VALEO EXHIBIT 1024
`Valeo v. Magna
`IPR2015-____
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`VALEO EX. 1024_001
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`JPL TECHNICAL
`
`REPORT NO. 32-877
`
`
`
`FIGURES (Cont'd)
`
`Simpie notch filter
`
`Mathematically correct version of simple notch filter
`
`.
`
`(at Noisy picture, (bl Two-dimensional frequency
`transform of picture .
`
`10.
`
`11.
`
`12.
`
`13.
`
`Scan-line filter
`
`System frequency-response curve .
`
`Ranger VIM frame after normal clean-up, (bi Ranger WU
`frame with sine-wave frequency correction
`
`Correction frequency-response curve
`
`(oi Ranger VH P. frame before (left) and after clean-up,
`(bl Mariner frame I before (left) and after clean-up
`
`10
`
`10
`
`ll
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`13
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`IV
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`-x...f-.
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`JPL TECHNICAL REPORT NO. 32-877
`
`ABSTRACT
`
`A technique has been developed which makes it possible to perform
`
`accurate, detailed operations and analyses upon digitized pictorial data.
`Television pictures transmitted from the Ranger and Mariner space-
`
`craft have been significantly improved in clarity by correcting those
`
`system distortions which affect photometric, geometric, and frequency
`
`fidelity. Various classes of structured noise have also been detected
`
`and removed digitally by means of newly devised two—dimensional
`filters. Although mathematically the filters are easier to describe in the
`
`frequency domain, they are more effectively applied as a convolution
`
`operation on the original digitized photographs. The cleaned—up, en-
`hanced pictures are then used by the computer for further interpretive
`and statis tical analyses.
`
`I. OBJECTIVES
`
`It is the function of the video-data~handlirig system to
`reproduce the original scene of transmitted television
`pictures as faithfully as possible in terms of resolution,
`geometry, photometry, and perhaps color. The difficulty
`lies in overcoming limitations imposed by the noise, dis-
`tortions, and information bandwidth of the system. These
`corrections are performed by computer after the pictures
`have been digitized. The pictures in cieaned—up form
`can be enhanced in contrast and used for detailed visual
`
`photodnterpretation.
`
`Once the pictures have been corrected, information can
`
`be extracted from them. Since the pictures are now in
`
`digital form, some of the analyses can be performed by
`the computer. In the case of the Moon (where surface
`photometric properties can be considered reasonably
`homogeneous),
`the slope and relative elevation can be
`calculated from the relation of the surface to the bright-
`
`ness as a function of Sun, observation point, and surface
`location.
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`JPL. TECHNICAL REPORT NO. 32-877
`
`ll. PROBLEMS
`
`There are several significant differences between taking
`a picture with a film camera and a television vidicon
`camera. Assuming that
`the lenses are not
`the limiting
`factor, the differences appear in the manner in which the
`image projected onto the receiving surface is sensed. Spec-
`tral and dynamic sensitivity and linearity differ. Grain
`size limits film resolution, and scanning-beam spot size
`limits vidicon resolution. Geometric fidelity is worse in
`the vidicon scanning camera than in fiim. Noise in trans-
`mission is unique to electrically encoded pictures.
`
`There are several other problems unique to film, but
`emphasis here is upon those weaknesses of
`television
`systems which add to the photo-interpretive and map-
`mal-cing difficulties.
`
`Several years ago, when the Ranger effort was first
`proposed, no known methods existed of performing by
`analog means alone all the desired operations of clean-
`up, calibration correction, and information extraction on
`video data. The most practicable approach to the solution
`
`of these prolilcms available at that time was to digitize
`the data and perform these operations on a computer.
`The next problem was the conversion of analog video
`data to and from digital form. A determined effort was
`undertaken by the video-processing group to digitize the
`data directly from photographs produced from an analog
`signal. Although it was possible to recover everything
`that was on the film, there was already too great a system
`loss from the film recording itself. However, if the signals
`were recorded on magnetic tape at the time of trans-
`mission, the analog video could be digitized directly from
`the tape, and ground recovery losses became minimal.
`
`After the analog tapes were converted to digital tapes,
`the remaining major problem was reduced to creating
`the computer programs which would perform the cor-
`rections, enhancements, and analyses.
`
`The last step in the sequence was the conversion of
`the digital
`tapes
`to an accurate visual presentation
`(Ref. 1).
`
`Ill. COMPUTER MANIPULATIONS
`
`A. Corrections
`
`The first of the computer operations is the reconstitu-
`tion of the picture array from the digitized data. This
`process amounts to an interleaving or a sorting by com-
`puter. The picture is then packed, six digital samples of
`six bits each (64 gray levels), into one 36-bit word of the
`IBM 7094 computer. During any computer operation, the
`picture is brought into core memory a few video scan
`lines at a time from tape (or disk) and unpacked to one
`
`video brightness point per computer word. The picture
`is now an array in computer memory and is available for
`correction.
`
`The following series of corrections evolved as a result
`of working with the pictures themselves. (Other photo or
`video systems may or may not require these operations.)
`
`1. Geometric correction—physical straightening
`of photo image.
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`JPL TECHNICAL REPORT NO. 32-877
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`
`
`.s;::::.
`Iguana:
`
`
`
`
`II I I
`
`‘
`rlfl
`
`
`
`
`.r'.-'
`
`
`Fig. la. Image of a uniform grid as seen by
`an early Ranger camera
`
`
`
`
` ;.'..=..-.:=.r.—»..\
`nun
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`
`Photometric correction —correction of nonuniform
`
`brightness response of vidicon.
`
`3. Random-noise removal — superposition and compar-
`ison (anticipated but not necessary for Rcmgcr).
`
`removal — elimination of
`(periodic)
`4. System-noise
`spurious visible frequencies superimposed on image.
`
`5. Scan-line-noise removal——correction of nonuniform
`
`response of camera with respect to successive scan
`lines.
`
`6. Sine-wave correction—cornpensation for attenua-
`tion of higlbfrequency components.
`
`1. Geometric
`
`The first calibration to be applied must be geometric
`in order to ensure the proper registration of other cali-
`brations. This correction is determined from prellight
`grid measurements as well as postflight reseau measure-
`ments.
`
`The geometric correction is measured from the dis-
`torted image of the calibration grid, which has about ten
`to fifteen rows per picture height and width. The corre-
`sponding video elements between these intersections are
`shifted by a linear interpolation to the corresponding
`original position. If it appears by visual inspection that
`the change between grid points warrants more than a
`single interpolation because of severe nonlinearity, then
`more correction points may be chosen between rows.
`Vi/hile these shifts could be determined prior to flight,
`in practice,
`the measurements are made after success is
`assured. In fact, calibration and reseau-shift information
`
`are combined into one geometric correction (Fig. 1).
`This program is also used to reproject the picture to the
`normal direction (Fig. 2).
`
`2. Photometric
`
`If the camera characteristics as measured on the ground
`could withstand launch and the interplanetary voyage,
`their measurements could be applied to the data later.
`However. such an assumption cannot realistically be
`made. The only trustworthy method of calibration is that
`performed against a standard immediately before, during,
`and after
`the experimental measurements have been
`made. For Hanger, the "after" was too late; and there was
`no inilight calibration incorporated into the mission
`design for "during." (Inflight calibration was also not
`performed for Mariner.) Therefore,
`the preflight mea-
`surements alone had to be depended upon.
`
`
`
`-11-
`
`'
`
`‘
`
`E
`
`1:1’
`
`-
`
`'
`
`tfi an-.r.-.-_P4:-u""|\‘
`
`t.
`
`Fig. ‘lb. Corrected grid after moving intersections back
`to a square array (Note that some distortion remains
`in the third row as ct result of extreme nonlinear
`distortion.’ Reference points could have been
`selected in a finer mesh to create
`better results.)
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`3
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`JPL TECHNICAL REPORT NO. 32-877
`
`
`
`Fig. 2a. Ranger VIN frame reproiecfed using geomefric-correction program
`as it would appear from vertical viewing
`
`.'.:.|.n:'uaoi.4u|-usin-.|u..
`
`Fig. 2b. Ranger VH1 frame converted to elevalions showing contours as
`well as darker—appeuring elevaled regions
`
`4
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`'
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` JPL TECHNICAL REPORT NO. 32-877
`
`
`
`Examination of the photometric response to a uniformly
`lit field along a singie scan line for each of sevcrai illu-
`minations (Fig. 3) shows that the response is not uniform
`in either sensitivity or magnitude. Photometric measure
`ments are made For each line over the entire picture
`frame. The calibration data are unique for each point
`of the vidicon-camera surface and must be applied indi-
`vidually. Since there were so many points in the Ranger
`cameras, a simple linear interpolation was used to adjust
`the actual data lying between calibration brightnesses.
`The nonuniformity in the Rmigcr VII, VIII and [X par-
`tial~scan (P) cameras, with 300 lines/frame, was not too
`severe. It was very pronounced in the Eull—scan-camera
`(F) frames of 1100 scan lines/frame, and in the iliarincr
`data (Fig. 4). In such severe cases, very careful adjust-
`ment of the calibration data for postlaunch change in
`parameters is required to flatten the resultant image field.
`The assumption that the viewed terrain is essentially flat
`in brightness over the whole frame is used as the "inflight
`calibration." In general, the correction is performed by
`summing a number of frames and taking the result as an
`approximate gray calibration.
`
`INTENSITY
`
`ISO
`
`SAMPLES PER LINE
`
`Fig. 3. Photometric calibration (Abscissa represents
`distance along one particular scan line —- in about
`the middle of a video frame. Ordinate shows
`
`voltage response to three levels of light
`from a uniformly lit screen;
`white is downJ
`
`Fig. 4b. Mariner frame 11 after preliminary,
`experimental field-flattening ‘correction
`and contrast enhancement
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`JPL. TECHNICAL REPORT NO. 32-877'
`
`
`
`3. Random Noise
`
`4. System Noise
`
`Most of the noise discovered in the Itringer pictures
`had not been anticipated. The programs for its removal
`were written after the data were received.
`
`There were, however, two classes of noise which had
`been anticipated and for which programs were written
`in advance. This noise was caused by a poor signal-to-
`noise ratio, which created random points of bad data. In
`one case, the random noise gave rise to the appearance
`of "snow." However, this extreme change in the data can
`be detected, and the affected points can be replaced by
`the average of the neighboring points. If the amount of
`snow is extreme, the theoretical picture resolution is de-
`graded by this method of clean—up; but without it, the
`picture would be too hard to interpret.
`
`The second class of noise is less apparent. However, it
`can be detected by superimposing pictures with
`overlapping areas of view. This process requires a very
`accurate registration of data, which,
`in turn,
`involves
`adjustments in translation, rotation, and magnification.
`The magnitude of these matching parameters can be de-
`termined visually, but a computer program has been
`developed which registers at least two small correspond-
`ing sectors in two pictures and determines their trans-
`lation differential. For local regions, a translation
`correlation calculation is reasonably accurate and inde-
`pendent of small amounts of rotation and magnification.
`The vector differences between the two regions are suffi-
`cient
`to enable the computer
`to calculate the three
`parameters of translation, rotation, and magnification for
`matching the whole frame.
`
`Once the pictures are matched, one way to improve
`the image is.by simple averaging of the repeated areas.
`A more powerful approach utilizes the trustworthiness of
`each contribution. This reliability factor is derived from
`the history of that point— either from its magnification
`or calibration adjustment, or from the validity of
`the
`measurement in terms of the noise recognized in the indi-
`vidual frame. This judgment associates a weight with
`each point, which is then incorporated into the averaging.
`
`In addition, after the average has been computed,_a
`Comparison of the original points can be made against
`the neighboring points and the average. If the deviation
`of an original point from the average is
`too high,
`then
`that point can be omitted and the remaining points re-
`averaged. This method of majority logic is far superior to
`that of
`\/‘N’
`improvement
`in the signal-to—noise ratio
`derived by straight averaging (where N is the number of
`averaged frames).
`
`The lilin records of the first Hanger mission were such
`an overwhelming success that no further improvement
`appeared to be possible. The indication that improve-
`ment of the results was possible was the suspicion that
`some loss of resolution must have taken place in the
`ground film recorder because of its finite recording-beam
`spot size. A concentrated effort was made to take the
`data directly from the magnetic tape, with the result that
`the picture obtained did indeed retrieve the resolution
`lost by the prime film record.
`
`Examiiiation of this new picture disclosed a systematic
`frequency superimposed upon the original image (Fig. 5).
`Closer inspection indicated that this noise, even though
`superficially of a single frequency, did in fact drift in
`phase throughout the picture to such an extent that no
`singie application of the formula
`
`N(.'c, 5:): No cos 21-r (fix + log + A)
`
`(where N is the magnitude of noise at coordinates x and y
`in the picture, A represents the phase shift, and h and k
`are the horizontal and vertical frequency components)
`would match the noise at all times.
`
`The parameters N0, in, k, and A were therefore not
`unique. The vertical and horizontal frequency compo-
`nents could be selected reasonably well in a local region;
`amplitude No and phase A remained to be chosen. At any
`particular point, the noise could be considered as a sum
`of cosine and sine components of the original noise, each
`with zero phase shift relative to that point; i.e.,-it was
`necessary to determine only the cosine component of the
`noise. (Note that a sine component of zero phase at
`the origin is zero.) This determination can be made by
`performing a cross-correlation of the picture against the
`function N cos 21-:
`(112: + icy), where N is a normalizing
`factor and h and l-: are chosen approximately by visual
`examination of the picture. The calculation becomes
`
`p(x.,, yo) = N Z B0 (x+x.,, y-t-y.,) cos 2:: (hx-Hty)
`r:-r U:-a
`1
`l‘
`S
`—N,- = E’ vzgacosz ?.n-(l1x+l'<y)
`
`image brightness and
`the original
`is
`where Bn(:co, y,,)
`p(x.,, y,,) then gives the magnitude of noise contributing to
`that point. It should be noted that r and s are chosen
`somewhat arbitrarily to accommodate the computer time
`taken in these calculations. It should also be mentioned
`that the function is stored in memory as a table and not
`recalculated for each point.
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`JPL. TECHNICAL REPORT NO. 32-877
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`9
`
`F
`
`ig. Sc. Magnitude of noise
`found in {bi
`
`F.5w
`H...0.drwee.meegrVhmcamBERePe
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`fiduau
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`flllulGuelle0...iD..f.
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`rnmconI.CLwun
`nWnrnm
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`..ISSOPisO.mneUVOH.5.I...nan
`ofihea.wHO«flu-ms
`JUFEC
`
`
`
`FWDme.m.v._r
`
`m90es
`fCOO
`
`F
`
`u..
`
`de
`
`Fig. 5d. Result of subtracting
`noise from (bi
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`JPL TECHNICAL REPORT NO. 32-877
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`
`
`The correction to the picture is simply
`
`B(x.y) = Ba (x. 1/) r“ r»(-W)
`
`(9)
`
`which is a triangular truncation of a single frequency ft“,
`and the truncation factor n is related to the sliarpness
`of cntoif.
`
`It becomes very useful to generalize these calculations
`in terms of the Fourier or frequency transform. For sim-
`plicity,
`the discussion can temporarily be kept
`to one
`dimension without
`immediate loss of generality. The
`Fourier transform of a real function in 3: (either time or
`distance), P(:c)—->A(l'i)
`to a frequency domain la, is
`
`AU!) = f P(:c) cos 2:r(l1.r+A)cl.r
`
`(3)
`
`where A(h) is the amplitude of each component of the
`original picture with frequency it. ‘Where 3:
`is discrete,
`the integral becomes a summation. The original picture
`can then be represented in the frequency domain as a set
`of vectors whose direction normal to the base line indi-
`
`cates the phase angle A, and where A is the length of the
`vector for each I1. This vector can point in any direction
`between the real and imaginary planes.
`
`Let us consider the probable envelope of the A-vectors
`in the real plane only as being random but distributed
`(roughly uniformly) over all possible frequencies. Sys-
`tematic noise, however, as found in these pictures,
`is
`clustered very heavily around a single frequency. A filter
`peaked near this frequency is all that is needed to clean
`out the noise, but if the noise is not exactly at a single
`frequency, then too sharp or accurate a filter will not
`remove all of it. Yet, too broad a filter removes too much
`
`of the picture. Subjective judgment and consideration of
`computer time now become factors as various trials are
`made to determine the optimum filter.
`
`to design would be a very
`The easiest digital Filter
`sharp one, consisting of essentially a delta function in
`frequency and an infinite cosine wave of a single fre~
`quency in the real domain.
`
`‘vVhen this filter is subtracted from the original data,
`a notch results at the dominant noise frequency, as seen
`in Fig. 6. Mathematically, the filtered frequency is posi-
`tive and negative, as shown in Fig. 7, which gives rise to
`a cosine transform of zero. phase (no sine component).
`Rather than multiplying the -Fourier transform of the
`picture by this notch filter in the frequency domain and
`then inverse-transforming back to the real dimension, it is
`more practical to perform a convolution operation of the
`inverse transform of the filter and the picture. The convo-
`lution operation is identical to Eq. (1) for the sharp trun-
`cation and becomes Eq. (6) for the triangular truncation.
`8
`
`p,,,(x,,, y.,) = N Z Z B,,(.r-l—.\:.,, g+y.,) cos 2rr(l1.1‘+ky)
`4,-:—r y:—.y
`
`X [rrrlxl] [S-Slut]
`%,- = : J2 cos’ 2rr(.l1J."l-ffy) (r_lxl) <S__Slyl)
`
`J:=—r y=—.s
`
`r
`
`5. Scar1~Line Noise
`
`The treatment of other kinds of noise requires bringing
`the discussion back to two dimensions in both the real and
`
`frequency domains. Among other things, television pic-
`tures are different from film in that they are scanned in
`some particular direction. Because not every scan "line is
`
`The filter next in complexity as well as effectiveness
`would be
`
`Fig. 6. Simple notch filter
`
`I
`
`—:_..
`I
`I
`I
`I
`I
`
`no
`
`I|
`
`_i_
`|
`I
`I
`I
`
`0
`
`--!i
`
`Fig. 7. Mathematically correct version of
`simple notch filter
`
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`sin 21rE(f1—.l1n)I1]
`2ar (.li.—-h,,)n
`
`(4)
`
`which in the real domain consists of a square truncation
`of a cosine wave of frequency Fig.
`
`The chosen filter is of the form
`
`sin“ 2vr[(h—h.,)n]
`
`.‘'1
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`

`
` JPL TECHNICAL REPORT No_ 32 577
`
`carefully reproduced, noise is generated as a series of
`frequencies at
`right angles
`to the scan.
`In the two»
`dimensional frequency domain,
`these noises appear as
`high frequencies on the vertical axis (Fig. 8).
`
`After some mathematical manipulation, the filter which
`will remove these frequencies can be described as follows.
`Take the average value of the scene brightness in the
`
`OF SCAN
`
`DlRECTlON
`...._..j__.—_
`
`REAL
`
`Fig. Ba. Noisy picture
`
`—n
`
`0
`
`+n +/r
`
`None
`
`SPECTRUM
`
`0
`
`_,r
`
`region of the point to be corrected. Compare the average
`of the scan line containing this point, and apply the differ-
`ence between the scene average and the line average as
`a correction to the point. Application of the truncation
`logic of Section 4 to this filter results in a gentler response
`to areas more remote from the point (Fig. 9).
`
`Some diiliculties have arisen from features which are
`
`very sharp in contrast. These features make a significant
`contribution to the frequencies being removed by the
`filter. When the filter comes into such an area, it resonates
`and gives rise to false echoes of the feature. A second~
`order logic has been developed to be applied with this
`filter. The filter is turned off in the sensitive vicinity by
`comparing the difference between the origin and the sur-
`rounding region against some chosen threshold. When a
`point in the surrounding area is greater in difference than
`the threshold,
`it
`is replaced by the origin point. This
`logic is more subtle than that of standard electronic filter-
`ing because of the interaction with the real domain.
`
`The scan—line filter is particularly useful for almost all
`classes of video data, but
`it does take about 5 min of
`IBM 7094 time to correct a picture of 300 X 300 elements.
`Proposed improvements of this computer algorithm should
`allow a general reduction of computer running time by
`at least a factor of 20. The modification amounts to sliding
`the filter along the scan line by adding the leading line and
`subtracting the trailing line from the previous calculation.
`
`FREQUENCY
`
`G. Sine "Wave
`
`Fig. 8b. Two-dimensional frequency
`transform of picture
`
`The camera scan beam is finite in size and somewhat
`Gaussian in shape. If it scans a scene which has a reso-
`
`CENTFML POINT (ONLY ONE ELEMENT)
`
`
`
`/
`
`2| DIGITIHL
`ELEMENTS
`
`4
`
`4| DIGITAL
`ELEMENTS
`
`'
`
`,/
`
`Fig. 9. Scam-line filter
`
`DlRECT|0N——?e—b-
`OF SCAN
`
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`
`JPL TECHNICAL REPORT NO. 32-877
`
`
`
`volution of this inverse function and the brightness of the
`original photograph enhances the higher frequencies to
`a point equivalent to the original-scene (Fig. 11). Not only
`
`lution finer than the beam spot, there will be a significant
`loss in the transmitted resolution; the higher frequencies
`will be severely attenuated, if not lost completely. In the
`frequency domain (using one«dimensional logic to begin
`with),
`the desired system response (modulation transfer
`function) would be unity for all frequencies out to the
`upper-limit cutoff (Fig. 10). Calibration measurements of
`the actual frequencies show the response illustrated in
`Fig. 10b. If, for each frequency in the reciprocal of the
`response is plotted, then the curve plotted in Fig. 10c
`results.
`
`the
`To avoid overemphasis of high-frequency noises,
`to
`upper bound of the curve is arbitrarily chosen not
`exceed 5. The product of the actual— and inverse-response
`curves (Fig. 10d) gives a Hat response out to the point
`where the original response has fallen to 1/5
`its original
`value. The filtering program can again be applied, using
`the Fourier inverse of the reciprocal response. The con-
`
`lo}
`
`200 Ice -b-
`
`(b)
`
`--
`
`200 kc —i-fr
`
`(cl
`
`200 kc -|- I:
`
`(d)
`
`200 kc '-h- /1
`
`I
`
`r
`
`,
`
`I
`
`:I
`
`iI I
`
`I
`'
`
`I II
`
`I
`
`THEORETICAL
`RESPONSE
`
`ACTUAL RESPONSE
`
`INVERSE
`
`RESPONSE
`
`CORRECTED
`RESPONSE
`
`I
`
`I
`
`0.2-
`
`I
`
`i
`
`o
`
`Fig. 10. System frequency-response curve
`
`10
`
`Fig. Hb. Ranger WU frame with sine-wave
`frequency correction
`
`VALEO EX. 1024_012
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`

`
`
`
`JPL TECHNICAL REPORT NO. 32-877
`
`is the horizontal response measured but the vertical re«
`sponse provides information regarding the ellipticity of
`the beam, and the results are incorporated into a two-
`dimensional Filter. Typically, the correction function for
`the Ranger VIII P3 camera appears in the real domain
`along each axis, as shown in Fig. 12.
`
`HORIZONTAL
`
`x
`
`VERTICAL
`
`y
`
`Fig. ‘[2. Correction frequency—response curve
`
`B. Analyses
`
`1. Brightness-to-Slope
`
`Once the pictures have been converted to an absolute
`brightness with geometric and resolution distortions re-
`moved, analysis of their contents can proceed. The concept
`
`of converting lunar brightness to slope was recently
`proposed by Eugene Shoemaker of
`the United States
`Ceological Survey (USCS), and was worked out in detail
`independently by Thomas Rindfleisch of ]PI_. (lief. 2) and
`Kenneth VVatson at USCS. Although this method of
`determining elevation has some severe theoretical
`limi-
`tations,
`it surpasses lunar stereo photography in high-
`resolution texture evaluation (Fig. 2).
`
`2. Statistical
`
`One of the operations to be performed with respect to
`the elevation array of the lunar landscape is that of simu-
`lated spacecraft
`landings. The Surveyor spacecraft
`is
`presently designed to accept a maximum 15-deg slope of
`terrain and allows for no protuberances which would
`nullify the effectiveness of the crushable aluminum honey-
`comb bloclcs located near the tripod landing feet. A sta-
`tistical analysis of the lunar terrain has been performed
`which calculates the probability of distribution of slopes
`and protuberances relevant to the Surveyor spacecraft
`configuration.
`
`VALEO EX. 1024_013
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`
`

`
`JF'L TECHNICAL REPORT NO. 32-877
`
`IV. CALIBRATION
`
`The application of computer correction nictliotls re-
`quires knowiedge of the video system. Therefore, a careful
`and extensive program of calibration measurements to
`detemiine the photometric, geometric, and frequency
`responses of each camera had to be undertaken. These
`measurements were recorded on magnetic tape at JPL
`and repeated at the launch site.
`
`Geometric fidelity was measured by taking pictures of
`a two-dimensional grid. As a second-order precaution,
`reticle marks were placed on the camera face to establish
`the calibration. If the system changed after launch,
`the
`infiight measurement of reticle shift was used to recorrect
`the picture geometry.
`
`Pictures of uniform white Fields of known brightness
`levels were also taken and recorded on magnetic tape.
`
`These records provided a brightness calibration for each
`point on the vidicon-camera surface.
`ln addition, each
`color filter (for missions such as Mariner) was recorded
`separately.
`
`To determine the resolution of the vidicon. sine-wave
`charts were recorded in both the vertical and horizontal
`
`directions. A large black bar on a white field, followed
`by sine waves of varying frequencies, was used as the
`resolution target.
`
`The shutter mechanism also had to be taken into account
`
`in the calibration of brightness. The shutter timing on
`alternate frames differed significantly because of
`the
`difference in speed between the forward and backward
`motion during a picture exposure.
`
`V. RANGER AND MARINER RESULTS
`
`1. Photographs from digitized tapes (not yet computer-
`modified) reveal higher resolution than the prime
`analog film records, but also some system noises
`(see Fig. 5).
`
`2. Several classes of noise were removed from various
`
`frames (see Fig. 13).
`
`3. The effect of photometric calibration was shown in
`field flattening; a numerically meaningful set of
`brightness values resulted from this correction.
`
`4. Sine-wave correction enhanced high frequencies to
`give a significant increase in usable resolution (see
`Fig. 11).
`
`5. A geometriccorrection program was used to reorient
`(reproject) frames to lunar normal (see Fig. 2a).
`
`6. Data were converted to elevations and contoured
`
`(see Fig. 2b).
`
`12.
`
`VALEO EX. 1024_014
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`
`

`
`JPL TECHNICAL REPORT NO. 32-877
`
`Fig. 13b. Mariner frame 1 before (left! and after clean—up
`
`VALEO EX. 1024_015
`VALEO EX. 1024_015 13
`
`

`
`JPL TECHNICAL REPORT NO. 32-877
`
`
`
`REFERENCES
`
`1. Billingsley, F. C., "Digital Video Processing at JPL," Paper No. 15, Seminar Pra-
`ceedings of Eiectronic imaging Techniques for Engineering, Laboratory, Astranomicai
`and Other Scientific Measurements, Society of Photo-Optical Instrumentation Engi-
`neers, April 2<5—27', 1965.
`
`2. Rindfleisch, T. C., A Photometric Method for Deriving Lunar Topographic informa-
`tion, Technical Report No. 32-786, Jet Propulsion Laboratory, Pasadena, California,
`September 15, I965.
`
`14
`
`VALEO EX. 1024_016
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`

`
` JPL TECHNICAL REPORT NO. 32.877
`
`APPENDIX
`
`two-
`The following are simplified examples of (1) it
`dimensional scan-nnisc line filter and (2) L1()Ht:-(lltl‘l(.‘I1St(}IIt1l
`
`l1igl1—l'reqL1ency recovery Iilter.
`
`where 1/rt, = the number of elements in the filter array
`(:11 = ‘/3), rind n._. = n. X the number of rows in the filter
`array (n._. 2 1:, X 3 = ';;’g).
`
`test zipplication of filter F on a received noisy
`As 11
`signal B, consider a 6 X 6 array of numbers representing
`briglitness A. ToA:1dd some scan-line noise N to produce
`received image 13.
`
`
`
`346431
`
`5732_1_[2
`311 6
`3 2[1
`5|3344|3
`3lii3_il4
`423623
`
` 1
`
`2 —1[?T3I“:I"—1 -1
`3
`3|
`3
`3
`3
`3|
`3
`I
`4
`i
`]
`5
`“it:-l__‘_1_‘_1:£l'1
`
`+
`
`6 3
`
`46481
`
`1 2
`
`45-2-1-FI1
`3 9I4935|4
`4 5[3344|3
`ZBLLH3
`
`5 3
`
`VALEO EX. 1024_017
`VALEO EX. 1024_017 T "5
`
`3 1 2 3 4
`
`5 6
`
`The computer presently uses :1 21 X 41-element army;
`obviously, the 3 X 3 array (used in the line filter) does
`not work as well as the larger matrix but is still effective.
`
`The high-frequency enhancement filter operates iden-
`tically to the periodic-noise filter, but the example pre-
`sented here has the added complexity of illustrating the
`determination of
`the frequencies to be enhanced and
`the extent of enhancement provided.
`
`Example I
`
`Let us construct a simple scan-line filter F of :1 3 X 3
`array:
`
`F(x,y)=n1
`
`1
`
`1
`
`1
`
`1
`
`1
`
`1
`
`1
`
`1
`
`1
`
`-11,
`
`+
`
`0
`
`1
`
`0
`
`0
`
`O
`
`0
`
`O
`
`1
`
`O
`
`0
`
`l
`
`0
`
`0
`
`1
`
`0
`
`0
`
`O
`
`0
`
`% ‘-'/6
`
`‘/6
`
`0
`
`0
`
`0
`
`= %i1xé‘/9
`
`“'
`
`% % %
`
`1/6
`
`1/in
`
`‘/6
`
`0
`
`0
`
`0
`
`0
`
`-0
`
`0
`
`1
`
`0
`
`0
`
`0
`
`0
`
`O
`
`+
`
`1/9
`
`1/9
`
`1/9
`
`=
`
`-23
`
`as —%
`
`‘xi; %
`
`‘/9
`
`or
`
`F
`
`:1
`
`O
`
`1
`
`y
`
`

`
`JF'L TECHNICAL REPORT NO. 32-877
`
`Perform a convolution of filter F and array B to give approximate recovery H
`back to A:
`
`H(xo.yn) = i i B<x..-I-r,yo+y>F(x,y>
`z=—1y=-I
`
`for each Ix" 2 2t05
`{yo =2to5
`
`The error of recovery is E =
`
`
`
`
`Effectiveness may be measured by comparing average noise [17] against error
`matrix
`over the range at = 2 to 5 and y = 2 to 5.
`5
`5
`H
`{N} % Z Z)
`1:22
`=2
`‘E
`
`|N(x,y)| = 1.25
`
`1
`[V]-.1
`1E1=—16 M
`
`E1'2
`
`]E(:r,y)| = 0.75
`
`Hence, a decided improvement is shown for a very small filter.
`
`Example 2
`Let us consider a one-dimensiotial scene in x with brightness A(:'c).
`
`29
`
`24
`20
`
`l6
`
`l2
`
`(A);
`
`16
`
`"
`
`'
`
`VALEO EX. 1024_018
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`
`

`
` JPL TECHNICAL REPORT NO. 32-877
`
`Let A be scanned by 11 bez1n1 with the rcsprmse shape S(x):
`
`Stx)
`
`The tmnsmitted brightness is 21 convolution of A and S to form B(.r):
`
`B(x) =
`
`.l':—!
`
`/\(x.. + x) S(.1')
`
`forez1cl1.'c.. = lto 15
`
`There is a visible drop in resolution from A to B.
`
`X
`
`E5
`
`0
`
`-2
`
`4
`
`-1--I
`
`-5
`
`4 —3
`
`I
`
`-4 -2
`
`I0 -7
`
`I
`
`o
`
`(ERROR=B-A)
`
`The Fourier transform of S(x) is (sin 2»-la)”/(21:11)? = Ts U1).
`
`FREQUENCY f
`
`VALEO EX. 1024_019
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`
`17
`
`

`
`JF’L. TECHNICAL REPORT NO. 32-877
`
`
`
`Now, let us take the reciprocal of T5-,
`
`but T" Q 5 is an arbitrary upper bound to avoid noise enhancement.
`
`1/4
`
`I/2
`
`f
`
`77:
`
`5
`
`0
`
`I 0
`
`Let us subtract T“ from 5 and take an inverse Fourier transform to real space.
`
`4.0
`
`0
`
`o
`
`5—r,(/r)
`
`I/4
`
`1/2
`
`;
`
`f
`
`
`
`:7
`
`7
`
`O
`_2
`
`VVe now have an unnormalized correction function C.
`
`C(x}
`
`-4
`
`-3
`
`c‘(x)
`
`-2
`
`—-2
`
`-1
`
`7
`
`o
`
`IT
`
`I
`
`7
`
`2
`
`-2
`
`3
`
`4
`
`18
`
`'
`
`VALEO EX. 1024_020
`VALEO EX. 1024_020
`
`

`
`______—————————————————_—u—_~.u_.d.._._.____________——__—_—.___.________————____————
`
`JPL TECHNICAL REPORT NO. 32-877
`
`'
`
`In order to convert C into a filter, an adjustment must be made for the fact that
`the transform of this function was subtracted from S in the frequency domain.
`Two constants, K. and K-_., must be determined for the filter.
`
`F{x) = K, 5(0) — K2 C(x)
`
`where 6(0) is a delta function { = 0 for x % 0.
`
`=lfor:c=0
`
`The convolution of F(x) and :1 brightness of very high frequency will cause
`C(x) to drop out, and an enhancement factor of 5 will result (see T3 at high
`frequency).
`
`Therefore,
`
`The convolution of F (x) and a constant brightness of magnitude 1 should give
`an enhancement factor of 1 [see T,,(0)].
`
`l = _2Z_zl F(x) =
`
`32-2
`
`[53(0) - K2 C{x)]
`
`=5-—K2[-2+7+17+7-2]
`
`Therefore,
`
`
`
`Ft x)
`
`o
`
`0.3
`
`-L0
`
`2.4
`
`-LO
`
`0.3
`
`0
`
`When a convolution is performed between F(x) and B(x}, the result H(x) repre-
`sents a reconstruction of A(x) to the degree permitted by the enhancement of the
`
`VALEO EX. 1024_021
`VALEO EX. 1024_021
`
`19
`
`

`
`JPL. TECHNICAL REPORT NO. 32-87?
`
`
`
`higher frequencies, as indicated by TS Tr.-.
`
`1{(x,,) = i B
`z':—2
`
`+ x) F(x>
`
`for x., z 1 to 15
`
` X
`
`o
`
`ER
`E3
`
`2
`-u
`;
`0 -2
`
`4
`-2
`-I
`
`5
`-—4
`2
`-1 -5
`
`2
`4
`
`3
`-2
`-3
`
`r
`4
`
`IO
`-2
`0
`-4 -2
`
`o
`I
`
`:2
`-4
`5
`I0 -7
`
`:4
`2
`:
`
`-2
`o
`
`:5
`(ER=f?—A)
`(Eg=B—A)
`
`Compare the error E“ caused by the scanning beam against
`remaining in the reconstructed image.
`
`the error E:
`
`1
`——
`|E"|=’1§,=.
`
`15
`
`This is :1 distinct im