ORDER

MIRANDA M. DU, District Judge.

I. SUMMARY

This Order addresses a single remaining issue raised in Google Inc.'s Motion for Summary Judgment of Invalidity of U.S. Patent Nos. 6,684,087 and 6,292,657 on Grounds of Indefiniteness ("Motion") (dkt. no. 389). The Court previously resolved the Motion in part and directed a status report on the impact of the Court's Claim Construction Order. (Dkt. no. 465.) In particular, the Court asked the parties to meet and confer to determine whether the Court's Claim Construction Order affected their arguments regarding the invalidity of certain claims in U.S. Patent No. 6,684,087 ("'087 Patent"). The parties agree that their arguments are unaffected by the Claim Construction Order. In light of the parties' Status Report, the Court now addresses the remaining issue in Defendant's Motion — whether Claims 1, 17, 27, and 31 of the '087 Patent are invalid for indefiniteness. For the reasons discussed below, the Court will grant in part and deny in part Defendant's Motion with regard to the '087 Patent.

II. BACKGROUND1

Plaintiff Unwired Planet Inc. asserts Claims 1, 17, 27, and 31 of the '087 Patent against Defendant. (Dkt. no. 389-1 ¶ 1; dkt. no. 414-1 ¶ 1.) The '087 Patent "relates generally to the area of image display, and more particularly to a method and system for displaying recursively images on a display screen of a mobile device, wherein the images are of larger dimensions than that of the display screen." '087:1:8-13.2 Claims 1 and 17 describe methods for "recursively displaying on a screen of a mobile device an image having dimensions much larger than the dimension of the screen." '087:9:28-30, 10:61-63. Claims 27 and 31 describe apparatuses associated with those methods. See '087:11:65-12:14, 12:24-41. Both apparatuses also provide "for recursively displaying on a screen of a mobile device an image having dimensions much larger than the dimension of the screen." '087:12:24-26; see '087:11:65-67.

Plaintiff initiated this action in September 2012, alleging that Defendant directly, indirectly, and willfully infringes claims in 10 patents relating to mobile device technology. (Dkt. no. 1 ¶¶ 27-31.) The Court convened a Markman hearing in August 2014 (dkt. nos. 393, 394); the Court's Claim Construction Order was issued in December 2014. (Dkt. no. 450.) Among other disputed terms, the Claim Construction Order construed terms that appear in Claims 1, 17, 27, and 31 of the '087 Patent, including "reduced image." (Dkt. no. 450 at 5, 38-42.) The Court construed "reduced image" as "an uncropped version of the image with smaller dimensions." (Id. at 38-39; see also dkt. no. 404 (stipulating that "image" should be construed as "a stored description of a graphic picture").) Neither party, however, sought to construe "an image having dimensions much larger than the dimension of the screen," the term in the '087 Patent at issue in Defendant's Motion. (See dkt. no. 351-1 at 16-17; dkt. no. 404.)

Defendant filed the Motion in August 2014, seeking summary judgment on the basis of alleged invalidity of Claims 1, 17, 27, and 31 for indefiniteness. (Dkt. no. 389.) In reviewing the Motion alongside the Claim Construction Order, the Court questioned whether the construction of "reduced image" would affect the parties' indefiniteness arguments. The Court therefore deferred judgment on the '087 Patent in issuing its first Order on Defendant's Motion on March 27, 2015. (Dkt. no. 465.)

III. LEGAL STANDARD

A. Summary Judgment

The purpose of summary judgment is to avoid unnecessary trials when there is no dispute as to the facts before the court. Nw. Motorcycle Ass'n v. U.S. Dep't of Agric., 18 F.3d 1468, 1471 (9th Cir.1994). Summary judgment is appropriate when "the movant shows that there is no genuine dispute as to any material fact and the movant is entitled to judgment as a matter of law." Fed.R.Civ.P. 56(a); see Celotex Corp. v. Catrett, 477 U.S. 317, 322-23, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986). An issue is "genuine" if there is a sufficient evidentiary basis on which a reasonable fact-finder could find for the nonmoving party and a dispute is "material" if it could affect the outcome of the suit under the governing law. Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 248-49, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986). Where reasonable minds could differ on the material facts at issue, however, summary judgment is not appropriate. Nw. Motorcycle Ass'n, 18 F.3d at 1472. "The amount of evidence necessary to raise a genuine issue of material fact is enough `to require a jury or judge to resolve the parties' differing versions of the truth at trial.'" Aydin Corp. v. Loral Corp., 718 F.2d 897, 902 (9th Cir.1983) (quoting First Nat'l Bank of Ariz. v. Cities Serv. Co., 391 U.S. 253, 288-89, 88 S.Ct. 1575, 20 L.Ed.2d 569 (1968)). In evaluating a summary judgment motion, a court views all facts and draws all inferences in the light most favorable to the nonmoving party. Kaiser Cement Corp. v. Fischbach & Moore, Inc., 793 F.2d 1100, 1103 (9th Cir.1986).

The moving party bears the burden of showing that there are no genuine issues of material fact. Zoslaw v. MCA Distrib. Corp., 693 F.2d 870, 883 (9th Cir.1982). "In order to carry its burden of production, the moving party must either produce evidence negating an essential element of the nonmoving party's claim or defense or show that the nonmoving party does not have enough evidence of an essential element to carry its ultimate burden of persuasion at trial." Nissan Fire & Marine Ins. Co. v. Fritz Cos., 210 F.3d 1099, 1102 (9th Cir.2000). Once the moving party satisfies Rule 56's requirements, the burden shifts to the party resisting the motion to "set forth specific facts showing that there is a genuine issue for trial." Anderson, 477 U.S. at 256, 106 S.Ct. 2505. The nonmoving party "may not rely on denials in the pleadings but must produce specific evidence, through affidavits or admissible discovery material, to show that the dispute exists," Bhan v. NME Hosps., Inc., 929 F.2d 1404, 1409 (9th Cir.1991), and "must do more than simply show that there is some metaphysical doubt as to the material facts." Orr v. Bank of Am., NT & SA, 285 F.3d 764, 783 (9th Cir.2002) (citation and internal quotation marks omitted). "The mere existence of a scintilla of evidence in support of the plaintiff's position will be insufficient." Anderson, 477 U.S. at 252, 106 S.Ct. 2505.

B. Indefiniteness

Section 112 of the Patent Act requires a patent specification to "conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention." 35 U.S.C. § 112, ¶ 2.3 This definiteness requirement helps ensure that a patent is "precise enough to afford clear notice of what is claimed, thereby `apprising the public of what is still open to them.'" Nautilus, Inc. v. Biosig Instruments, Inc., ___ U.S. ___, 134 S.Ct. 2120, 2129, 189 L.Ed.2d 37 (2014) (quoting Markman v. Westview Instruments, Inc., 517 U.S. 370, 373, 116 S.Ct. 1384, 134 L.Ed.2d 577 (1996)) (alteration omitted). "A lack of definiteness renders invalid the `patent or any claim in suit.'" Id. at 2125 (quoting 35 U.S.C. § 282, ¶ 2(3)). A patent is "invalid for indefiniteness if its claims, read in light of the specification delineating the patent, and the prosecution history, fail to inform, with reasonable certainty, those skilled in the art about the scope of the invention." Id. at 2124. This standard "mandates clarity, while recognizing that absolute precision is unattainable." Id. at 2129. The definiteness standard also comports with the notion that "the certainty which the law requires in patents is not greater than is reasonable, having regard to their subject-matter." Id. at 2129-30 (citation and internal quotation marks omitted).

Patents are "presumed valid," and the "burden of establishing in-validity of a patent or any claim thereof ... rest[s] on the party asserting such invalidity." Microsoft Corp. v. i4i Ltd. P'ship, 564 U.S. 91, 131 S.Ct. 2238, 2242, 180 L.Ed.2d 131 (2011) (quoting 35 U.S.C. § 282) (internal quotation marks omitted). Whether a patent is invalid for indefiniteness is a question of law. See id. at 2242-43; see Biosig Instruments, Inc. v. Nautilus, Inc., 783 F.3d 1374, 1377 (Fed.Cir.2015) (noting that "general principles of claim construction apply" in an indefiniteness inquiry, and that de novo review is appropriate after Teva Pharmaceuticals USA, Inc. v. Sandoz, Inc., ___ U.S. ___, 135 S.Ct. 831, ___ L.Ed.2d ___ (2015), where a district court's indefiniteness inquiry is based on intrinsic evidence). But factual aspects of an invalidity defense must be proved by clear and convincing evidence. See Microsoft Corp., 131 S.Ct. at 2242; Biosig Instruments, 783 F.3d at 1377-78.

IV. ANALYSIS

Defendant contends that Claims 1, 17, 27 and 31 of the '087 Patent are indefinite because a person of ordinary skill in the art would not understand, with reasonable certainty, what the claims mean by "an image having dimensions much larger than the dimension of the screen." '087:9:28-30; see '087:10:61-63, 11:65-67, 12:24-26. Defendant argues that neither the claims nor the specification suggests how a person of ordinary skill in the art would measure whether an image's dimensions are "much larger" than a mobile device's screen, or how she would determine which dimension of the mobile device's screen is operative. (Dkt. no. 389 at 13.)

This disputed language, however, appears in the claims' preambles, and the parties disagree over whether those preambles limit the scope of Claims 1, 17, 27 and 31. See Catalina Mktg. Int'l, Inc. v. Coolsavings.com, Inc., 289 F.3d 801, 808-10 (Fed.Cir.2002) (describing guideposts to determine whether a preamble limits the scope of a claim). Defendant acknowledges that if the preambles are not limiting, then Defendant's indefiniteness arguments fall short — the Court cannot conclude that Claims 1, 17, 27 and 31 are invalid for indefiniteness due to alleged ambiguity in preambles that do not substantively limit them. (See dkt. no. 389 at 13.) Thus, as a threshold matter, the Court will address whether the preambles limit Claims 1, 17, 27 and 31.

A. Limiting

"Generally ... the preamble does not limit the claims." Am. Med. Sys., Inc. v. Biolitec, Inc., 618 F.3d 1354, 1358 (Fed.Cir.2010) (quoting Allen Eng'g Corp. v. Bartell Indus., Inc., 299 F.3d 1336, 1346 (Fed.Cir.2002)) (internal quotation marks omitted). Whether a preamble is limiting requires reviewing "the entire patent to gain an understanding of what the inventors actually invented and intended to encompass by the claim." Catalina Mktg. Int'l, 289 F.3d at 808 (quoting Corning Glass Works v. Sumitomo Electric U.S.A., Inc., 868 F.2d 1251, 1257 (Fed.Cir.1989)) (alterations and internal quotation marks omitted). A preamble is not limiting if it states "a purpose or intended use for the invention," and if the claim body defines a "structurally complete invention." Id. (quoting Rowe v. Dror, 112 F.3d 473, 478 (Fed.Cir.1997)) (internal quotation marks omitted). A preamble limits a claim, however, "if it recites essential structure or steps, or if it is necessary to give life, meaning, and vitality to the claim." Id. (quoting Pitney Bowes, Inc. v. Hewlett-Packard Co., 182 F.3d 1298, 1305 (Fed.Cir. 1999)) (internal quotation marks omitted).

No single "litmus test" exists to determine whether a preamble is limiting, but the Federal Circuit has developed several guideposts. Id. A preamble may limit a claim's scope by providing an antecedent basis4 for a phrase that appears in the claim's body. Id.; see Pacing Techs., LLC v. Garmin Int'l, Inc., 778 F.3d 1021, 1023-24 (Fed.Cir.2015) (holding that a preamble was limiting because it provided the antecedent basis for two terms in the disputed claim). Moreover, a preamble that "recit[es] additional structure or steps underscored as important by the specification" may limit a claim, as will a preamble that "is essential to understand limitations or terms in the claim body." Catalina Mktg. Int'l, 289 F.3d at 808; see C.W. Zumbiel Co., Inc. v. Kappos, 702 F.3d 1371, 1385 (Fed.Cir.2012) ("[T]he preamble constitutes a limitation when the claim(s) depend on it for antecedent basis, or when it is essential to understand limitations or terms in the claim body." (citation and internal quotation marks omitted)). A preamble generally is not limiting if it can be deleted without affecting "the structure or steps of the claimed invention." Catalina Mktg. Int'l, 289 F.3d at 809. Such preambles may "merely extoll[] benefits or features of the claimed invention" or "describe[] the use of an invention." Id.

Here, Defendant contends that the preambles are limiting because they provide an antecedent basis for the term "image," which appears in the body of each claim at issue. (Dkt. no. 389 at 14-17; dkt. no. 432 at 10-11.) Defendant additionally argues that the preambles limit the claims' scope by defining a structure that is important to the invention — the relative size difference between an image and the screen of a mobile device. (Dkt. no. 389 at 14; dkt. no. 432 at 11.) Plaintiff insists that the preambles are not limiting, arguing that if the preambles are deleted from Claims 1, 17, 27 and 31, the claim bodies are structurally complete. (Dkt. no. 414 at 11-14.) The Court agrees with Plaintiff that Claims 1 and 27 are structurally complete absent their preambles. The Court finds, however, that Claims 17 and 31 are limited by their preambles.

1. Claims 1 and 27

According to their preambles, Claims 1 and 27 provide for "recursively displaying on a screen of a mobile device an image having dimensions much larger than the dimension of the screen." '087:9:28-30; see '087:11:65-67. Without its preamble, the body of Claim 1 reads:

'087:9:31-39. Claim 1 thus describes a method of (1) displaying a "reduced image" on a mobile device's screen, where an "image" has been "transformed" into the reduced image according to "parameters associated with the screen;" (2) generating a request when a subarea of the reduced image is activated; and (3) receiving a more detailed image of the subarea. (See dkt. no. 414 at 12.) The claim makes clear that the image displayed on a mobile device's screen — the "reduced image" — is transformed from an image in accordance with the screen's parameters. Read alongside the Court's construction of "reduced image" as "an uncropped version of the image with smaller dimensions," the body of Claim 1 suggests that the "reduced image" is smaller than "the image" described in the claim. (See dkt. no. 450 at 38-40.)

Claim 27 replicates this language in describing an apparatus that includes a processer that causes another component of the invention to:

'087:12:5-14. Like Claim 1, the apparatus facilitates displaying a "reduced image" on the screen of a mobile device, where that reduced image has been "transformed from the image" according to "a set of parameters associated with the screen." '087:12:5-8. Because the "reduced image" is a smaller version of the "image," Claim 27, absent its preamble, indicates that the screen of the mobile device is smaller than the image. (See dkt. no. 450 at 38-40 (construing "reduced image" as "an uncropped version of the image with smaller dimensions").)

The concepts disclosed in the bodies of Claims 1 and 27 allow a mobile device with a screen that is smaller than an image to display a version of the image that is reduced in size. Defendant contends that "an image having dimensions much larger than the dimension of the screen," '087:9:28-30, is an "essential structural feature" of the '087 Patent's invention. (Dkt. no. 432 at 11.) The specification describes the invention as relating "to a method and system for displaying recursively images on a display screen of a mobile device, wherein the images are of larger dimensions than that of the display screen." '087:1:9-12; see also '087:3:11-12 ("a server that reduces the dimensions of the image to proper dimensions for display on the screen of the mobile device"); (dkt. no. 389 at 14). But those structural features are reflected in the bodies of Claims 1 and 27, which describe an "image" that is "transformed" into a "reduced image" for display on a mobile device's screen. See '087:9:31-34, 12:5-8. Because the bodies of Claims 1 and 27 stand on their own, the preambles' reference to "an image having dimensions much larger than the dimension of the screen" is not an additional structural limitation of the claims. See Catalina Mktg. Int'l, 289 F.3d at 809; cf. Proveris Scientific Corp. v. Innovasystems, Inc., 739 F.3d 1367, 1372-73 (Fed. Cir.2014) (holding that a preamble was limiting because, in part, it served as the only reference in an independent claim to an important inventive concept that was not clear in the body of the claim).

Nor is the Court persuaded by Defendant's argument that the preambles to Claims 1 and 27 are limiting because they provide an antecedent basis for "the image," a term that appears in the claim bodies.5 (See dkt. no. 389 at 14-17.) The Federal Circuit has indicated that "dependence on a particular disputed preamble phrase for antecedent basis may limit claim scope." Catalina Mktg. Int'l, 289 F.3d at 808 (emphasis added). Although Defendant is correct that "the image" referenced in the bodies of Claims 1 and 27 first appears in their preambles, it is not clear that this antecedent basis, alone, is sufficient to render the preambles limiting. See C.W. Zumbiel Co., 702 F.3d at 1385 (quoting Catalina Marketing International, 289 F.3d at 808, in suggesting that a preamble may be limiting either because it provides an antecedent basis for a claim term, or because it "`is essential to understand the limitations or terms in the claim body'"). Even in light of the fact that the antecedent basis for "image" appears in the preambles, the bodies of Claims 1 and 27 are structurally complete on their own. Thus, the Court finds that Claims 1 and 27 are not limited by their preambles.

2. Claims 17 and 31

Similar to Claims 1 and 27, Claims 17 and 31 describe a method and an apparatus, respectively, with preambles that state: "recursively displaying on a screen of a mobile device an image having dimensions much larger than the dimension of the screen." '087:10:61-63, 12:24-26. Plaintiff contends that Claims 17 and 31 are complete even when their preambles are removed, just like Claims 1 and 27. (Dkt. no. 414 at 11-14.) The Court disagrees.

Without its preamble, Claim 17 reads:

'087:10:65-11:6. Unlike the method disclosed in Claim 1, which indicates that the image is transformed into a reduced image to facilitate its display on a mobile device, see '087:9:31-39, this claim involves "generating" an "image hierarchy" from the "image." '087:11:1-4. The hierarchy "start[s] with a reduced image" that is "equally divided" into subareas and "forward[ed]... to the mobile device for display." '087:11:1-6.

The body of Claim 31 describes an apparatus with a processor that causes another component of the invention to:

'087:12:33-42.6 Here, an "image hierarchy" is "generate[d]" from an "image" that has been "fetched ... according to a request from the mobile device." '087:12:33-40. Just as in Claim 17, the image hierarchy "start[s] with a reduced image" that is divided and forwarded for display on a mobile device. '087:12:37-42.

As discussed above, "a preamble is not limiting where a patentee defines a structurally complete invention in the claim body and uses the preamble only to state a purpose or intended use for the invention." Poly-America, L.P. v. GSE Lining Tech., Inc., 383 F.3d 1303, 1310 (Fed.Cir.2004) (citation and internal quotation marks omitted). Absent their preambles, however, these claims do not make the relationship between an image, an image hierarchy, and a reduced image clear. Even if a reduced image is read as "an uncropped version of the image with smaller dimensions" in light of the Court's construction of the term (dkt. no. 450 at 38-40), Claims 17 and 31 merely state that the reduced image starts the image hierarchy and is forwarded to a mobile device for display. The claims fail to indicate that the image hierarchy — or the reduced image that it starts with — is a smaller version of the image, or that the image had been reduced in size according to the mobile device's screen. The only suggestion in Claims 17 and 31 that the image is larger than the mobile device's screen is in the preambles.7 Thus, the preambles are "essential to understand limitations or terms in the claim body" — namely, the size difference between an image and the screen of a mobile device. Catalina Mktg. Int'l, 289 F.3d at 808. Accordingly, the Court finds that Claims 17 and 31 are limited by their preambles.

B. Indefiniteness of Claims 17 and 31

Because the Court finds that the preambles to Claims 17 and 31 are limiting, the Court must address whether, as Defendant argues, those preambles render the claims indefinite. Based on the undisputed intrinsic evidence, the Court finds that they do.8

Defendant contends that the term "an image having dimensions much larger than the dimension of the screen" is indefinite for two reasons. First, the Patent allegedly fails to define a standard for measuring whether an image's dimensions are "much larger" than the dimension of a screen. (Dkt. no. 389 at 17-18.) Second, Defendant argues that "dimension of the screen" lacks an antecedent basis, leaving a person of ordinary skill in the art without reasonable certainty about which dimension of the screen is at issue. (Id. at 19-20.) Plaintiff insists that a person of ordinary skill in the art would understand that the dimensions of an image are "much larger than the dimension of the screen," '087:9:28-30, when "either [the image's] width or height is at least twice as large as the corresponding width or height of the screen." (Dkt. no. 414 at 21.) The Court finds that the term's ambiguity renders Claims 17 and 31 indefinite and invalid.

In describing an image that is "much larger" than a mobile device's screen, the allegedly indefinite term involves "words of degree," which often give rise to definiteness problems. Seattle Box Co., Inc. v. Indus. Crating & Packing, Inc., 731 F.2d 818, 826 (Fed.Cir.1984). Imprecise words of degree, however, do not necessarily render a claim indefinite. Id.; see Nautilus, 134 S.Ct. at 2129 (acknowledging that "absolute precision is unattainable"); Interval Licensing LLC v. AOL, Inc., 766 F.3d 1364, 1370 (Fed.Cir.2014) ("Claim language employing terms of degree has long been found definite where it provided enough certainty to one of skill in the art when read in the context of the invention."). But "it is not enough ... to identify some standard for measuring the scope of the phrase .... The claims, when read in light of the specification and the prosecution history, must provide objective boundaries for those of skill in the art." Interval Licensing, 766 F.3d at 1370-71 (citations and internal quotation marks omitted), quoted in Biosig Instruments, 783 F.3d at 1378-79.

Plaintiff relies on the specification — and one expert's reading of it9 — to support its theory that an image is "much larger" if one of its dimensions is at least twice as large as a screen's corresponding dimension. (See dkt. no. 414 at 19 (citing dkt. no. 414-5 ¶ 23).) According to the specification, "an image being requested by a mobile device is first preprocessed in a server that reduces the dimensions of the image to proper dimensions for display on the screen of a mobile device." '087:3:9-12. Through a process of dividing the reduced image into grids, "a user is able to see recursively all the details that the original image provides." '087:3:19-20. As one example of this process, the specification notes: "Image 500 ... has a size of 640 by 480 pixels and a screen of mobile device 350 can display an image of 70 by 60 pixels. One aspect of preprocessing is to reduce or decimate image 500 to the size of 70 by 60 pixels." '087:7:16-20. The specification further states that "the original image 500, regardless of the dimensions thereof, can be displayed, block by block and hierarchically, on the small screen of a mobile device." '087:7:53-56. But, as Defendant argues, the specification does not clarify whether an image with a size of, for instance, 640 by 480 pixels is "much larger" than a screen with a size of 70 by 60 pixels. (See dkt. no. 389 at 17-18.)

Neeraj Gupta, Plaintiff's expert, draws on these and other passages in the specification to analyze how a person of ordinary skill in the art would understand the disputed phrase. (See dkt. no. 414-5 ¶¶ 20, 22, 24, 26). Mr. Gupta reasons that, in order to display an image block-by-block, hierarchically, or recursively, the image must be divisible into more than one block. (See id. ¶ 21.) Because an image must be divided into blocks, Mr. Gupta concludes that one dimension of an image — either its width or its height — must be at least twice as large as the corresponding width or height of the screen. (Id. ¶ 23.) Citing to Mr. Gupta's analysis, Plaintiff argues that the '087 Patent "describes with reasonable certainty the relationship between the size of the image and the size of the mobile device screen." (Dkt. no. 414 at 18.)

Defendant points out several flaws in Mr. Gupta's analysis. First, during his deposition, Mr. Gupta clarified an assumption underlying his analysis by comparing an image to cookie dough, and suggesting that "screen size blocks are cookie cutters." (Dkt. no. 432-8 at 41.) As Defendant emphasizes, however, Mr. Gupta's reasoning could apply to an image that is divided into blocks that are too small to fill a mobile device's screen. (See dkt. no. 432 at 14-17.) According to this logic, the width or height of a "much larger" image would not need to be at least twice as large as the corresponding width or height of the screen. See dkt. no. 432-8 at 154 (deposition testimony suggesting that a detailed version of an image might not fill a mobile device's screen).

Moreover, Mr. Gupta modified his definition of a "much larger" image during his deposition, clarifying that an image is much larger than a screen "if the image's width and height is at least as large as the corresponding width and height of the screen ... and at least one of the image's width or height is at least twice as large as the corresponding width or height of the screen." (Dkt. no. 432-8 at 37 (emphasis added).) Mr. Gupta clarified that he thought this additional element — where the image's width or height must be at least as large as the screen's corresponding width or height — was implicit in his initial definition. (Id. at 35-37.) But Mr. Gupta's clarification suggests that his definition could be subject to different interpretations. In light of this ambiguity, as well as the logical inconsistencies between Mr. Gupta's reasoning and his conclusions, the Court finds untenable Mr. Gupta's and Plaintiff's assertions that a person of ordinary skill in the art would understand a "much larger" image to have a width or height that is at least twice as large as the corresponding width or height of a screen.

Finally, as noted above, the specification includes at least one example that describes an image and a mobile device's screen in terms of pixels. See '087:7:16-20. The specification thus indicates that the size difference between an image and a screen could be defined with more precision than the ratio that Plaintiff identifies. See Nautilus, 134 S.Ct. at 2129 ("[A] patent must be precise enough to afford clear notice of what is claimed."); Biosig Instruments, 783 F.3d at 1382 ("As [the Federal Circuit has] stated in the past, the degree of precision necessary for adequate claims is a function of the nature of the subject matter." (alterations, citation, and internal quotation marks omitted)). The '087 Patent fails to define an adequately precise and objective standard for measuring or comparing a "much larger" image to a mobile device's screen. Accordingly, Claims 17 and 31 do not "inform, with reasonable certainty, those skilled in the art about the scope of the invention." Nautilus, 134 S.Ct. at 2124. The Court therefore finds that Claims 17 and 31 of the '087 Patent are invalid for indefiniteness.

V. CONCLUSION

The Court notes that the parties made several arguments and cited to several cases not discussed above. The Court has reviewed these arguments and cases and determines that they do not warrant discussion as they do not affect the outcome of the Motion.

It is ordered that Defendant's Motion for Summary Judgment (dkt. no. 389) is granted in part and denied in part with respect to U.S. Patent Number 6,684,087. Claims 17 and 31 of U.S. Patent Number 6,684,087 are invalid for indefiniteness.