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`UNITED STATES PATENT AND TRADEMARK OFFICE
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`BEFORE THE PATENT TRIAL AND APPEAL BOARD
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`APPLE INC.,
`Petitioner,
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`v.
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`IMMERVISION, INC.,
`Patent Owner.
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`Case IPR2023-00471
`Patent 6,844,990
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`PETITIONER’S REPLY TO
`PATENT OWNER’S RESPONSE
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`Proceeding No.: IPR2023-00471
`Attorney Docket: 50095.0114IP1
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`TABLE OF CONTENTS
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`
`
`I.
`
`Claim 27 is Rendered Obvious by the Presented Combination of Baker and
`Shiota ............................................................................................................... 1
`The Petition and Dr. Kessler’s Testimony—When Considered in Their
`Proper Context—Demonstrate that Shiota’s Teachings as Applied in
`Combination with Baker Render Obvious Limitation [27f] ........................ 3
`ImmerVision’s Rebuttals are Premised on Mischaracterizations of the
`Record .......................................................................................................... 7
`ImmerVision’s Attempts to Distinguish Shiota Fail Because Shiota’s
`Image Transformation Techniques are Commensurate to Those Disclosed
`by the ’990 Patent’s Specification ............................................................. 14
`Claim 2, 4, 29, and 30 Are Rendered Obvious by the Presented Baker-Shiota
`and Baker-Shiota-Fisher Combinations ........................................................ 23
`III. Conclusion ..................................................................................................... 24
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`
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`
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`A.
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`B.
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`C.
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`II.
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`
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`i
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`Proceeding No.: IPR2023-00471
`Attorney Docket: 50095-0114IP1
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`PETITIONER’S EXHIBIT LIST
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`APPLE-1001
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`U.S. Patent No. 6,844,990 to Artonne et al. (“the ’990 patent”)
`
`APPLE-1002
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`Prosecution History of the ’990 Patent (“Original Prosecution
`History”)
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`APPLE-1003
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`Declaration of Dr. David Kessler, Ph.D.
`
`APPLE-1004
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`Curriculum Vitae of Dr. David Kessler, Ph.D.
`
`APPLE-1005
`
`Service of complaint in ImmerVision, Inc. v. Apple, Inc., D.Del.
`1:21-cv-01733-MN-CJB (January 18, 2022)
`
`APPLE-1006
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`U.S. Patent No. 5,686,957 to Baker (“Baker”)
`
`APPLE-1007
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`“Fish Eye Lens” by K. Miyamoto (Feb. 19, 1964) (“Miyamoto”)
`
`APPLE-1008
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`Service of complaint in ImmerVision, Inc. v. Apple, Inc., D.Del.
`1:21-cv-01484-MN-CJB (January 18, 2022)
`
`APPLE-1009
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`U.S. Patent No. 3,953,111 to Fisher et al. (“Fisher”)
`
`APPLE-1010
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`U.S. Patent No. 6,128,145 to Nagaoka (“Nagaoka”)
`
`APPLE-1011
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`Reexamination File History for the ’990 Patent (“Reexam
`History”)
`
`APPLE-1012
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`EP 1028389 A2 to Shiota et al. (“Shiota”)
`
`APPLE-1013
`
`APPLE-1014
`
`Rebiai et al., “Image Distortion from Zoom Lenses: Modeling
`and Digital Correction,” 1992 IBC International Broadcasting
`Convention (July 1992) (“Rebiai”)
`
`JP 2000-242773 to Matsui et al. (“Matsui”) (original and
`translated documents also provided in APPLE-1011, 43-51, 180-
`198, as provided by Patent Owner during reexamination)
`
`ii
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`
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`APPLE-1015
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`APPLE-1016
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`APPLE-1017
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`APPLE-1018
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`APPLE-1019
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`APPLE-1020
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`APPLE-1021
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`APPLE-1022
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`Proceeding No.: IPR2023-00471
`Attorney Docket: 50095-0114IP1
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`
`U.S. Patent No. 5,861,999 to Tada (“Tada”)
`
`Zeljko Andreic, “Simple 180o field-of-view F-theta all-sky
`camera,” SPIE Proc. 1500 (Oct. 1, 1991) (“Andreic”)
`
`Abed Kassim et al., “Optical Performance of axial gradient and
`aspheric surface lenses: study and analysis,” SPIE’s 1994
`International
`Symposium
`on Optics,
`Imaging,
`and
`Instrumentation, Vol. 2263 (Sept. 30, 1994) (“Kassim”)
`
`Susan Houde-Walter, “Recent Progress In Gradient-Index
`Optics,” SPIE Proc. 0935 (Apr. 8, 1988) (“Houde-Walter”)
`
`Petition for Inter Partes Review of U.S. Patent No. 6,844,990,
`filed by Panasonic System Networks Co., Ltd. (IPR2014-01438)
`
`Paul K. Manhart et al., “Fundamentals of macro axial gradient
`index optical design and engineering,” SPIE Opt. Eng. 36(6),
`1607-1621 (June 1997) (“Manhart”)
`
`Vidal, “Interim Procedure for Discretionary Denials in AIA Post
`Grant Proceedings with Parallel District Court Litigation”
`(USPTO, June 2021)
`
`Scheduling Order entered in ImmerVision, Inc. v. Apple, Inc.,
`D.Del. 1:21-cv-01733-MN-CJB and ImmerVision, Inc. v. Apple,
`Inc., D.Del. 1:21-cv-01484-MN-CJB (entered on June 21, 2022)
`
`APPLE-1023
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`Second Declaration of Dr. David Kessler, Ph.D.
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`APPLE-1024
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`U.S. Patent No. 4,364,643 to Momiyama (“Momiyama”)
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`APPLE-1025
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`Deposition Testimony of Mr. James F. Munro
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`APPLE-1026
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`
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`Excerpts from “Modern Lens Design,” textbook authored by
`Warren J. Smith (1992 edition)
`
`iii
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`APPLE-1027
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`Proceeding No.: IPR2023-00471
`Attorney Docket: 50095-0114IP1
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`J. Weng, “Motion and Structure from Line Correspondences:
`Closed-Form Solution, Uniqueness, and Optimization,” IEEE
`Transactions on Pattern Analysis and Machine Intelligence, Vol.
`14, No. 3 (Mar. 1992)
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`iv
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`Proceeding No.: IPR2023-00471
`Attorney Docket: 50095-0114IP1
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`Petitioner Apple Inc. (“Apple” or “Petitioner”) submits this Petitioner Reply
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`(“Reply”) to ImmerVision’s Patent Owner Response (“POR”) to the IPR Petition
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`(“Petition”) of U.S. Patent 6,844,990 (“’990 Patent”), which challenges independent
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`claim 27 and claims 2, 4, 29, and 30 that depend from claim 27 (collectively, the
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`“Challenged Claims”).
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`
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`I.
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`CLAIM 27 IS RENDERED OBVIOUS BY THE PRESENTED
`COMBINATION OF BAKER AND SHIOTA
`ImmerVision does not dispute that a POSITA would have combined the Baker
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`and Shiota references, nor does it dispute that the resulting combination of Baker
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`and Shiota would have rendered obvious claim elements [27pre] to [27e]. See
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`generally POR. ImmerVision’s arguments are limited to limitation [27f], which
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`recites that “correcting the non-linearity of the initial image” is “performed by
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`retrieving image points on the obtained image in a coordinate system of center O’
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`using at least the non-linear distribution function and a size L of the obtained image.”
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`See POR, 1-2, 14-19; EX-2001, ¶¶49-58.
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`To demonstrate obviousness of this limitation, the Petition and the supporting
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`expert testimony of Dr. Kessler leveraged teachings of the Shiota reference as
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`applied in combination with the teachings of the Baker reference. See Petition, 45-
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`55, 22-27; APPLE-1003, ¶¶191-213, 128-139, 105-121. ImmerVision and its expert
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`(Mr. Munro) assert that Petitioner has failed to demonstrate that the Baker-Shiota
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`combination would render this claim feature obvious. POR, 1-2, 14-19; EX-2001,
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`¶¶49-58. However, in advancing their rebuttals, ImmerVision and its expert
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`mischaracterize the Petition by omitting key portions of the Petition’s analysis and
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`the corresponding testimony of Dr. Kessler, as well as the cited disclosures of the
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`Shiota reference, as applied in combination with Baker. See APPLE-1023, ¶¶50-76.
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`As explained below, Patent Owner’s arguments incorrectly characterize Dr.
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`Kessler’s testimony as mapping the claim feature of “size L of the obtained image”
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`to only Shiota’s reference to “magnification adjustment” in paragraph 23 of its
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`disclosure. This characterization, however, omits the surrounding context of that
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`paragraph in Shiota as relied upon by Dr. Kessler—namely, Shiota’s teachings of
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`variations in image size with image sensor size, using a normalized image size of 1
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`for its distribution function, and performing magnification adjustment to the image
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`in actual use—and how those teachings would have rendered obvious using the
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`actual image size (i.e., using size L of the obtained image, as claimed) as part of the
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`image transformation/correction. Id. Moreover, ImmerVision’s incomplete
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`narrative also omits that Shiota’s teachings (as leveraged in combination with Baker)
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`are commensurate with how the ’990 Patent’s specification describes performing the
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`correction of non-linearity of the image using the non-linear distribution function
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`and size L of the image, as recited in claim 27. APPLE-1023, ¶¶77-93.
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`2
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`Proceeding No.: IPR2023-00471
`Attorney Docket: 50095-0114IP1
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`A. The Petition and Dr. Kessler’s Testimony—When Considered in
`Their Proper Context—Demonstrate that Shiota’s Teachings as
`Applied in Combination with Baker Render Obvious Limitation
`[27f]
`The Petition, citing Dr. Kessler’s testimony, explained that the Baker-Shiota
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`combination would have rendered obvious limitation [27f], which recites correcting
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`the non-linearity of the image by retrieving image points on the obtained image in a
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`coordinate system of center O’ using at least the non-linear distribution function and
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`a size L of the obtained image. Petition, 22-27, 45-55; APPLE-1003, ¶¶191-213.
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`Specifically, and as explained in the Petition and Dr. Kessler’s supporting
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`testimony, the Baker-Shiota combination would have leveraged Shiota’s teachings
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`describing image correction by applying a correction coefficient (k2)—which is
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`determined based on a non-linear image distribution function—to the captured
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`image, to obtain transformed image points that compensate for the distortion in the
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`captured image. See Petition, 48-49; APPLE-1012, [0022]-[0024], [0037]-[0042];
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`APPLE-1003, ¶¶116-121, 128-138, 191-213. Specifically, Dr. Kessler explained
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`that Shiota determines this correction coefficient, k2, using the following equation:
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`k2 = h/r, where (1) h represents the height of an image point from the origin,
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`expressed using a non-linear image distribution function and (2) r is the distance
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`from the origin of an X, Y, Z coordinate system to the projected point on the image
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`plane. APPLE-1003, ¶¶116-121, 128-138, 201-202; APPLE-1012, [0037]-[0042],
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`[0036] (explaining that height (h) from the origin on the fisheye image face (origin
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`of the p, q coordinate system) to an image point w is expressed as a function of the
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`field angle and the focal distance).
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`The Petition further explained that the Baker-Shiota combination would have
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`also leveraged Shiota’s teachings to render obvious “using the size of the image” as
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`part of Shiota’s described image transformation/correction:
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`For its described image transformation operations, Shiota
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`assumes a normalized radius of 1 of the image circle at a
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`field angle of 90° (from the front of the lens). APPLE-
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`1012, [0023]. However, Shiota acknowledges that the
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`image circle diameter (i.e., the size of the image) “differs
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`according to at least the size of the [CCD] image pickup
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`device” (the size of the image disk/sensor) and that “at the
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`time of actual[] use, magnification adjustment
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`is
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`performed.” Id.
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`Attorney Docket: 50095-0114IP1
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`Petition, 50-51; APPLE-1003, ¶205. The cited portion of Shiota is reproduced
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`below (APPLE-1012, [0023] (annotated)):
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`
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`Given these disclosures in Shiota and in view of the above analysis, Dr.
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`Kessler opined that “these references to ‘magnification adjustment’ and variation in
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`image size based on size of the image disk/sensor refer to an adjustment that
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`accounts for the actual size of the image pickup device—and by extension, the actual
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`size of the image—as part of the image transformation.” APPLE-1003, ¶205. Dr.
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`Kessler further opined that “a POSITA would have understood or found obvious that
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`the image transformation described in Shiota, when applied to an actual
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`application[,] accounts for the size of the actual image for the underlying image
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`transformation.” APPLE-1003, ¶206.
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`Because the size of the image pickup device (and by extension the size of the
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`image) varies depending on the implementation (as Shiota expressly teaches), Dr.
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`Kessler explained that “a POSITA would have found it obvious to use the actual size
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`of the image—as applicable in Baker’s system—as part of the image transformation
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`to generate a properly compensated/transformed image for display.” APPLE-1003,
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`¶¶205-206; APPLE-1012, [0023]. Dr. Kessler further explained that a POSITA
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`would have understood or found obvious that the size of the image would be
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`represented using any appropriate units, e.g., pixels, inches, millimeters, etc.
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`APPLE-1003, ¶¶207-213 (citing APPLE-1006, 14:64-15:19; APPLE-1012, [0022]-
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`[0023], [0025], [0049]).
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`In this manner, the Petition in view of Dr. Kessler’s supporting testimony
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`demonstrated that the Baker-Shiota combination would have rendered obvious the
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`claim features reciting “correcting the non-linearity of the image by retrieving image
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`points on the obtained image … using at least the non-linear distribution function
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`and a size L of the obtained image,” where the size L of the obtained image would
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`be expressed in units of pixel or another appropriate unit. See Petition, 45-55;
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`APPLE-1003, ¶¶191-213.
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`ImmerVision’s Rebuttals are Premised on Mischaracterizations of
`the Record
`As explained below, ImmerVision advances multiple rebuttal arguments, each
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`B.
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`of which is premised on mischaracterizations of the Petition, Dr. Kessler’s
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`testimony, and the express teachings of Shiota. APPLE-1023, ¶¶50-76.
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`First, ImmerVision characterizes Dr. Kessler as relying on Shiota’s
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`disclosures of—“the radius of the fisheye image [being] set to 1” and that “‘[a]t the
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`time of actually (sic) use, magnification adjustment is performed’”—and
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`“conclusorily leap[ing]” from these teachings to the “assumption” that Shiota’s
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`described “magnification adjustment” is “an adjustment that accounts for the actual
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`size of the image.” POR, 15-16; see id. (similarly alleging that “Petitioner and Dr.
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`Kessler rely on Shiota’s reference to ‘magnification’ … as evidence of the [] claim
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`element” reciting “retrieving image points on the obtained image … using at least
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`… a size L of the obtained image”).
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`This mischaracterizes Dr. Kessler’s testimony because it omits key portions
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`of Shiota’s cited disclosures that formed the predicate for his testimony. APPLE-
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`1023, ¶¶50-51. The cited testimony (which is reproduced above and excerpted in
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`part below) confirms that Dr. Kessler was not limiting his discussion to just Shiota’s
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`reference to “magnification adjustment.” Id. Rather, Dr. Kessler’s testimony relied
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`upon Shiota’s teachings that: (1) the image circle diameter varies according to the
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`size of the image pickup device, and (2) while a normalized radius of 1 is assumed
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`at a field angle of 90 degrees, “magnification adjustment” is performed in “actual[]
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`use” as part of Shiota’s image transformation operations that retrieve the corrected
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`image points (id.):
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`Dr. Kessler’s Testimony
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`Cited Disclosure in Shiota
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`(APPLE-1003, ¶¶205-206)1
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`(APPLE-1012, [0023] (annotated))
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`image
`described
`its
`For
`transformation operations, Shiota
`assumes a normalized radius of 1
`of the image circle at a field angle
`of 90° (from the front of the lens).
`APPLE-1012, [0023]. However,
`Shiota acknowledges that the
`image circle diameter (i.e., the
`size of
`the
`image) “differs
`according to at least the size of
`the [CCD] image pickup device”
`(the size of the image disk/sensor)
`and that “at the time of actual[]
`use, magnification adjustment is
`performed.” Id.
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`
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`Second, ImmerVision and
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`its expert state
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`that magnification
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`is a
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`
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`“dimensionless quantity” and that “Dr. Kessler offers no explanation as to how or
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`why a POSA would have initially understood from Shiota’s reference to a
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`dimensionless number that Shiota suggests using the claimed linear quantity for
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`Emphasis added unless otherwise noted.
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`1
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`retrieving image points and correcting image distortion.” POR, 16; see EX-2001,
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`¶¶50-52. This argument again rests on the faulty premise that Dr. Kessler’s analysis
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`for this claim feature is exclusively limited to Shiota’s reference to “magnification
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`adjustment.” APPLE-1023, ¶52.
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`Moreover, ImmerVision fails to give proper weight and consideration to the
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`entirety of Dr. Kessler’s testimony for this limitation. Indeed, when considered in
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`its proper context, Dr. Kessler’s testimony demonstrated how the above-described
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`teachings in Shiota, as applied in combination with Baker, would have rendered
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`obvious using the non-linear distribution function and the size of the image to
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`retrieve the corrected image points for display. See APPLE-1023, ¶¶52-63.
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`Specifically, as Dr. Kessler explained, Shiota’s image transformation
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`algorithm uses a non-linear image distribution function, which Shiota refers to as the
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`quantity “h” representing a “height” from “the origin on the fisheye image face” to
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`“the point w” as expressed as a function of theta. See APPLE-1012, ¶¶[0036]-
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`[0042]; APPLE-1003, ¶¶120-121, 201-206; APPLE-1023, ¶¶53-54 (explaining that
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`the height also refers to radial distance or image height, and that angle θ relates to
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`the field angle). Shiota further states that the image size or radius, which is image
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`height, h, at a field angle of 90 degrees, is normalized to 1. APPLE-1012, [0023];
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`APPLE-1003, ¶¶205-206; APPLE-1023, ¶¶55-56 (explaining that h, or image height
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`at the extent of the image, occurs at the field angle of 90 degrees and constitutes the
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`image radius). Because Shiota’s image distribution function uses a normalized
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`image size/radius of 1, this function therefore identifies heights of image points
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`normalized on a scale ranging from 0 to 1. EX-1003, ¶¶205-206; APPLE-1023,
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`¶¶55-56 (because image height or distance is computed using a function that uses a
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`normalized image size of 1, the image height/distance in Shiota would be provided
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`in relative terms, on a scale ranging from 0 to 1); APPLE-1025, 23:14-21, 15:5-17:8,
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`37:18-38:6; APPLE-1012, [0023].
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`Notably, such normalization of image parameters (e.g., image size and focal
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`length) to a normalized value (e.g., 1) was well known and common in optics.
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`APPLE-1023, ¶¶56-58 (citing APPLE-1024, FIGS. 1-6, 2:6-8; APPLE-1009, FIGS.
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`3 and 4 (showing “normalized image height” ranging from 0 to 1); APPLE-1026,
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`53, 199 (showing full field/image size normalized to 1 while acknowledging the
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`actual image height of obtained image (referenced as GIH or gaussian image height)
`
`is 52.94 mm); APPLE-1027, p. 320 (normalizing image size and focal length to 1));
`
`APPLE-1025, 21:9-22:8, 23:6-24:10, 16:16-18:3 (Patent Owner’s expert confirming
`
`the same), 18:8-19:13. Indeed, Patent Owner’s expert confirmed that normalizing
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`the image size to 1 was “commonly done throughout the field of optics and lens
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`design” because “it makes the math more generic” (since “it is now independent of
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`actual image size”), “applicable to wider range of lens configuration” and “easier to
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`communicate” image heights “on that scale of 0 to 1.” APPLE-1025, 21:9-22:8,
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`23:6-24:10.
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`While the image heights are normalized on a scale of 0 to 1 to make the math
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`“independent of actual image size,” Patent Owner’s expert further confirmed that,
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`“when you are considering an actual application, then you would have to scale up to
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`account for the actual image size.” APPLE-1025, 21:9-22:8, 23:14-24:10; see also
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`id., 25:19-26-21, 39:1-18; APPLE-1023, ¶¶59-60; see APPLE-1026, pp. 53, 57; see
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`also APPLE-1027, p. 320. Consistent with this well-established practice in optics
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`of scaling normalized image heights using the actual size of the image to obtain
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`actual points of an image, the Baker-Shiota combination renders obvious computing
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`corrected image points using a non-linear distribution function, which uses a
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`normalized image size of 1, and scaling using the actual image size to obtain the
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`corrected, actual image points. EX-1003, ¶¶191-213; EX-1023, ¶¶59-60.
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`Specifically, Dr. Kessler testified that Shiota uses the non-linear distribution
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`function in computing its correction parameter (k2) that is used to obtain corrected
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`image points for display. APPLE-1003, ¶202 (citing APPLE-1012, ¶¶[0022]-
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`[0024], [0037]-[0042]). And, while the heights of the image points obtained using
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`this distribution function are normalized values (given that the function applies a
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`normalized image size/radius 1), Shiota also recognizes that, as part of its image
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`transformation, “projection coordinates” or image points on the “image pickup face
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`11
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`
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`are obtained ….” APPLE-1023, ¶61; APPLE-1012, [0023], [0036]-[0042]; APPLE-
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`Proceeding No.: IPR2023-00471
`Attorney Docket: 50095-0114IP1
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`1003, ¶¶199-213; see APPLE-1025, 29:22-30:4, 29:22-30:4. A POSITA would
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`have therefore recognized that, retrieving the coordinates/points on the image pickup
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`face (and within the projected image circle) would involve retrieving image points
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`on the actual image circle projected on an actual image sensor/image pickup
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`device—and not the image circle that has a radius/size normalized to 1. APPLE-
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`1003, ¶¶205-206; APPLE-1023, ¶61. Indeed, Shiota acknowledges this when it
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`states that “[i]n a position on an image pickup face (for example, position of a pixel
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`on a CCD image pickup device), the image circle diameter differs according to the
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`size of the image pickup device and the focal distance of the fisheye lens.” APPLE-
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`1023, ¶62; APPLE-1012, [0023]; APPLE-1003, ¶¶205-206.
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`As a consequence, while Shiota normalizes the image circle to a radius of 1,
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`Shiota unequivocally states that “magnification adjustment is performed” “[a]t the
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`time of actual[] use.” APPLE-1012, [0023]; APPLE-1023, ¶¶61-63, 55-60; APPLE-
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`1003, ¶¶191-213; see also APPLE-1003, ¶¶205-206; APPLE-1025, 23:6-24:10.
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`Thus, given Shiota’s express teaching that size of the image pickup device (and by
`
`extension size of the image) varies depending on the implementation, and because
`
`Shiota’s image transformation is illustrated using a normalized image size of 1, “a
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`POSITA would have found it obvious” to perform scaling or “magnification
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`adjustment”—which, again, was common and conventional in optics—by “us[ing]
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`the actual size of the image” to obtain the corrected image points (as obtained on the
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`actual image sensor/pickup device) for display. Id.
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`Third, ImmerVision and its expert characterize Dr. Kessler as “link[ing]”
`
`certain operator selected parameters described in paragraphs 24 to 26 of Shiota as
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`relating to the magnification adjustment referenced in Shiota’s paragraph 23. POR,
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`1-2, 16-19; EX-2001, ¶¶53-56. This is incorrect. Dr. Kessler cited to paragraphs 24
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`to 26 for their summary teachings of Shiota’s overall image transformation process
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`(see APPLE-1003, ¶205), which is further elaborated upon throughout Dr. Kessler’s
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`testimony for the present limitation (limitation [27f]). See APPLE-1003, ¶¶191-213;
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`see also id., ¶151 (similarly citing Shiota’s paragraphs 22-26 as well as 37-42 to
`
`reference its image transformation process); APPLE-1023, ¶¶64-65.
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`Moreover, ImmerVision and its expert concede that these allegedly operator-
`
`selected parameters in paragraphs 24 and 26 of Shiota relate to the “plane image”
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`referenced in Shiota (expressed in u,v coordinates) (see POR, 17-19; Ex. 2001, ¶¶54-
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`57)—and not to the obtained image on the image pickup face (expressed in p, q
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`coordinates) that Shiota refers to as the “fisheye image.” APPLE-1012, [0023]-
`
`[0024]; APPLE-1023, ¶66. And, paragraph 23 of Shiota and Dr. Kessler’s opinions
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`with respect to the same, confirm that the Shiota’s references to the “image circle
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`diameter,” the normalized/assumed radius of 1, and the “magnification adjustment”
`
`due to “the image circle diameter differ[ing] according to the size of the image
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`Proceeding No.: IPR2023-00471
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`pickup device—all relate to the fisheye image obtained on the image pickup device
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`(which corresponds to the “obtained image” on the “image sensor,” as recited in
`
`claim 27). APPLE-1003, ¶¶205-206; see id., APPLE-1012, [0023]-[0024]; APPLE-
`
`1023, ¶67.
`
`
`
`C.
`
`ImmerVision’s Attempts to Distinguish Shiota Fail Because
`Shiota’s Image Transformation Techniques are Commensurate to
`Those Disclosed by the ’990 Patent’s Specification
`ImmerVision’s attempts to avoid Shiota’s disclosures ring hollow when
`
`considering that the image correction techniques described in the ’990 Patent’s
`
`specification that relate to the claimed functionality at issue in limitation [27f], are
`
`commensurate with Shiota’s teachings (as applied in combination with Baker).
`
`APPLE-1023, ¶¶77-93.
`
`As a starting point, like Shiota’s image transformation process, the ’990
`
`Patent’s specification describes an image circle diameter/image disk with a
`
`normalized image heights ranging from 0 to 1. For example, the ’990 patent’s
`
`specification states that: “FIG. 4B represents the shape of the distribution function
`
`Fdc of a classical panoramic objective lens, which determines the relative distance
`
`dr of an image point in relation to the center of the image disk according to the field
`
`angle α of the corresponding object point. The relative distance dr is between 0 and
`
`1 and is equal to the distance of the image point in relation to the center of the
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`image divided by the radius of the image disk.” APPLE-1001, 2:30-41 (emphasis
`
`added); APPLE-1023, ¶¶77-78.
`
`
`
`Moreover, Patent Owner’s expert confirmed that the relative distance dr refers
`
`to a normalized measure of distance of image points in an image, with a maximum,
`
`normalized distance (i.e., the image size) of 1 at the maximum field angle of 90
`
`degrees (as represented by largest circle C90 in FIG. 4A above). EX-2001, ¶32;
`
`APPLE-1025, 16:6-19:13 (confirming the same and further testifying that (1)
`
`relative distance is “like a percentage” or “normalized distance value” ranging from
`
`0 to 1 and (2) noting that relative distance and relative image height are equivalent
`
`in field of optics), 14:4-16:4.
`
`FIGS. 7A and 7B of the ’990 Patent similarly show the same reference to the
`
`normalized distance of image points in the image (dr), with the maximum image size
`
`normalized to 1 for the corresponding field angle of 90 degrees (and represented
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`Proceeding No.: IPR2023-00471
`Attorney Docket: 50095-0114IP1
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`using circle C90 in FIG. 7A below). APPLE-1001, FIG. 7 (and corresponding
`
`disclosure); see id., FIG. 9 and corresponding disclosures; APPLE-1025, 20:2-21:8;
`
`APPLE-1023, ¶79.
`
`
`Thus, the above embodiments in the ’990 Patent’s specification use an image
`
`
`
`distribution function, referred to as Fd, that uses a normalize image size of 1 and
`
`therefore, identifies relative or normalized distances of image points ranging from 0
`
`to 1. APPLE-1023, ¶¶77-80; see EX-2001, ¶¶36-37 (ImmerVision’s expert
`
`acknowledged that (1) α-dr curve in the ’990 patent represents the claimed non-linear
`
`distribution function and (2) dr represents a “relative distance,” which is a
`
`“dimensionless” quantity that has values ranging from 0 to 1); APPLE-1025, 16:16-
`
`19:13, 20:2-21:8.
`
`Similar to this disclosure in the ’990 Patent’s specification, and as explained
`
`above (see §§I.A-B supra), Shiota follows the conventional practice in the field of
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`optics and optical design when it discloses the use of a non-linear image distribution
`
`function where the size of the image is normalized—i.e., has an “assumed” radius 1
`
`of an image of an object positioned at the field angle of 90 degrees. APPLE-1012,
`
`[0023]; APPLE-1023, ¶¶81, 55-60.
`
`Moreover, like the image transformation process of the Baker-Shiota
`
`combination, the ’990 Patent similarly describes its correction technique as using a
`
`non-linear distribution function (where the function uses a normalized image
`
`size/radius of 1) and scales this value using the size L of the obtained image
`
`disk/circle. APPLE-1023, ¶¶82-85; APPLE-1025, 26:22-30:4. Specifically, as part
`
`of its description of the correction techniques, the ’990 patent’s specification states
`
`that “the image points p(pu, pv) corresponding to the image points E(i, j) of the
`
`display window DW are ‘retrieved’ from the image disk ID1, by means of the
`
`function Fd.” APPLE-1001, 13:25-30. The ’990 specification further explains that
`
`function “Fd” refers to the “non-linear distribution function Fd according to the
`
`present invention”—which as described above—is an image distribution function,
`
`with a maximum image size normalized to 1. APPLE-1023, ¶82; APPLE-1001,
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`13:9-13 (“The image points P thus determined are then projected onto the image disk
`
`Imgl by means of the non-linear distribution function Fd according to the present
`
`invention ….”); see EX-2001, ¶¶36-37.
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`However, given that the non-linear distribution function uses a normalized
`
`image size/radius of 1, simply multiplying the relative or normalized distance values
`
`for an image point with the corresponding image coordinates of that point would not
`
`retrieve the actual and corrected image points. APPLE-1023, ¶83; APPLE-1025,
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`38:7-11 (“Q: Could the non-linear distortion be removed using only the non-linear
`
`distribution function and not the size of the image? A: It would be incomplete. The
`
`answer really is no.”); see also id., 30:5-31:8, 32:1-4, 35:10-36:18. As a result, when
`
`the ’990 specification describes the correction method using its image distribution
`
`function, Fd that is provided in relative term, it applies the actual image size L as a
`
`scale factor to retrieve the actual, corrected image points (e.g., multiplying the size
`
`L with the product of image coordinates U and V and image distribution function,
`
`Fd(α):
`
`
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`APPLE-1001, 14:10-35; see id., 13:45-47 (stating that “pu and pv are the Cartesian
`
`coordinates of an image point p of the image disk in the coordinate system O'UV,”
`
`and “L is the size of the image disk, in number of pixels”); APPLE-1025, 39:1-7
`
`(testifying that “[b]ecause the [non-linear distribution] function is provided in
`
`relative terms, one would need to scale that using the image size to obtain” the
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`“actual image point, that is corrected.”); APPLE-1023, ¶¶84-85 (explaining that size
`
`L of the image is multiplied with the non-linear distribution function Fd).
`
`Relatedly, ImmerVision’s expert testified that the size L of the obtained
`
`image—as used in the ’990 Patent’s specification—corresponds to the extent or edge
`
`of the image from the optical axis, which he further explained is the radius of the
`
`image. APPLE-1025, 16:5-15 (explaining that the radius of an image is the distance
`
`of the extent of the image (as produced by the lens) from the optical axis), 37:15-
`
`38:6 (testifying that quantity L as described in the specification is the distance to the
`
`extent of the image produced by the lens from the optical axis), 39:1-7.
`
`Similarly, in view of Shiota’s described image transformation operations as
`
`applied in combination with Baker and as explained above (see §§I.A-B supra),
`
`Shiota’s image distribution function uses a normalized radius of 1, which a POSITA
`
`would have found obvious to scale using the actual image size to obtain the actual
`
`and corrected/transformed image points on the fisheye image. APPLE-1012, [0023];
`
`APPLE-1003, ¶¶205-206; APPLE-1023, ¶¶86-92; see APPLE-1025, 21:9-22:8,
`
`23:6-24:10; APPLE-1026, pp. 53, 57, 199; APPLE-1027, p. 320. As explained
`
`above, Shiota teaches that (1) the “image circle diameter differs according to the
`
`size of the image pickup device and the focal distance of the fisheye lens,” (2) while
`
`a normalized image radius of 1 is used, “magnification adjustment is performed” in
`
`“actual[] use, and (3) as part of its image transformation, “projection coordinates”
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`on the “image pic
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