer system. A computer-readable medium that stores computer-executable instructions is a non-transitory computer-readable storage medium (device). A computer-readable medium that carries computer-executable instructions is a transmission medium. Thus, by way of example and not limitation, embodiments of the present disclosure can include at least two distinct types of computer-readable media: non-transitory computer-readable storage media (devices) and transmission media.

[0043] Non-transitory computer-readable storage media (devices) include RAM, ROM, EEPROM, CD-ROM, solid state drives (“SSDs”) (e.g., RAM-based), flash memory, phase change memory (“PCM”), other types of memory, other optical disk storage devices, magnetic disk storage devices, or other magnetic storage devices, or any other medium that can be used to store the desired program code components in the form of computer-executable instructions or data structures and that can be accessed by a general-purpose or special-purpose computer.

[0044] A digital communication interface or network is defined as one or more data links that enable the transfer of electronic data between computer systems and / or modules and / or other electronic devices. When information is transmitted or provided to a computer via a network or another communication connection (wired, wireless, or a combination of wired or wireless), the computer properly views the connection as a transmission medium. Transmission media can include networks and / or data links that can be used to carry the desired program code components in the form of computer-executable instructions or data structures and that can be accessed by a general-purpose or special-purpose computer. Combinations of the above should also be included within the scope of computer-readable media.

[0045] In addition, upon reaching various computer system components, program code components in the form of computer-executable instructions or data structures can be automatically transferred from a transmission medium to a non-transitory computer-readable storage medium (device) (or vice versa). For example, computer-executable instructions or data structures received via a network or data link can be buffered in RAM within a network interface card or module (e.g., a “NIC”) and then ultimately transferred to the computer system RAM and / or a less volatile computer storage medium (device) at the computer system. Thus, it should be understood that non-transitory computer-readable storage media (devices) can be included in computer system components that also (or even primarily) utilize a transmission medium.

[0046] Computer-executable instructions include, for example, instructions and data that, when executed at a processor, cause a general-purpose computer, a special-purpose computer, or a special-purpose processing device to perform a particular function or group of functions. In some embodiments, computer-executable instructions are executed on a general-purpose computer to transform the general-purpose computer into a special-purpose computer implementing elements of the present disclosure. For example, computer-executable instructions can be binary, intermediate format instructions such as assembly language, or even source code. Although the subject matter has been described in language specific to structural features and / or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the features or acts described above. Rather, the described features and acts are disclosed as example forms of implementing the claims.

[0047] Those skilled in the art will appreciate that the present disclosure may be practiced in a network computing environment having many types of computer system configurations, including personal computers, desktop computers, laptop computers, messaging processors, handheld devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, mobile phones, PDAs, tablet computers, pagers, routers, switches, and the like. The present disclosure may also be practiced in a distributed system environment where local and remote computer systems, which are linked through a network (either by a hardwired data link, a wireless data link, or a combination of hardwired and wireless data links), both execute tasks. In a distributed system environment, program modules may be located in both local and remote memory storage devices.

[0048] Embodiments of the present disclosure may also be implemented in a cloud computing environment. In this specification, "cloud computing" is defined as a model for enabling on-demand network access to a shared pool of configurable computing resources. For example, cloud computing may be adopted in the marketplace to provide ubiquitous and convenient on-demand access to a shared pool of configurable computing resources. The shared pool of configurable computing resources can be rapidly configured via virtualization and released with little administrative effort or service provider interaction, and then scaled accordingly.

[0049] The cloud computing model may consist of various characteristics, such as, for example, on-demand self-service, broad network access, resource pooling, rapid elasticity, measured service, and the like. The cloud computing model may also disclose various service models, such as, for example, software as a service ("SaaS"), platform as a service ("PaaS"), and infrastructure as a service ("IaaS"). The cloud computing model may also be deployed using different deployment models such as private cloud, community cloud, public cloud, hybrid cloud, and the like. In this specification and the claims, a "cloud computing environment" is an environment in which cloud computing is adopted.

[0050] In one embodiment, a system for determining a color formulation for a target color includes a computing device having non - volatile instructions that, when executed by a processor, cause the computing device to: generate a plurality of candidate color formulations to reproduce the target color; for each candidate formulation, determine a predicted Delta E that indicates the difference between the predicted color of the candidate formulation and the target color; for each candidate formulation, generate a confidence value in the predicted Delta E by summing the weighted average standard deviation (pSD) of the predicted spectral response of the colorant with respect to spectral measurements of a plurality of colorant samples, where the samples are prepared at different colorant concentrations, and where the weighted representation of the figure of merit represents the proportion of each colorant in the candidate formulation; and indicate to the user a formulation based on the predicted Delta E and the confidence value.

[0051] In the foregoing specification, the invention has been described with reference to specific exemplary embodiments of the invention. Various embodiments and aspects of the invention have been described with reference to the details discussed herein, and the drawings illustrate the various embodiments. The above description and drawings are illustrative of the invention and should not be construed as limiting the invention. Numerous specific details have been described to provide a thorough understanding of the various embodiments of the invention.

[0052] The invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The described embodiments are to be considered in all respects only as illustrative and not restrictive. For example, the methods described herein may be performed with fewer or more steps / actions, or the steps / actions may be performed in a different order. Additionally, the steps / actions described herein may be repeated or performed in parallel with each other, or in parallel with different instances of the same or similar steps / actions. Accordingly, the scope of the invention is indicated by the appended claims rather than the foregoing description. All changes within the meaning and scope of the claims will be included within the scope of the claims.

Claims

1. A method for determining a color formulation for a target color, comprising: Generate multiple candidate color formulations to reproduce a target color; For each candidate formulation, determine a predicted Delta E that indicates the difference between the predicted color of the candidate formulation and the target color; for each candidate formulation, generate a confidence value in the predicted Delta E by summing weighted quality factors for each colorant in the candidate formulation, where the weighting of the quality factors represents the proportion of each colorant in the candidate formulation; And Select a formulation based on the predicted Delta E and the confidence value.

2. The method according to claim 1, wherein the figure of merit comprises an average standard deviation pSD of the predicted spectral response of the colorants relative to the spectral measurements of a plurality of colorant samples, wherein the samples are prepared at different colorant concentrations.

3. The method according to claim 2, wherein the pSD for each colorant is obtained by: Obtaining spectral measurements of a plurality of samples made with colorants at different colorant concentrations; Generating a plurality of formulations by generating at least one formulation to match the spectral measurements of each sample; Generate a predicted spectral response for each formulation; And Determine the mean standard deviation between the predicted spectral response of the formulation and the spectral measurement of the sample.

4. The method according to claim 3, wherein the confidence value is generated by: Determining the percentage of each colorant in the candidate formulation; Multiplying the pSD of each colorant by its percentage in the formulation to obtain a weighted pSD for each colorant; Summing the weighted pSDs; and Dividing the sum of the weighted pSDs by the maximum pSD and multiplying by 100 to obtain a percentage confidence.

5. The method according to claim 1, wherein the target color is defined according to a multidimensional color space.

6. The method according to claim 1, wherein the figure of merit comprises an average predicted Delta E of the predicted color of the colorants relative to the spectral measurements of the colorant samples.

7. The method according to claim 1, wherein the method is executed on a computing device, and the method further comprises the computing device indicating the best candidate color formulation.

8. The method according to claim 1, wherein the predicted Delta E and the confidence value comprise a plurality of predicted Delta Es and confidence values determined at a plurality of illumination angles or viewing angles.

9. A system for determining a color formulation to match a target color, comprising a computing device having non-volatile instructions that, when executed by a processor, cause the computing device to: Generate a plurality of candidate color formulations to reproduce the target color; For each candidate formulation, determine the predicted Delta E, which indicates the difference between the predicted color of the candidate formulation and the target color; for each candidate formulation, generate a confidence value in the predicted Delta E by summing the weighted quality factors of each colorant in the candidate formulation, where the weighting of the quality factors represents the proportion of each colorant in the candidate formulation; and Indicate the formulation based on the predicted Delta E and the confidence value.

10. The system according to claim 9, wherein the quality factor includes the average standard deviation pSD of the predicted spectral response of the colorant relative to the spectral measurements of a plurality of colorant samples, wherein the samples are prepared at different colorant concentrations.

11. The system according to claim 10, wherein the pSD of each colorant is obtained by: Obtain spectral measurements of a plurality of samples made with colorants at different colorant concentrations; Generate a plurality of formulations by generating at least one formulation to match the spectral measurements of each sample; Generate a predicted spectral response for each formulation; And Determine the mean standard deviation between the predicted spectral response of the formulation and the spectral measurement of the sample.

12. The system according to claim 11, wherein the confidence value is generated by: Determine the percentage of each colorant in the candidate formulation; Multiply the pSD of each colorant by its percentage in the candidate formulation to obtain the weighted pSD of each colorant; Sum the weighted pSDs; and Divide the sum of the weighted pSDs by the maximum pSD and multiply by 100 to obtain the percentage confidence.

13. The system according to claim 9, wherein the target color is defined according to a multidimensional color space.

14. The system according to claim 9, wherein the quality factor includes the average predicted Delta E of the predicted color of the colorant relative to the spectral measurements of the colorant samples.

15. The system according to claim 9, wherein the system is further configured to indicate the best candidate color formulation.

16. The system according to claim 9, wherein, Where the predicted Delta E and confidence values include multiple predicted Delta E and confidence values determined at multiple illumination angles or viewing perspectives.

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