Apparatus and method using a mask producing a halftone image with centroids of clusters distributed stochastically and bridged-cluster combinations depending on threshold lightness levels

Abstract

There is provided an ink-deposition device suitable for depositing ink on a target surface and a printing system comprising the same. In operation in a printing system, the ink-deposition device can convert digital images into ink images on the target surface using pixel-masks and methods as disclosed herein. Advantageously, the ink-deposition device, the printing system comprising it and the methods of using the same can reduce or prevent the occurrence of some undesired ink-formations typically governed by the respective physical and/or chemical properties of the surface and ink being used or mitigate their effect on print quality. Application of the pixel-image mask yields a binary image that exhibits pixel-clusters with stochastically distributed centroids.

Claims

1. A method of digital printing comprising: a. electronically applying an N×M pixel-image mask to a target non-binary multi-level digital image to obtain therefrom a target binary digital image; and b. converting the target binary digital image into an ink image by ink deposition onto a target surface, wherein variables L, M, N, r, s, p, y are defined such that L is a positive integer equal to at least 64, M and N are each positive integers that are each equal to at least 16, s is a positive integer having a value between 1 and y*L, p is a positive number having a value of at least 30, y is a positive number having a value of at most 0.05, and r is a positive number having a value of at least 0.5, and wherein the N×M pixel-image mask has all of the following properties: i. a total number of lightness levels of the pixel-image mask is at least L; ii. at sub-threshold lightness levels below a threshold lightness level, application of the pixel-image mask to a uniform-lightness N×M digital image yields a sub-threshold-lightness-level binary image characterized by an array of pixel-clusters, centroids of clusters of the array being spatially distributed according to a stochastic pattern; iii. at the threshold lightness level, application of the pixel-image mask to a uniform-lightness N×M digital image yields a threshold-lightness-level binary image characterized by an array of pixel-clusters, centroids of clusters of the array being spatially distributed according to a stochastic pattern, the threshold-lightness-level binary image being further characterized such that, within an ink-image-space defined according to the ink-deposition process of step (b), at least p % of all pixels-clusters of the array of pixel-clusters nearly touch a neighboring pixel-cluster without touching; iv. at a threshold-succeeding lightness level that is s lightness levels above the threshold lightness level, application of the pixel-image mask to a uniform-lightness N×M digital image yields a threshold-succeeding binary image characterized, within the ink-image-space, by a ratio r between (i) a number of 3+-bridged-cluster combinations and (ii) a number of 2-bridged-cluster combinations.

2. The method of claim 1, wherein a value of p is at least 40.

3. The method of claim 1, wherein a value of r is at least 0.6.

4. The method of claim 1, wherein a product of N and M is at least 250.

5. The method of claim 1, wherein at least a majority, or at least a substantial majority, or all of the pixel-clusters of the threshold-lightness-level binary image are of substantially the same size.

6. The method of claim 1, wherein the stochastic pattern is a blue-noise pattern.

7. The method of claim 1, wherein the target surface is a surface of an intermediate transfer member (ITM), the method further comprising transferring the ink-image from the surface of the ITM to a printing substrate.

8. The method of claim 1, wherein the N×M pixel-image mask is defined so that the threshold-lightness-level binary image comprises at least 10 pixel-clusters.

9. The method of claim 1, wherein the N×M pixel-image mask is defined so that the threshold-lightness-level binary image comprises at least 10 pixel-clusters.

10. The method of claim 1, wherein the ink is aqueous and/or the target surface is hydrophobic.

11. The method of claim 1, wherein the ink substantially does not penetrate into the target surface.

12. A printing system for converting digital images into ink-images, the printing system comprising: a. an ink-deposition device capable of depositing ink on a target surface to form the ink-images thereon; b. an electronic controller for regulating the ink depositing by the ink-deposition device so that the printing system converts digital images into the ink-images according to a N×M pixel-mask such that wherein variables L, M, N, r, s, p, y are defined such that L is a positive integer equal to at least 64, M and N are each positive integers that are each equal to at least 16, s is a positive integer having a value between 1 and y*L, p is a positive number having a value of at least 30, y is a positive number having a value of at most 0.05, and r is a positive number having a value of at least 0.5, and wherein the N×M pixel-image mask has all of the following properties: i. a total number of lightness levels of the pixel-image mask is at least L; ii. at sub-threshold lightness levels below a threshold lightness level, application of the pixel-image mask to a uniform-lightness N×M digital image yields a sub-threshold-lightness-level binary image characterized by an array of pixel-clusters, centroids of clusters of the array being spatially distributed according to a stochastic pattern; iii. at the threshold lightness level, application of the pixel-image mask to a uniform-lightness N×M digital image yields a threshold-lightness-level binary image characterized by an array of pixel-clusters, centroids of clusters of the array being spatially distributed according to a stochastic pattern, the threshold-lightness-level binary image being further characterized such that, within an ink-image-space defined by the ink-deposition device, at least p % of all pixels-clusters of the array of pixel-clusters nearly touch without touching; iv. at a threshold-succeeding lightness level that is s lightness levels above the threshold lightness level, application of the pixel-image mask to a uniform-lightness N×M digital image yields a threshold-succeeding binary image characterized, within the ink-image-space, by a ratio r between (i) a number of 3+-bridged-cluster combinations and (ii) a number of 2-bridged-cluster combinations.

13. The system of claim 12, wherein a product of N and M is at least 250.

14. The system of claim 12, wherein at least a majority, or at least a substantial majority, or all of the pixel-clusters of the threshold-lightness-level binary image are of substantially the same size.

15. The system of claim 12, wherein the stochastic pattern is a blue-noise pattern.

16. The system of claim 12, wherein the surface is an intermediate transfer member (ITM), the system further comprising an impression station configured to transfer the ink-images from the surface of the ITM to a printing substrate.

17. The system of claim 12, wherein the threshold-lightness-level binary image comprises at least 10 pixel-clusters.

18. The system of claim 12, wherein the threshold-lightness-level binary image comprises at least 10 pixel-clusters or at least 20 pixel-clusters.

19. The system of claim 12, wherein the ink is aqueous and/or the target surface is hydrophobic.

20. The system of claim 12, wherein the ink substantially does not penetrate into the surface.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will now be described further, by way of example, with reference to the accompanying drawings, in which:

(2) FIG. 1 is a flow-chart illustrating a prior-art technique for half-toning.

(3) FIG. 2 illustrates a binary digital image comprising two square-clusters of pixels as well as an associated ink-image derived from the binary digital image.

(4) FIG. 3 illustrates a system for performing the method of FIG. 1.

(5) FIGS. 4-5 respectively illustrate first and second examples of touching pixel clusters.

(6) FIGS. 6A-6B illustrate examples of nearly-touching pixel clusters.

(7) FIG. 7 illustrates an example of a sub-threshold-lightness-level binary image.

(8) FIGS. 8A-8C respectively illustrate examples of a sub-threshold-lightness-level binary image, a threshold-lightness-level binary image and a threshold-succeeding binary image.

(9) FIG. 9 is a magnification of FIG. 8C.

(10) FIG. 10 is a flow chart for generating a series of binary images that each represents a respective result when the MASK is applied to digital images of different lightness levels.

(11) FIG. 11 is a flow-chart illustrating a technique for half-toning according to some embodiments of the invention.

(12) FIG. 12 presents one heuristic example explaining how to compute a percentage p of pixel-clusters that ‘nearly touch’ a neighboring pixel-cluster in an array of pixels.

(13) FIGS. 13A-13E present examples of 3+-bridged-cluster combinations and 2-bridged-cluster combinations.

DETAILED DESCRIPTION OF EMBODIMENTS

(14) Embodiments of the present invention relate to ink deposition systems particularly suitable for printing systems where ink is deposited on a surface such that the geometry of the resulting ink-formations on the surface are governed, at least in part (for example, significantly), by the respective physical and/or chemical properties of the surface and ink being used. Typical such phenomena include beading of an ink droplet or formation of satellites and coalescence of separately deposited drops. Ink-formations having either smaller or greater area than intended by the binary image can degrade the print quality. Some embodiments of the present invention aim to mitigate the problems associated with prospective coalescence of ink on the target surface (e.g. as a result of surface tension). A fortiori in a digital image near touching clusters may contribute to undesired coalescence effects. Printing systems wherein aqueous ink droplets are deposited (e.g. jetted) onto a hydrophobic surface may, for example, be particularly demanding.

(15) Not wishing to be bound by theory, it is noted that in such situations of perceptible loss of print quality, patches of substantially-uniform gray-level image may be prone to non-uniform ink coalescence that introduces ‘graininess’ or ‘streakiness’ into the image. In some embodiments, the presently-disclosed teachings may minimize this ‘graininess’ or ‘streakiness.’

(16) The present inventors are now disclosing (i) an apparatus and method for depositing ink on a target surface in accordance with a novel pixel-mask and (ii) a routine for generating a series of binary images that describe features of the pixel-mask. Not wishing to be bound by theory, some embodiments are particularly useful for situations where the ink-droplets tend to coalesce (e.g. into relatively ‘large’ formations) on the surface. For situations where a ‘significant’ image (i.e. at least 16×16 pixels, or at least 50×50 pixels, or at least 100×100 pixels, or at least 200×200 pixels, or at least 500×500 pixels, or at least 1000×1000 pixels) has a uniform gray-scale or pixels with uniform lightness values, the aforementioned ink-coalescence might cause non-uniformities in an ink image or patch thereof that is supposed to be uniform.

(17) Towards this end, a technique is now disclosed whereby: (i) at relatively ‘low’ lightness values, a hybrid AM-FM printing technique is employed where multi-droplet ink-formations are disposed according to a stochastic pattern; (ii) at a ‘threshold’ lightness value, a mask is employed so that multi-cluster ink-formations (i.e. an ink formation derived from a plurality of pixel-clusters) tend to coalesce in a ‘balanced manner’ Thus, there is a preference for cluster-derived ink-formations to coalesce with two or more cluster-derived ink-formations, rather than with only a single cluster-derived ink-formation.

Definitions

(18) For convenience, in the context of the description herein, various terms are presented here. To the extent that definitions are provided, explicitly or implicitly, here or elsewhere in this application, such definitions are understood to be consistent with the usage of the defined terms by those of skill in the pertinent art(s). Furthermore, such definitions are to be construed in the broadest possible sense consistent with such usage.

(19) If a value of an integer A is at most B, and B is a real number (but not an integer), then the value of A is at most equal to the value of the largest integer that is smaller B.

(20) For the present disclosure ‘electronic circuitry’ is intended broadly to describe any combination of hardware, software and/or firmware. In some embodiments, a printing system includes an ‘electronic controller’ comprising ‘electronic circuitry’ and configured to regulate ink-deposition.

(21) As was discussed above, a ‘target digital image’ is an image that is actually converted into an ink-image. In contrast, there are certain digital images which are described only so as to define features of the pixel-image mask by means of describing the result when the pixel-image mask is applied to a particular multi-level non-binary digital image.

(22) Examples of digital images that are not ‘target’ digital images and are not required to be printed include sub-threshold-lightness-level binary image (see FIG. 7 and FIG. 8A), a threshold-lightness-level binary image (see FIG. 8B) and a threshold-succeeding binary image (see FIG. 8C).

(23) The modifier ‘sub-threshold-lightness-level’ as applied to a ‘binary image’ is not intended to limit the content of the sub-threshold-lightness-level binary image—instead, this modifier is only used as a label to distinguish this sub-threshold-lightness-level binary image from other binary images. This label was selected because it relates to how sub-threshold-lightness-level binary image could hypothetically be formed by applying a pixel-image mask to a sub-threshold-lightness-level uniform digital image (i.e. multi-level image).

(24) Similarly, the modifier ‘threshold-lightness-level’ as applied to a ‘binary image’ is not intended to limit the content of the threshold-lightness-level binary image—instead, this modifier is only used as a label to distinguish this threshold-lightness-level binary image from other binary images. This label was selected because it relates to how the threshold-lightness-level binary image could hypothetically be formed by applying a pixel-image mask to a threshold-lightness-level uniform digital image (i.e. multi-level image).

(25) Similarly, the modifier ‘threshold-succeeding’ as applied to a ‘binary image’ is also just a modifier to label a specific example of a binary image and to distinguish from other examples of a binary image.

(26) As noted above, an ink-deposition process may define a relation between the ‘space’ of binary digital images (i.e. to be printed) and ink-image ‘space.’

(27) An ink-deposition device may also define this relation. When the ink-deposition device defines this relation, this is according to operation of the ink-deposition device using a suitable or standard operating conditions using suitable ink and forming the ink-image on a suitable target surface (e.g. in a manner where mergers between ink-image formations may be correctable by any teaching disclosed herein). In different embodiments, this may be performed according to the teachings of any of the following patent documents, each of which are incorporated herein by reference: WO 2013/132439; WO 2013/132432; WO 2013/132438; WO 2013/132339; WO 2013/132343; WO 2013/132345; and WO 2013/132340.

(28) Embodiments of the invention are applicable to digital images in general (e.g. RGB images, CMYK images, etc.) and not just to gray-scale digital images. However, for simplicity, embodiments will be explained in terms of gray-scale—the skilled artisan will appreciate that the teachings disclosed herein are also applicable to any value for the a and b color dimensions in the Lab color space, not only images containing L*,0,0 pixel values.

(29) In some embodiments, the number of lightness levels (e.g. gray levels in the specific case of gray-scale) is at least L (L is a positive integer, for example L≧10, or L≧20, or L≧32, or L≧50, or L≧64, or L≧100, or L≧128, or L≧150, or L≧256). Alternatively the number of lightness levels may correspond to the bit depth of the digital image, e.g. 2-bit, 4-bit, 8-bit, 16-bit, 24-bit, 32-bit, etc.

(30) For the present disclosure, an image (e.g. a digital/pixel image or an ‘ink-image’) may refer to either an entire image or to a patch thereof.

(31) In some embodiments, the ink droplets deposited to form the ink-image on the target surface, whether having the same or different size, are jetted on a surface stationary relative to the ink-deposition device. Alternatively, the ink deposition device and the target surface can be in motion relatively to one another.

(32) Embodiments of the present invention relate to a method of digital printing comprising the steps of: (a) electronically applying an N×M pixel-image mask MASK to a target non-binary multi-level digital image to obtain therefrom a target binary digital image; and (b) converting the target binary digital image into an ink image by ink deposition onto a target surface.

(33) Properties of the presently disclosed image-mask MASK are discussed below.

(34) In particular, the presently-disclosed pixel image mask MASK is described in terms of the respective binary digital images obtained when the pixel-image mask is applied to a plurality of uniform pixel-images, each having a different respective uniform lightness level value. Three such images are (i) a sub-threshold-lightness-level binary image (one example is in FIG. 8A); (ii) a threshold-lightness-level binary image (one example is in FIG. 8B); and (iii) a threshold-succeeding binary image (one example is in FIGS. 8C and 9—FIG. 9 is a magnification of FIG. 8C).

(35) Sub-Threshold-Lightness-Level Binary Image:

(36) When the presently-disclosed pixel-image mask MASK is applied to a relatively ‘light’ uniform pixel-image (i.e. having a relatively high lightness level value), the resulting binary image is characterized by a plurality of distinct pixel-clusters {PC.sub.1, PC.sub.2, . . . PC.sub.Q} such that: (i) the centroids of the pixel clusters are defined as {centroid(PC.sub.1), centroid(PC.sub.2), . . . centroid(PC.sub.Q)}; (ii) these centroids are distributed according to a stochastic distribution scheme (e.g. a blue-noise scheme); (iii) the pixel clusters are distinct and do not ‘touch’ each other. As discussed above, the definition of ‘touching,’ nearly touching′ and ‘not touching’ is relative to a specific ink-deposition process and thus is relative to the ink used and the properties of the target surface upon which it is deposited. Examples of binary sub-threshold-lightness-level digital images resulting from applying a pixel-image mask MASK to a uniform digital image of the relatively ‘high’ lightness value are illustrated in FIGS. 7 and 8A. Q, the number of pixel-clusters, is a positive integer that may be at least 10, or at least 20, or at least 30.

(37) Threshold-Lightness-Level Binary Image:

(38) When the presently-disclosed pixel-image mask MASK is applied to a uniform-image at a lower lightness level value than the relatively ‘high’ lightness values of the previous paragraph, the resulting binary image is characterized as follows: (i) the centroids {centroid(PC.sub.1), centroid(PC.sub.2), . . . centroid(PC.sub.Q)} of the pixel-clusters are still distributed according to the stochastic distribution scheme (i.e. as was the case for the Sub-threshold-lightness-level binary image); and (ii) within an ink-image-space defined according to the ink-deposition process, at least some percentage p (e.g. at least 30%) of all pixel-clusters of the array nearly touch a neighboring pixel-cluster without touching. In different embodiments, a value of p is at least 30, or at least 40, or at least 50, or at least 60, or at least 70, or at least 80 or at least 90.

(39) One heuristic example explaining how to compute a percentage p of pixel-clusters in an array of pixels that ‘nearly touch’ (i.e. in ink-image-space defined according to the ink-deposition process) a neighboring pixel-cluster is discussed below, with reference to FIG. 12.

(40) Threshold-Succeeding Binary Image:

(41) For the present disclosure, this ‘lower’ lightness value is referred to as ‘nearly-touching threshold’ value (or simply a ‘threshold value’). In the present disclosure, nt_threshold is an abbreviation for ‘nearly-touching threshold.’ Assuming L lightness levels, nt_threshold is a positive integer less than L. When pixel-image mask MASK is applied to a uniform image having a lightness of nt_threshold, the resulting binary image is further characterized by the feature that the neighboring pixel-clusters nearly touch without touching. One example of such a binary image resulting from applying pixel-image mask MASK to a digital image having a uniform lightness value of nt_threshold is illustrated in FIG. 8B.

(42) When the presently-disclosed pixel-image mask MASK is applied to a uniform-image at an even lower lightness level value than nt_threshold, a result such as that illustrated in FIG. 8C is obtained. The ‘slightly lower lightness value’ is nt_threshold−s, where s is a positive integer equal to or less than the number of lightness-levels L (e.g. equal to at most 0.2*L, or at most 0.1*L, or most 0.05*L, or at most 0.03*L). In some embodiments s is a positive integer of at most 10, or at most 5, or exactly equal to 1.

(43) Thus, in FIG. 8B (illustrating one specific and non-limiting example of a ‘threshold-lightness-level binary image’), all neighboring pixel-clusters are ‘nearly-touching’—e.g. pixel-cluster 220B nearly touches pixel-cluster 220C. Pixel-cluster 220B does not nearly-touch pixel-cluster 220F—however, pixel-clusters 220B and 220F are not neighbors.

(44) The illustrations of FIGS. 7 and 8A-8C are not images of the actual binary-images obtained by applying the mask MASK to uniform digital images (i.e. the data structure in computer memory), but rather the results (according to a computer-simulation) of what happens when the resulting binary image is printed using a particular ink and where the ink is deposited onto a particular target surface (e.g. a hydrophobic surface) using a particular type of ink (e.g. an aqueous ink). In some embodiments, the ink and/or surface may provide any feature or combination of features disclosed in any of the following published patent applications, each of which are incorporated herein by reference in its entirety: WO 2013/132439; WO 2013/132432; WO 2013/132438; WO 2013/132339; WO 2013/132343; WO 2013/132345; and WO 2013/132340.

(45) Bridge-Pixel Groups and z-Bridged Cluster Combinations

(46) In FIG. 8C, clusters 220D, 220E, and 220F are touching and are ‘connected’. FIG. 9 is a close-up of FIG. 8C illustrating (i) a first bridge-pixel group 240A connecting pixel-cluster 220E with pixel-cluster 220D and (ii) a second bridge-pixel group 240B connecting pixel-cluster 220E with pixel-cluster 220F.

(47) A ‘bridge-pixel group’ comprises one or more pixels—for example, at most 10, or at most 5, or at most 3 pixels—whose presence causes pixel-cluster derived ink formations to be connected in situations where, in the hypothetical absence of the ‘bridge-pixel’ group of pixels, the pixel-cluster derived ink formations would be ‘not touching’ and would be distinct, when printed.

(48) For the present disclosure, for an integer z, a z-bridged-cluster combination is a cluster combination comprising exactly z members (i.e. comprised of z clusters). For the present disclosure, for an integer z, a z+-bridged-cluster combination is a cluster combination comprising at least z members (i.e. comprised of z or more clusters).

(49) FIG. 8C includes a single 3-cluster combination (i.e. comprised of pixel-clusters 220D, 220E and 220F) and no 2-cluster combinations. Thus, in the example of FIG. 8C, a ratio r between the number of 3+-bridged-cluster combination and the number of 2-bridged cluster combinations is infinity, since there is exactly one of the former, and none of the latter—the ratio of 1/0 is either undefined or defined as infinity.

(50) In some embodiments, the ratio between the number of 3+-bridged-cluster combinations to the number of 2-bridged-cluster combinations exceeds 0.5, or exceeds 0.6, or exceed 0.7, or exceeds 0.8, or exceeds 0.9, or exceeds 1, or exceeds 1.25, or exceeds 1.5, or exceeds 2, or exceeds 3, or exceeds 5, or exceeds 7.5, or exceeds 10, or exceeds 20, or exceeds 50, or exceeds 100.

(51) Heuristic examples explaining how to compute a ratio r between (i) a number of 3+-bridged-cluster combinations and (ii) a number of 2-bridged-cluster combinations are discussed below with reference to FIGS. 13A-13E.

(52) Two ‘pixel-clusters’ PCL_1 and PCL_2 are ‘substantially the same size’ if when printed to the surface to form corresponding ink structures, a ratio between an area of the larger corresponding structure to that of the smaller corresponding structure is at most 5, or at most 3, or at most 2.5, or at most 2, or at most 1.5, or at most 1.25.

(53) A ‘substantial majority’ is at least 75%. Substantially all is at least 90%, or at least 95%. To summarize: (i) FIG. 8A illustrates the ink-image that would be formed (i.e. according to a defined printing, ink-deposition process) by printing a sub-threshold-lightness binary image to the target surface; (ii) FIG. 8B illustrates the ink-image that would be formed by printing a threshold-lightness binary image to the target surface; and (iii) FIGS. 8C and 9 illustrates the ink-image that would be formed by printing a threshold-succeeding binary image to the target surface.

(54) FIG. 10 is a flow chart for generating a series of binary images that each represents a respective result when the MASK is applied to digital images of different lightness levels. The features of the binary images generated by FIG. 10 therefore describe properties of the pixel image-mask MASK.

(55) FIG. 10 describes a routine for iteratively generating a series of binary images. In step S201, an initial binary image is generated. The first time step S205 is performed, a successor binary image is generated from the initial binary image generated in step S201. When step S205 is subsequently performed, a successor binary image is generated from the previous binary image generated during the previous execution of step S205.

(56) Thus, in step S201, a binary image is generated to include a plurality of pixel-clusters {PC.sub.1, PC.sub.2, . . . PC.sub.Q} such that: (i) the centroids of the pixel clusters are defined as {centroid(PC.sub.1), centroid(PC.sub.2), . . . centroid(PC.sub.Q)}; (ii) these centroids are distributed according to a stochastic distribution scheme (e.g. a blue-noise scheme).

(57) Each time that step S205 is carried out, additional pixels are added to the previously-obtained binary image. The first time that step S205 is performed, additional pixels are added to the image of step S201—afterwards, additional pixels are added to the image obtained from the previous execution of step S205.

(58) Each time step S025 is performed, the pixels are added in a manner that maintains the clusters at substantially equal area and/or maintains the cluster centroids distributed according to the stochastic distribution scheme.

(59) In step S209, it is tested if the most recently generated binary image (i.e. at the highest-gray-level) is a threshold-lightness-level binary image—this would indicate if the threshold level is reached.

(60) If so, then all previously-generated images (i.e. generated before the iteration of step S205 that yields a threshold-lightness-level binary image) are sub-threshold-lightness-level binary images.

(61) Upon reaching the threshold level, the next binary image may be generated in step S213 from the most recent image of the last iteration of step S205—i.e. the ‘threshold-level’ binary image. In step S213, the image may be generated to obtain the result exemplified in FIGS. 8C and 9—i.e. first and second bridge pixel-groups are added to the threshold-level binary image.

(62) In some embodiments, one salient feature of all sub-threshold-lightness-level binary images is that (i) all centroids have the substantially same location (i.e. within a small tolerance—e.g. at most 10%, or at most 5%, or at most 3%, or at most 1%, or at most 0.5% of the square root of a region of the surface where the binary-image is printed); and (ii) none of the pixel clusters of the mask MASK are ‘touching’. This may also be true for a threshold-lightness-level binary image.

(63) Reference is now made to FIG. 11. Steps S301, S305 and S309 are respectively equivalent to step S101, S105 and S109 of FIG. 1—however, in the method of FIG. 11, the pixel-image mask is the presently-disclosed MASK.

(64) Reference is Now Made to FIG. 12.

(65) FIG. 12 presents one heuristic example explaining how to compute a percentage p of pixel-clusters that ‘nearly touch’ a neighboring pixel-cluster within an array of pixel-clusters (i.e. where the ‘nearly touch’ property is defined in ink-image-space defined according to an ink-deposition process).

(66) Thus, in FIG. 12, pixel-clusters 420A and 420B nearly touch, pixel-clusters 420E and 420F nearly touch, pixel-clusters 420E and 420G nearly touch, pixel-clusters 420F and 420G nearly touch, pixel-clusters 420H and 420I nearly touch, and pixel-clusters 420N and 420P nearly touch.

(67) The following pixel-clusters nearly touch a neighboring pixel-cluster without touching: 420A, 420B, 420E, 420F, 420G, 420H, 420I, 420N and 420P. Thus, a total of 9 pixel-clusters nearly touch a neighboring pixel-cluster without touching.

(68) The following pixel-clusters do not nearly touch any other pixel-cluster: 420C, 420D, 420J, 420K, 420L, 420M and 420O. Thus, a total of 6 pixel-clusters nearly touch a neighboring pixel-cluster without touching.

(69) Thus, in the example of FIG. 12, because the image has a total of 15 pixel-clusters, and because 9 of those pixel clusters nearly touch a neighboring pixel-cluster without touching, it may be said that 60% of all pixel-clusters of the array nearly touch a neighboring pixel-cluster without touching.

(70) Reference is now made to FIGS. 13A-13E. Heuristic examples explaining how to compute a ratio r between (i) a number of 3+-bridged-cluster combinations and (ii) a number of 2-bridged-cluster combinations are now discussed with reference to FIGS. 13A-13E. In FIG. 13A, the clusters 320A-320E are all distinct and unconnected—there are no bridges between the clusters. Therefore, the example of FIG. 13A only includes individual clusters, and lacks bridged-cluster combinations.

(71) In FIG. 13B, ink-image clusters 320B and 320C form a 2-bridged cluster. In addition, ink-image clusters 320D and 320E form a 2-bridged cluster—thus, there are two 2-bridged-cluster combinations and zero 3-bridged cluster combination.

(72) In FIG. 13C, ink-image clusters 320A, 320B and 320C form a 3-bridged cluster. In addition, ink-image clusters 320D and 320E form a 2-bridged cluster. Thus, there is one 2-bridged-cluster combination and one 3-bridged cluster combination. Because a 3-bridged cluster combination is one example of a 3+-bridged cluster combination, in FIG. 13C there is one 2-bridged-cluster combination and one 3+-bridged cluster combination.

(73) In FIG. 13D, former clusters 320C and 320F do not form a bridged cluster combination because they are now merged into each other—clusters 320C and 320F do not substantially retain their original shape (i.e. with only a ‘bridge’ as illustrated in the examples of FIGS. 13B-13C).

(74) In FIG. 13E, ink-image clusters 320A, 320B, 320C and 320D form a 4-bridged cluster which is a specific example of a 3+-bridged cluster combination since 4>3. In addition, ink-image clusters 320D and 320E form a 2-bridged cluster. Thus, there is one 2-bridged-cluster combination and one 4-bridged cluster combination. Because a 4-bridged cluster combination is one example of a 3+-bridged cluster combination, in FIG. 13E there is one 2-bridged-cluster combination and one 3+-bridged cluster combination.

(75) In some embodiments, an ink-deposition device includes and/or is controlled by ‘electronic circuitry.’

(76) Electronic circuitry may include any executable code module (i.e. stored on a computer-readable medium) and/or firmware and/or hardware element(s) including but not limited to field programmable logic array (FPLA) element(s), hard-wired logic element(s), field programmable gate array (FPGA) element(s), and application-specific integrated circuit (ASIC) element(s). Any instruction set architecture may be used including but not limited to reduced instruction set computer (RISC) architecture and/or complex instruction set computer (CISC) architecture. Electronic circuitry may be located in a single location or distributed among a plurality of locations where various circuitry elements may be in wired or wireless electronic communication with each other.

(77) The present invention has been described using detailed descriptions of embodiments thereof that are provided by way of example and are not intended to limit the scope of the invention. The described embodiments comprise different features, not all of which are required in all embodiments of the invention. Some embodiments of the present invention utilize only some of the features or possible combinations of the features. Variations of embodiments of the present invention that are described and embodiments of the present invention comprising different combinations of features noted in the described embodiments will occur to persons skilled in the art to which the invention pertains.

(78) In the description and claims of the present disclosure, each of the verbs, ‘comprise’ ‘include’ and ‘have’, and conjugates thereof, are used to indicate that the object or objects of the verb are not necessarily a complete listing of members, components, elements or parts of the subject or subjects of the verb. As used herein, the singular form ‘a’, ‘an’ and ‘the’ include plural references unless the context clearly dictates otherwise.