## United States Court of Appeals for the Federal Circuit

2008-1129, -1160

WAVETRONIX, Plaintiff-Appellant,

v. EIS ELECTRONIC INTEGRATED SYSTEMS, Defendant-Cross Appellant.

Brent P. Lorimer , Workman Nydegger, of Salt Lake City, Utah, argued for plaintiffappellant. With him on the brief were Thomas R. Vuksinick and David R. Todd . Of counsel were Chad E. Nydegger and L. David Griffin

. Richard D. Rochford , Nixon Peabody LLP, of Rochester, New York, argued for defendant-cross appellant. Of counsel on the brief were Michael F. Orman and Wendell W. Harris

. Appealed from: United States District Court for the District of Utah Senior Judge Bruce S. Jenkins

## United States Court of Appeals for the Federal Circuit

2008-1129, -1160

WAVETRONIX, Plaintiff-Appellant,

v. EIS ELECTRONIC INTEGRATED SYSTEMS, Defendant-Cross Appellant.

Appeal from the United States District Court for the District of Utah in Case No. 2:05- CV-73, Senior J udge Bruce Jenkins.

__________________ _________ DECIDED: July 29, 2009

__________________ _________ Before NEWMAN and SCHALL, Circuit Judges , and PATEL, District Judge

. ∗

PATEL, District Judge

. Wavetronix LLC (“Wavetronix”) brought th is patent infringement action against EIS Electronic Integrated Systems (“EIS”). The patent in suit is United States Patent No. 6,556,916 (“the ’916 patent”), entitled “Syst em and Method for Identification of Traffic Lane Positions.” Wavetronix and EI S both develop systems for monitoring the

∗ The Honorable Marilyn Hall Patel, Un ited States District Court for the Northern District of California, sitting by designation.flow of automobile traffic on thoroughfares. Wavetronix accuses the automatic setup feature of EIS’s Remote Tr affic Microwave Sensor (“RT MS”) X3 monitoring device of infringing one independent claim and seve ral dependent claims of the ’916 patent, literally or under the doc trine of equivalents. The district court granted summary judgm ent of non-infringement to EIS. Wavetronix appeals the judgment of non-infringement, and EIS cross-appeals dismissal of its counterclaims of invalidity and unen forceability. We conclude that summary judgment of non-infringement is proper, and we affirm the district court’s judgment. 1
I. BACKGROUND A. The Patent in Suit and Its Technological Field Urban planners require accurate counts of vehicular traffic in order to plan the construction of new thoroughfar es as well as to determine the optimal ways to use existing thoroughfares. It is often useful to know how much traffic travels in a particular lane, for instance a High-Occ upancy Vehicle (HOV) lane, as compared to other lanes on the same thoroughfare. Numerous sensor devices using, for example, radar or acoustic signals have been developed to monitor the flow of vehicle traffic across several lanes of a road or highway. The ’916 patent’s Figure 5 illustrates a roadside sensor unit with a field of vision extend ing across several lanes of a street.

1 Wavetronix argues that there are legal and factual errors in the district court’s opinion and that such errors warrant re versal. The existence of any such errors does not, in itself, compel reversal. This c ourt sits to review judgments, not opinions. Stratoflex, Inc. v. Aeroquip Corp. , 713 F.2d 1530, 1540 (Fed. Cir . 1983). The party that prevailed below may defend a judgment on any ground which the law and record permit that would not expand the re lief it has been granted. United States v. N.Y. Tel. Co. , 434 U.S. 159, 166 n.8 (1977).
2008-1129,-1160 2For these devices to accurately tally the number of vehicles traveling in each lane, they must “know” w here the lane boundaries are loca ted. While a human being can simply look at a highway and see where the lanes of tr affic are located, a sensing device must be “taught” the loca tion of the lanes before it can begin to serve its monitoring function. One wa y to achieve this is to a llow the device to detect some number of vehicles driving on the road and to extrapolate the locations of the lanes from an examination of where the detected vehicles have actua lly tended to drive. The underlying assumption (which highway patrol o fficers may dispute) is that drivers will more often than not drive near the centers of lanes, rather than near or over lane boundaries. If this assumption holds, then detecting where some number of vehicles have actually been driven can assist in identi fying the centers of lanes; likewise, the

2008-1129,-1160 3places on the road on which automobiles have tended not to drive can be identified as lane boundaries. The patent in suit is directed to a method of performing the initial step of “teaching” a monitoring device the location of the traffic lanes on a given thoroughfare using detection and observation of actual automobile traffic. In 2000, Wavetronix undertook the development of a new radar-based traffic monitoring system. Many of the prior art systems required manual adjustment to define the locations of the traffic lanes on the high way to be monitored. Wavetronix sought to improve the capability for automated lane definition. On September 27, 2001, three inventors filed the applicat ion for what became the ’916 patent, naming Wavetronix as the assignee. The pat ent issued on April 29, 2003. Only claim 1 is at issue on appeal. 2 That claim reads, in its entirety: 1. In a traffic monitoring system having a sensor, a method for defining traffic lanes, comprising the steps of: a. for a selectable plurality of vehicles, i. detecting each of said selectable plurality of vehicles present within a field of view of said sensor; ii. estimating a position of said each of said selectable plurality of vehicles; iii. recording said position of said each of said selectable plurality of vehicles; b. generating a probability density function estimation from each of said position of said each of said selectable plural ity of vehicles; and c. defining said traffic lanes within said traffic monitoring system from said probability density function estimation. The specification discloses several prefe rred embodiments, all of which are described through the use of histograms. Each of these histograms displays, in some form, a two-

2 Wavetronix has also accused EIS of infr inging claims 2, 8, 9, 15 and 16. Each of these is dependent upon claim 1’s limitations.
2008-1129,-1160 4dimensional grid with peaks a nd valleys representing the re lative heaviness of vehicle traffic across a set of “range bins” represent ing spatial distances from the sensor. These histograms, which are Figures 6, 7 and 8 in the patent, are shown below.

2008-1129,-1160 5The specification teaches that these histograms exemplify the kind of “probability density function estimation” recited in steps (b) and (c) of claim 1, and that the “peaks of the PDF represent the center of each lane and the low s pots (or valleys) of the PDF represent the lane boundaries (or regions wher e cars don’t drive).” ’916 patent col.6 ll.15-18. The specification also explains that statistical te chniques are used to identify the boundaries between lanes, a nd that these boundaries are then used to define the lanes for the purpose of detecting where vehicles drive. See id. col.7 l.51-col.9 l.6.

2008-1129,-1160 6B. The Accused Device As do prior art systems, EIS’s RTMS X3 detects and counts vehicles in several lanes of a thoroughfare over an extended period of time. T he initial determination of lane locations may occur manually or may be a ssisted by the auto se t-up feature of a program called the “Setup Wizard .” It is this auto set-up feature of the RTMS X3’s Setup Wizard that Wavetroni x accuses of infringement. While the parties emphasize different aspects of the system , there is no material disput e of fact as to how the accused system operates. The RTMS X3 sensor unit, or transceiver, has a field of view th at extends across a given roadway. The field of view is divi ded into thirty-two “range slices,” each having a width of about three meters, i.e., the approx imate width of a normal traffic lane. The transceiver is attached to a pole alongside the road, and a human installer connects the transceiver to a laptop computer. The tran sceiver detects passing automobiles, and a graphic on the computer screen displays small images to represent them. The system cannot accurately assign any particular aut omobile to a lane unt il range slices are matched up with actual lanes in the transceiv er’s field of vision. The human installer may define lanes manually by aligning the lane boundaries on the computer’s screen with the spaces between blip s displayed on the laptop that represent passing automobiles. Alternatively, t he installer may choose to use the Setup Wizard’s auto setup feature. If this feature is chosen, the installer tells the RTMS X3 how many lanes to expect. The RTMS X3 then monitors and records automotive traffic for one minute. 3

3 Naturally, this process will not work on an empty road but must rather be used at a time and place in which it may be expected that a significant number of automobiles will pass through the lanes on the road.
2008-1129,-1160 7During that one minute, the transceiver continuously transmits radar signals toward the roadway and detects the reflected signals, while the Setup Wizard processes the data so generated in se veral steps. First, every ten milliseconds the system generates a series of thirty-two numbers co rresponding to the strength of the reflected radar signal in each of the thirty-two range slices. A processor independently compares each of the thirty-two values to a particular “detection threshold.” The results of this comparison are stored in a thirty-two posi tion array, i.e., a s equence of thirty-two locations in the transceiver’s memory called the “Q-vector.” The Q-vector stores, for each range slice, the differ ence between its reflected radar strength and the detection threshold. Only if an automobile has dr iven in a particular range slice within the preceding ten milliseconds wil l the Q-vector contain a positive value corresponding to the position of that range slic e. The values in the Q-ve ctor are replaced every ten milliseconds as new signal measurements are taken by the sensor. During the oneminute set-up process, the contents of the Q- vector array are continuously sent to the laptop, where they are replic ated in an array called the “REQ array.” The REQ array processes only about twenty pe rcent of the Q-vector data that is generated, because the transceiver generates data faster t han it can be transmitt ed to the laptop. As data is sent to the laptop’s REQ array, the Setup Wizard software identifies “local maxima” for each ten-millisecond in crement of time. A local maximum is identified when the value at a particular position in the th irty-two position REQ array is greater than the values at the positions to t he immediate left or righ t. After identifying all of the local maxima present in the REQ arra y during a given ten-millisecond interval, the Setup Wizard software ignores everything except the “first” local maximum, which is the

2008-1129,-1160 8local maximum nearest to the sensor. T he various stages of processing so far described result in the production of one “f irst local maximum” corresponding to one of the thirty-two range bins every ten milliseconds. The next step involves an array called the “NAMP array.” Wavetronix contends that it is the NAMP array that “generat[e s] a probability density function estimation” as described in claim 1, step (b), of the ’916 patent. As a fi rst local maximum is produced every ten milliseconds, the NAMP array, wh ich like the other arrays has thirty-two positions, adds up the number of first local maxima per position over the course of the one-minute set-up period. The system reco rds first local maxima, not discrete automobiles. Unless an aut omobile is exceedingly fast or sm all, it is likely to produce multiple first local maxima when passing th rough the sensor’s field of vision. The following illustrations depict tw o notional automobile s driving through the RTMS X3 field of vision. Only five range slices, numbered 0 through 4, are depicted. Range slices 1-3 correspond to lanes, while range slices 0 and 4 correspond to shoulders. As each automobile drives through the field of vision in a given lane, a number of first local maxima register in the NAMP array. 4

4 These illustrations, taken from Wa vetronix’s principal brief, describe the graph on the right of each i llustration as a “NAMP Array His togram.” The court does not necessarily adopt the description of t he NAMP array as a “histogram.”
2008-1129,-1160 92008-1129,-1160 10As noted, the RTMX X3’s field of vision ac tually contains thirty-two range slices, not just five. Upon completion of the one minut e period, the NAMP array contains thirtytwo values corresponding to each of the th irty-two range slices. These NAMP array values are used to define lanes. Specifical ly, the Setup Wizard defines as a lane any range slice for which the final count in the NAMP array exceeds abo ut one percent of the total number of Q- vectors analyzed in the laptop. Because the set-up period lasts about one minute, a giv en range slice must register a minimum of approximately ten counts in order for the system to determine t hat the range slice corre sponds to a lane.

2008-1129,-1160 11A range slice is either found to correspond to a lane or it is not. If fewer lanes are found than the human installer told the system to expect, then the one-minute detection and recording stage repeats itsel f. If more lanes have been found than expected, the system deletes the lanes that registered the least number of first local maxima until the expected number of lanes is reached. Upon completion of the set-up phase, the Setup Wizard has identified which of the thirty-two range slices spanning the sensor’s field of vision actually correspond to traffic lanes. The system is then ready to begin the longterm monitoring of vehicle tra ffic within the i dentified lanes. C. Relevant Procedural History Wavetronix filed this action on January 27, 2005. On March 13, 2006, the district court granted summary judgment to Wavetroni x on EIS’s best mode defense, finding as a matter of law that EIS could not prevail on the defense. The district court similarly granted summary judgment to Wavetronix on EIS’s inequitable conduct defense, on May 18, 2006. The court conducted some f ourteen days of pre-trial hearings and, on September 21, 2007, ent ered an order granting summary j udgment of non-infringement. At no time did the court enter a claim construction order. After entry of judgment dismissing Wavetronix’s claim of infringement and EIS’s count erclaims of invalidity and unenforceability, Wavetronix timely appealed and EIS timely cross-appealed. We have jurisdiction pursuant to 28 U.S.C. § 1295(a)(1). II. DISCUSSION The appeal and cross-appeal are taken from judgment entered by the district court following grants of summary judgment. A court may grant summary judgment only when, drawing all inferences and resolving all doubts in favor of the non-moving party,

2008-1129,-1160 12there are no genuine issues of material fact and the moving party is entitled to judgment as a matter of law. F ed. R. Civ. P. 56(c). See generally Anderson v. Liberty Lobby, Inc. , 477 U.S. 242 (1986). A fact is “material” if it may affect the outcome of the proceedings, and an issue of material fact is “genuine” if the evidence is such that a reasonable jury could return a ve rdict for the non-moving party. Anderson , 477 U.S. at 248. The moving party bears the burden of identif ying those portions of the pleadings, discovery and affidavits that demonstrate t he absence of a genuine issue of material fact. Celotex Corp. v. Catrett , 477 U.S. 317, 323 (1986). On ce the moving party meets its initial burden, the non-moving party mu st go beyond the pleadi ngs and, by its own affidavits or discovery, set forth specific facts showing that there is a genuine issue for trial. Fed R. Civ. P. 56(e); see Anderson , 477 U.S. at 250. We re view a district court’s grant of summary judgment de novo. Netscape Commc’ns Corp. v. Konrad , 295 F.3d 1315, 1319 (Fed. Cir. 2002). A. Claim Construction The district court determined as a matter of law that the EIS system does not infringe the ’916 patent. Infringement analysis involves a two-step process: the court first determines the meaning of disputed claim terms and then compares the accused device to the claims as construed. Markman v. Westview Instruments, Inc. , 52 F.3d 967, 976 (Fed. Cir. 1995), aff’d , 517 U.S. 370 (1996); see also Middleton, Inc. v. Minn. Mining & Mfg. Co. , 311 F.3d 1384, 1387 (Fed. Cir. 2002). The district court did not explicitly cons true claim 1’s “probability density function estimation” limitation. The parties agree t hat this is the only claim term requiring construction. They urge this court to c onstrue the term on appeal rather than remand

2008-1129,-1160 13for claim construction. There being only one independent clai m in dispute and no material issues of fact as to how the accused system works, the construction of that term is the key issue for deciding infringement. Although claim construction is a question of law, we generally refuse to construe claims in the first instance. See, e.g. , Metro. Life Ins. Co. v. Bancorp Servs., L.L.C. , 527 F.3d 1330, 1336 (Fed. Cir. 2008); Electro Scientific Indus., In c. v. Dynamic Details, Inc. , 307 F.3d 1343, 1350 (Fed. Cir. 2002); Bayer AG v. Biovail Corp. , 279 F.3d 1340, 1349 (Fed. Cir. 2002). But see Frank’s Casing Crew & Rental Tools, Inc. v. PMR Techs., Ltd. , 292 F.3d 1363, 1373 (Fed. Cir. 2002). We hav e explained that this court’s review, although de novo, is not to function as an independent analysi s in the first instance. See Nazomi Commc’ns, Inc. v. Arm Holdings, PLC , 403 F.3d 1364, 1371 (Fed. Cir. 2005). In this case, however, we accept the parties’ invitation to construe the “probability density function estimation” claim term, for three reasons . First, although the district court did not specifically constr ue the claim term, its opinion references the question of claim construction, and it is apparent that the di strict court’s views on the matter have been exhausted. See id. (noting importance of taki ng into account views of trial judge); see also Fireman’s Fund Ins. Co. v. United States , 909 F.2d 495, 499 (Fed. Cir. 1990) (addressing new argument in fi rst instance where remand would serve no useful purpose). Second, both parties have agreed that we should construe the claim limitation. Third, we agree that the record , which includes consi derable evidence and expert testimony, has been sufficiently devel oped to enable us to construe the claim term without prejudicing either party. See Fireman’s Fund , 909 F.2d at 499; cf. Apex, Inc. v. Raritan Computer, Inc. , 325 F.3d 1364, 1374-75 (Fed. Cir. 2003) (declining to

2008-1129,-1160 14construe claim terms where record had not been sufficiently developed, because prejudice could result). A claim term is construed according to its ordinary and cust omary meaning as understood by a person of ordinary skill in th e art at the time of the invention. Phillips v. AWH Corp. , 415 F.3d 1303, 1312-13 (Fed. Cir. 2005) (en banc). 5 “[T]he court looks to those sources available to the public that show what a person of skill in the art would have understood disputed claim language to mean,” including “the words of the claims themselves, the remainder of the specificat ion, the prosecution history, and extrinsic evidence concerning relevant scientific principles, the m eaning of technical terms, and the state of the art.” Id. at 1314 (citations and internal quotation marks omitted). A dictionary definition may be reli ed upon “so long as [it] does not contradict any definition found in or ascertained by a re ading of the pat ent documents.” Id. at 1322-23 (quoting Vitronics Corp. v. Conceptronic, Inc. , 90 F.3d 1576, 1584 n.6 (Fed. Cir. 1996)). There is no dispute that a “probability density function estimation” (“PDFE”) is, in some manner, an “estimation” of a “probability density function” (“PDF”). In the words of Wavetronix’s expert, “probability density function is a precisely defined term in statistics which corresponds to the probabilities of the different possible outcomes of some experiment.” EIS agrees that “PDF” is a well known mathematics term and offers the following dictionary definition: “a function of a continuous variable whose integral over a region gives the probability that a random variable falls within the region.” 6 While the

5 Neither party has ar gued that the other party’s proffered experts are unqualified to opine as persons of ordinary skill in the art.

6 Random House Webster’s Unabridged Dictionary 1541 (2d ed. 2001). This definition comports with those found in other general reference and technical
2008-1129,-1160 15parties agree upon the definition of “PDF,” they dispute the definition of “PDFE.” We conclude below that the salient difference between the two concepts is that a PDF is a mathematical function, whereas a PDFE is an approximation of su ch a function using actual finite data. We al so explain below that, in li ght of the teachings of the specification and the recitation of the PDFE within the claim language, for the purposes of claim 1 a PDFE must estimate a PDF with sufficient precision to indicate both where vehicles are located and where they are not. In other words, as the specification teaches, a PDFE should at a minimum pr ovide enough data to ascertain “peaks” and “valleys” approximating the centers and boundaries of traffic lanes, respectively. In advocating for its construction of “PDFE,” EIS focuses on the term “probability” and argues that a PDFE must represent some sort of probabilistic analysis. Wavetronix argues that the “E” in “PDFE” modifies the whole phrase “PDF,” not just “P” or “probability.” According to Wavetronix, an “estimate” of a PDF need not have all of the characteristics of an actual PDF, includi ng estimating the actual probability that a vehicle has driven in a give n lane. Rather, as we u nderstand Wavetoni x’s argument, any histogram that allows for an estimati on of lane boundaries is a PDFE, because any graph that accurately allows for lane detection must have some correlation with the number or probability of cars in each lane. Wavetronix argues that the definition that most aligns with the specific ation and includes all of the disclosed embodiments is “a tabulation of frequencies of vehicle positions.”

dictionaries. See, e.g. , Webster’s Third New International Dictionary 1806 (2002) (“a function of a continuous random variable w hose integral over an interval gives the probability that its value will fall within the interval”); McGraw-Hill Dictionar y of Scientific and Technical Terms 1674 (6th ed. 2003) (“[a] real-valued function whose integral over any set gives the probability that a random variable has values in this set”).
2008-1129,-1160 16The claim language itself provides littl e guidance on how to define “PDFE,” and the parties have not relied u pon the patent’s prosecution history to define the proper scope of the claim limitations referencing a PDFE. 7 The patent’s specification does provide guidance, but its refer ences to PDFE are not entirely consistent. Nowhere does the patent set forth an explic it definition of PDFE. See Phillips , 415 F.3d at 1316 (patentee may act as own lexicographer); Johnson Worldwide Assocs., Inc. v. Zebco Corp. , 175 F.3d 985, 990 (Fed. Cir. 1999) (same). Th e specification refers variously to: a PDF “as estimated,” ’916 pat ent col.6 l.6; using a PDF “t o estimate” lane boundaries, id. col.6 ll.14-15; “PDF estimation,” id. col.6 l.32; a “PDF estimator,” id. col.6 l.33; and “estimated PDFs,” id. col.8 l.13. In some places, the specification appears to refer to PDF and PDFE interchangeably. Id. col.4 ll.1-7, col.7 ll.30-39. The concept of “PDF” is defined with greater clarity and consistency in the specification than is the concept of “PDFE” standing alone. Both the summary of the invention and the description of the preferred embodiment s describe the concept of PDF in terms of a graph in which enough dat a is collected to observe peaks, which

7 The parties look to the patent’s pr osecution history only for the purposes of supporting their respective positions on the question of whether claim 1 requires the counting of discrete vehicles. EIS points out that Wavetronix remained silent in the face of the patent examiner’s characterization of the patent’s method as “determining . . . the number of cars which pass beneath [the sens or].” According to EIS, Wavetronix conceded through its silence that the patent claimed the counti ng of discrete vehicles as opposed to mere vehicle detections that may or may not yield an accurate tally of individual vehicles. The parties have expended considerable effort arguing this point. Whatever the merits of the argument, see 3M Innovative Props. Co. v. Avery Dennison Corp. , 350 F.3d 1365, 1373-74 (Fed. Cir. 2003) (sile nce does not necessarily indicate acquiescence to examiner’s characterization when allowance is on grounds unrelated to characterization), it is unnecessary to dec ide whether the clai m encompasses only detections of discrete vehicles . Even if the claim also encompasses vehicle detections, an accused system must still g enerate a PDFE and define la nes from said PDFE to infringe. For the same reason, it is also unnecessary to dete rmine whether a PDFE requires “unbiased” or “normalized” data, as asserted by EIS.
2008-1129,-1160 17represent the centers of lanes, and valleys, which represent the lane boundaries or edges. See, e.g. , id. col.4 ll.2-7 (summary of inv ention) (“The probability density function describes the probability that a vehicl e will be located at any range. The peaks of the probability function repr esent the center of each la ne and the valleys of the probability density function represent the lane boundaries.”); id. col.6 ll.15-19 (explanation of Figure 3, a diagram of t he method) (“The peaks of the PDF represent the center of each lane and the low spots (or valleys) of the PDF represent the lane boundaries (or regions where cars don’t drive). The lane boundaries are set to be the low spots (or valleys) between peaks.”). This “peaks and va lleys” arrangement allows for the definition of lanes from the PDFE as recited in step (c) of claim 1. The understanding of PDF as a data plot showing a range of high values (“peaks”) and low values (“valleys”) as explicat ed in the specificatio n aligns well with the standard mathematics defin ition of PDF. A PDF is a theor etical mathematical function that seeks to model reality. As Wavetronix’s expert not ed, a PDF does not represent actual data. When displayed on a histogram , a PDF is a smooth line or curve, because it is produced by a mathematical equation. When a finite set of actual data is plotted on a histogram, the resulting plot will not be a smooth curve but rather a disjointed one. See, e.g. , ’916 patent fig.8. Such a plot ma y be represented by points connected with lines or by a series of bars. The more dat a that is collected and plotted, the smoother the line will be; however, a pl ot based on data would require an infinite number of data points to duplicate the perfect smoothness of a mathematical function. In real-world situations such as traffic monito ring, it is impossible to collect infinite data, but a plot of a significant number of automobiles can estima te the mathematical curve that would

2008-1129,-1160 18describe the automobiles’ distri bution. A PDF and a PDFE do not, therefore, differ in the sense of allowing for a comparison of values over a range of positions. The distinction between them lies, rather, in the fact that a PDF is a perfectly smooth mathematical function, whereas a PDFE is an estimation of some hypothetical PDF. The PDFE is not perfectly sm ooth, but it has the advantage of being based on actual data. The specification is hardly a paragon of clarity, but this understanding of PDF estimation comports with the various descrip tions and explanations of the PDF and PDFE concepts found in the specification. There are differences between the embodiments disclosed in the specification, but each of them suggests that a number of data points is used to esti mate a hypothetical mathematical model, i.e., a PDF. One embodiment (shown in the hist ogram at Figure 7) uses “normalized” data, i.e., data displayed as a percentage of a total rather than as raw counts, while at least one (shown in the histogram at Figure 8) does not. 8 Two embodiments apparently refer to a count of individual vehi cles (Figures 6 and 8), see ’916 patent col.7 l.25 (“The number of vehicles in each bin is counted . . . .”), while a third (Figure 7) could just as easily refer to vehicle detections, i.e., the number of signals bounced back to the transceiver, which may be more than one per vehicle. What is the same about all of the disclosed embodiments (Figures 6, 7 and 8) is that each of them r epresents, in the form of a histogram, a comparison of the number of vehicles or vehicle detections across a range.

8 That Figure 7 represents a normalized graph is indicated by the fact that the y-axis is scaled from zero to one. A gi ven value is expressed as a fraction of the whole, rather than as a raw count of detections. Determini ng the fraction of the whole represented by a given value in Figure 8, which is not normalized, would require dividing that value by the total number of counts measured in all positions.
2008-1129,-1160 19This ability to compare the data across a range is significant, because it provides information not only about wher e vehicles are but where they are not—i.e., where traffic lanes begin and end. 9 Such data is used for “defining . . . traffic lanes . . . from said [PDFE].” The record reveals no material intrinsi c or extrinsic evidence indicating that the attribute of a PDF that a PDFE does not possess is the fundamental property of functioning over a range. In summary, what makes a PDFE an estimate of a PDF in the context of the ’916 patent is the fact that a PDFE is based on actual data points, ra ther than a perfectly smooth, if hypothetical, mathem atical function or model. But a PDFE, like a PDF, has the characteristic of comparing values acro ss a range of positions. The court therefore construes a PDFE to be “a finite data set large enough to approx imate a function of a continuous variable whose integral over a r egion gives the probabili ty that a random variable falls within the region.” Th is construction applies equally to step (b) (“generating a [PDFE] . . .”) and step (c) (“def ining . . . traffic lanes . . . from said [PDFE]”) of claim 1; however, our infringement analysis infra focuses on step (c).

9 The patent contains two referenc es suggesting that some embodiments may have only one range bin per lane. See ’ 916 patent col.7 ll.7-8 (“[A] lane may be comprised of a plurality of bins) (emphasis added); id. col.9 ll.58-61 (a limitation in claim 3 claiming a plurality of r ange bins in each lane, whic h appears redundant if claim 1 already implies this limitation). No doubt, usi ng one bin per lane would not result in an optimal lane definition using the “peaks” and “valleys” met hod. Nevertheless, there is nothing plainly suggesting that, if only one bi n per lane were used, the method would take advantage of some technique other than comparing values acro ss a range of lanes to define lanes. The specification teaches t hat range bins of a wid th that results in histograms without “peaks” and “v alleys” are incapable of providing useful information about where vehicle lanes begin and end. This t eaching is an essential characteristic of the patented system, and is relevant to the analysis of both literal infringement and infringement under the doctrine of equivalents.
2008-1129,-1160 20B. Literal Infringement Aided by our construction of PDFE, we now turn to the question of literal infringement. “Literal infringement of a properly construed claim is a question of fact.” Applied Med. Res. Corp. v. U.S. Surgical Corp. , 448 F.3d 1324, 1332 (Fed. Cir. 2006). “We affirm a district court’s grant of summary judgment of non-infringement only if, after viewing the alleged facts in the light most favorable to the non-movant, there is no genuine issue as to whether the accused dev ice is encompassed by the claims.” Combined Sys., Inc. v. Def. Tech. Corp. of Am. , 350 F.3d 1207, 1210 (Fed. Cir. 2003) (citation omitted). Wavetronix contends that the RTMS X3 Se tup Wizard uses the NAMP array data to perform the step of “definin g . . . traffic lanes” as set forth in step (c) of claim 1. Wavetronix characterizes the operation of the Setup Wizard software as using detections of first local maxima to conclude “it is probable” vehicles travel in certain range slices. EIS counters that the accu sed device performs no probability analysis, and indeed that no such probability analysis could be perfo rmed using the NAMP array. While the NAMP array collects data for a number of bins corresponding to spatial positions, these data cannot fairly be said to represent probabilities. EIS states that its device never conducts any probabilistic analysis to search for “peaks” and “valleys” in a histogram, wherein valleys would represent boundaries betwe en the lanes. Rather, because the EIS system uses bins that are the full width of normal traffic lanes, the data collected in the NAMP array is simply too coarse to reveal any “peaks” representing lane centers or any “valleys” representing lane boun daries. EIS argues that its system actually employs a much simpler methodology that identifies traffic lanes by applying a

2008-1129,-1160 21common threshold value to the NAMP data. EIS also notes that the system requires manual intervention by a human to set the pr ecise boundaries of traffic lanes. Because the NAMP array does not have any of the essential properti es of the PDFEs described in the ’916 patent, EIS argues t hat its system cannot meet the “defining said traffic lanes . . . from said [PDFE]” limitation, either literally or by equivalents. Properly construed, the PDFE claim term requires a representation of vehicle frequencies across a range of pos itions with sufficient deta il to provide meaningful information about where traffic lanes begin and end. This detail allows for the definition of lanes claimed in step (c). In contrast, the processing of the s ensor data in the NAMP array, which the parties agree is used to select lanes, does not involve comparisons among values for the range slices. As noted, the parties are in agreement as to how the accused system operates. In the words of Wavetronix’s brief, “[T]he Wizard defines a lane as any range slice for which the final count in the NAMP array exceeds about one percent of the total number of Q-vectors analyzed in the laptop.” The analysis of the NAMP array data does not involve com parisons across lanes using “peaks” and “valleys” or any similar method. The det ermination that any particular range slice corresponds to a lane is made independently fo r each range slice, without reference to the values in other range slic es. In other words, the r ange of highs and lows in the NAMP array does not provide data from wh ich the user could extrapolate lane boundaries. Thus, the character of t he NAMP data does not comport with our previously stated construction of PDFE. As an example, imagine a four-lane highwa y, and imagine further that the NAMP array values collected for the f our lanes are x, x-1, x+2 and x+1, in that order. The fact

2008-1129,-1160 22that x+2 is the highest value (and could accordingly be de scribed as a “peak”) and that x-1 is the lowest value (and could be descr ibed as a “valley”) is irrelevant to the definition of traffic lanes. T here is only one value per lane; therefore, both the “peak” and the “valley” represent whole lanes, rat her than lane centers or boundaries. This illustrates that the data set produced in the NA MP array is too coarse to be a PDFE in the sense required by the ’ 916 patent. The RTMS X3 selects lanes by analyzing the NAMP array data, and the NAMP array cannot be a PDFE. Accordingly, we hold as a matter of law the RTMS X3 does not practice the “defining . . . traffic lanes” step of claim 1 and therefore does not litera lly infringe the ’916 patent. C. Doctrine of Equivalents Wavetronix argues that the district cour t failed to give adequate consideration to the possibility of infringement by equivalents. EIS contends that Wavetronix waived the argument below. We assume without decidi ng that Wavetronix did not waive the argument. The essential inquiry under the doctrine of equivalents is whether “the accused product or process contain[s] elements identical or equivale nt to each claimed element of the patented invention.” Warner-Jenkinson Co., Inc. v. Hilton Davis Chem. Co. , 520 U.S. 17, 40 (1997). As with literal infringement, infringe ment by equivalents is a question of fact. Id. at 38. “An element in the accuse d product is equivalent to a claim limitation if the differ ences between the two are ‘insubstantial’ to one of ordinary skill in the art.” Eagle Comtronics, Inc. v. Arrow Commc’n Labs., Inc. , 305 F.3d 1303, 1315 (Fed. Cir. 2002) (citing Warner-Jenkinson , 520 U.S. at 40); see also Graver Tank & Mfg. Co. v. Linde Air Prods. Co. , 339 U.S. 605, 609 ( 1950). A plaintiff can prove equivalence

2008-1129,-1160 23by showing on a limitation-by-limitation basis that the accu sed product performs substantially the same function in substant ially the same way with substantially the same result as each claim lim itation of the patented product. Eagle Comtronics , 305 F.3d at 1315 (quoting Graver Tank , 339 U.S. at 608); see also Warner-Jenkinson , 520 U.S. at 39-40. A court ma y not apply the doctrine of equivalents where so doing would effectively eliminate a cl aim element in its entirety. Warner-Jenkinson , 520 U.S. at 29; Carnegie Mellon Univ. v. Hoffmann-La Roche, Inc. , 541 F.3d 1115, 1129 (Fed. Cir. 2008). The Setup Wizard does not define lanes in substantially the same way as the patented method because it simply confirms whether the range slices of uniform width set in the system by the operat or are aligned with actual tr affic lanes on a one-to-one basis. Indeed, the Setup Wizard’s determinati on of where lanes are located is made in relation to a specific threshold, rather than as a comparison between different range slices. The significance of this difference ma y be illustrated by returning to the example of the series of four hypothet ical NAMP array values x, x-1, x+2 and x+1. If the threshold value were, for exampl e, x-3, then all four of t he values would be determined by the EIS system to represent lanes, regardless of any “peak” or “valley,” because they all exceed the threshold. If, on the other han d, the threshold val ue were x+3, then none of the values would be determined to represent lanes. 10 The “peaks” and “valleys” that are so critical to the met hod of the ’916 patent are irrele vant to the way the Setup Wizard uses data to select lanes. Claim 1 of the ’916 patent requires the definition of

10 To put it another way, the integral over a given NAMP region does not indicate the probability a vehicle has driven within that region, as is required by our construction of PDFE.
2008-1129,-1160 24lane boundaries by analyzing vehicle tra ffic both among and within lanes to determine where cars are actually driving, which as a matter of probability should reveal the centers of the lanes. In contrast to the ’9 16 patent’s definition of traffic lanes from a PDFE, none of the operations on or by t he Q-vector, REQ array or NAMP array use any meaningful information about where traffic lanes begin and end to accomplish lane selection. The system can us e the data only to confirm w hether a range slice that is already pre-selected to be the fu ll width of a traffic lane is or is not within the trafficked roadway—it does not compare data across di fferent bins to locate the boundaries between lanes. Assuming arguendo that the EIS system can be said to “define” traffic lanes, it does so in a very different way than the way taught by the ’916 patent. It cannot be said that these diffe rences are insubstantial. Wavetronix has focused exclusively on th e NAMP array as the step in EIS’s process that purportedly gener ates a PDFE from which la nes are defined. Data is processed using several arrays, however. In the context of a patent in the mechanical arts, we have noted: “[T]wo physical comp onents of an accused device may be viewed in combination to serve as an equivalent of one element of a claimed invention, as long as no claim limitation is thereby wholly vitiated.” Searfoss v. Pioneer Consol. Corp. , 374 F.3d 1142, 1151 (Fed. Cir. 2004) (alter ation in original) (quoting Ethicon Endo-Surgery, Inc. v. U.S. Surgical Corp. , 149 F.3d 1309, 1320 (Fed. Cir. 1998)). If the data associated with some other array could be de scribed as a PDFE, it could be argued that the combination of that arra y and the NAMP array infringes the “defining . . . traffic lanes” step by equivalents. As noted above, some comparisons across lanes are made in relation to the REQ array to the extent th at a local maximum is defined at any array

2008-1129,-1160 25position having a higher value than do the positions to its i mmediate left or right. This suggests that the operations carried ou t with the REQ array could perhaps be expressed in terms of PDFEs. Concei vably, expert testimony on remand might establish that each of t hese repeated comparisons across a few range slices approximates a function of a continuous variabl e whose integral over that limited region gives the probability that some random variable falls within the region, as required by our construction of “PDFE.” Even so, there would be no infringement by equivalents. Even if these comparisons within the REQ array were de termined to be PDFEs, the “way” in which the combination of the REQ array and the NAMP array defines lanes—assuming the EIS system “defines” lanes at all, in the sense of the ’9 16 patent—is much different. During the one minute set-up period, a multit ude of comparisons are made in the REQ array to generate the NAMP data that is used to define lanes by applying a threshold. Neither claim 1 nor the specification foresees the use of a multiplicity of PDFEs to define lanes. The claim languag e describes defining lanes fr om “said” PDFE, and every embodiment in the specification teaches the us e of a method that can be described by a single PDFE. This problem notwithstanding and as noted above, the RTMS X3 does not assist in the identification of traffic lane boundaries: it ca n only use the data it collects to confirm whether a ra nge slice that is already pre- selected to be the full width of a traffic lane is or is not within the tr afficked roadway. Accordingly, even if the combination of the NAMP array and the REQ a rray could be said to “defin[e] . . . said traffic lanes . . . from said [PDFE]”—and it c annot—it would still do so in a very different way than the patented invention. For these reasons, looking beyond the NAMP array

2008-1129,-1160 262008-1129,-1160 27 would not salvage Wavetronix’s infringement ca se. There is as a matter of law no infringement by equivalents. D. Cross-Appeal The district court determined on summary judgment that EIS could not prevail on its inequitable conduct and be st mode counterclaims. EIS has cross-appealed these two rulings. Having considered the cross-appeal , we affirm the distri ct court’s grant of summary judgment on the counterclaims. III. CONCLUSION We agree with the district court, albeit on different grounds, that as a matter of law the RTMS X3 does not infringe claim 1 of the ’916 patent. We also agree that defendant-cross appellant’s counterclaims should be dismissed.
AFFIRMED

. COSTS Each party shall bear its own costs on appeal.