`Valeo v. Magna
`IPR2015-____
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`JPL TECHNICAL
`
`REPORT NO. 32-877
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`
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`FIGURES (Cont'd)
`
`Simple notch filter
`
`Mathematically correct version of simple notch filter
`
`.
`
`lle Noisy picture, lb} Two-dimensional frequency
`transform of picture .
`
`10.
`
`11.
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`12.
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`13.
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`Scan—line filter
`
`System frequency-response curve .
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`Ranger Vlll frame after normal clean-up, lb) Ranger Vi“
`frame with sine-wave frequency correction
`
`Correction frequency-response curve
`
`la] Ranger V“ P. frame before (left) and after clean—up,
`lb] Mariner frame I before (left) and after clean-up
`
`10
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`10
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`ll
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`13
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`IV
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`mall.
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`JPL. TECHNICAL REPORT NO. 32-877
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`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 allect 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. Althoagh 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 statistical analyses.
`
`l. OBJECTIVES
`
`It is the function of the video-datadtandling 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 cleaned—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
`calcuiated from the relation of the surface to the bright-
`
`ness as a function of Sun, observation point, and surface
`location.
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`JF’L TECHNICAL REPORT NO. 32-877____________._____._.__—.....——_-——_———-——-
`
`ll. PROBLEMS
`
`There are several significant dillcrcnccs 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
`televisiori
`systems which acid to the photo-interpretive and map-
`making 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 problems 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-pmcessing 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 canversion of
`the digital
`tapes
`to an acourate visual presentation
`(Ref. 1).
`
`III. 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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`'{O
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`Photometric correction —correction of nonuniform
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`brightness response of vidicon.
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`3. Random-noise removal — superposition and compar-
`ison (anticipated but not necessary for Ranger).
`
`removal — elimination of
`(periodic)
`4. System-noise
`spurious visible frequencies superimposed on image.
`
`5. Scan—line-noise removal—correction of nonuniform
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`response of camera with respect to successive scan
`lines.
`
`6. Sine-wave correction—compensation for attenua—
`tion of hig11~frequency 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.
`While 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 rcproject the picture to the 4‘
`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 inllight 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.
`
`
`an...
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`IIIIIIIII
`inl-
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` .r'.’
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`Fig. la.
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`image of a uniform grid as seen by
`an early Ranger camera
`
`
`
`Fig. ‘lb. corrected grid after moving intersections back
`to a square array (Note that some distortion remains
`in the third row as a result of extreme nonlinear
`distortion: Reference points could have been
`selected in a finer mesh to create
`better results.)
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`JPL TECHNICAL REPORT NO. 32-877
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`III$I|1II'I|ti'A|II|l'l‘lltll
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`Fig. 2a. Ranger VIN frame reproieded using geomefric-carrection program
`as it wouid appear from vertical viewing
`
`
`
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`Fig. 2b. Ranger Vi" frame converted to elevalions showing contours as
`well as darker—appearing elevaled regions
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`4
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`_._______________,____________JPL TECHNICAL REPORT NO. 32-877
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`Examination of the photometric response to a uniformly
`lit field along a single scan line for each of several 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, :1 simple linear interpolation was used to adjust
`the actual data lying between calibration brightnesses.
`The nonuniformity in the Ranger VII, VIII and IX par-
`tial~scan (P) cameras, with 300 lines/frame, was not too
`severe. It was very pronounced in the full-scan-camera
`(F) frames of 1100 scan lines/frame, and in the Mariner
`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 "inHight
`calibration.” In general, the correction is performed by
`summing a number of frames and taking the result as an
`approximate gray calibration.
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`INTENSITY
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`ISO
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`SAMPLES PER LINE
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`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 down.)
`
`Fig. 4b. Mariner frame 11 after preliminary,
`experimental field-flattening correction
`and contrast enhancement
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`JPL. TECHNICAL REPORT NO. 32~877
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`3. RandOm Noise
`
`4. System Noise
`
`Most of the noise diseovered in the Ranger 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
`acourate 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 VW improvement
`in the signal-to-noise ratio
`derived by straight averaging (where N is the number of
`averaged frames).
`
`The film 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.
`
`Examination 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
`single application of the formula
`
`N(x, g): No cos 21v (fix + icy + 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 ND, h, 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.,vit 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 27‘:
`(1:2: + icy), where N is a normalizing
`factor and h and l: are chosen approximately by visual
`examination of the picture. The calculation becomes
`
`p(xu, yo) = N Z 2 B0 (x+xu, y-t-yu) cos 2::- (hx-i-ky)
`r=—r u=-a
`
`(l)
`
`l- = Z Z coszgn-(hx-t-ky)
`N
`r=-l' V=-8
`
`image brightness and
`the original
`is
`where Bn(:co, y“)
`p(x.,, yo) then gives the magnitude of noise contributing to
`that point. It should be noted that r and s are chosen
`somewhat arbitrarily to accornmodate 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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`.MubulbF5W9F
`1]min—Iwpmm
`hmcam
`
`idwanumnmC
`mn0es
`-msraown55e..he
`fmiei
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`fl!dlih
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`rcan-
`m.nbwma)us.mJ
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`
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`00...!Jared
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`
`
`5SOwn“man“mw:.mnmmshameWW.
`FWOmehw:
`RePe
`
`Fig. 5d. Resuil of subtracting
`nonse from (bi
`
`B
`
`r‘lo
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`F
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`i9. 5c. Magnitude of noise
`found in (bi
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`m.
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`JPL TECHNICAL REPORT NO. 32-877
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`The correction to the picture is simply
`
`Buy) = 13.. (x. if) *- p (r. u)
`
`{9)
`
`which is a triangular truncation of a single frequency it",
`and the truncation factor n is related to the sharpness
`of cutoil'.
`
`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. Tile
`Fourier transform of a real function in 3: (either time or
`distance), P(:c)—->A(li)
`to a frequency domain h, is
`
`A(h) =f1w P(:c) cos 21r(li.t-i-A)d.r
`
`(3)
`
`where A(h) is the amplitude of each component of the
`original picture with frequency it. Where I 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 [1. 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.
`
`The easiest digital filter to design would be a very
`sharp one, consisting of essentially a delta function in
`frequency and an infinite cosine wave of a single fre~
`quency in the real domain.
`
`5. Scan~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
`
`no
`
`sin 2x [(h— h")n]
`2.1r(ll—'lt(,)il
`
`(4)
`
`which in the real domain consists of a square truncation
`of a cosine wave of frequency ho.
`
`The chosen filter is of the form
`
`i
`I
`I
`|
`I
`
`0
`
`4
`
`sin2 27r[(ll—h.,)n]
`Lira-“(h—l‘nVM“
`
`(5)
`
`Fig. 7. Mathematically correct version of
`simple notch filter
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`1’'1
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`When 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
`
`pm(.r,., y.,) = N Z Z Bu(.r+x.,, y-i-yu) cos 27r(hx+ky)
`::—r y:—.!
`
`
`
`Wit-ii
`%,- = i i cos2 217(hx—i-ky) (ll—I'll) (fl)
`
`z:—r ye—s
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`r
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`_____________________________________JPL TECHNICAL REPORT NO. 32 877
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`carefully reproduced, noise is generated as a series of
`frequencies at
`right angles
`to the scan.
`In the lWU»
`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
`
`DlRECTION
`....._.—__.—
`
`REAL
`
`Fig. Ba. Noisy picture
`
`-h
`
`0
`
`+5
`
`I. H
`
`OQ.V
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`_,r
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`FREQUENCY
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`SPECTRUM A
`
`region of the point to he 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 difficulties have arisen from features which are
`
`very sharp in contrast. These features make a significant
`coutribution 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 800 X 300 elements.
`Preposed 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.
`
`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| DIGIThL
`
`ELEMENTS
`
`4
`
`4| DIGITAL
`ELEMENTS
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`Fig. 9. Scan-line filter
`
`DiRECTION
`——————b-
`OF SCAN
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`JPI. TECHNICAL REPORT NO. 32-877
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`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 oneaclimensional 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 h the reciprocal of the
`response is plotted, then the curve plotted in Fig.
`lOe
`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 flat response out to the point
`where the original response has fallen to 14;
`its original
`value. The filtering program can again be applied, using
`the Fourier inverse of the reciprocal response. The con-
`
`In}
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`200 kc —b-
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`(b I
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`200 kc —i-n
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`(CI
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`200 kc -I- h
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`(d)
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`200 RC -u- r:
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`..._.
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`I
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`I
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`1
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`r
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`II
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`iII
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`I
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`:
`:I
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`II
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`I
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`THEORETICAL
`RESPONSE
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`ACTUAL RESPONSE
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`INVERSE
`
`RESPONSE
`
`CORRECTED
`RESPONSE
`
`I
`
`I
`
`0.2-
`
`I
`
`i
`
`O
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`Fig. ID. System frequency-response curve
`
`10
`
`Fig. IIb. Ranger VIII frame with sine-wave
`frequency correction
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`JPL TECHNICAL REPORT NO. 32~877
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`is the horizontal response measured but the vertical re«
`sponse provides information regarding the eliipticity of
`the beam, and the results are incorporated into a two-
`dimensional filter. Typically, the correction function for
`the Ranger VIII l?3 camera appears in the real domain
`along each axis, as shown in Fig. 12.
`
`HORIZONTAL
`
`x
`
`VERTICAL
`
`y
`
`Fig. 12. Correction frequency-response curve
`
`8. Analyses
`
`l. Brightness-to-SIOpe
`
`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
`Geological Survey (USCS), and was worked out in detail
`independently by Thomas Rindfleisch of JPL (Ref. 2) and
`Kenneth Watson 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 lS-deg slope of
`terrain and allows for no protuberances which would
`nullify the effectiveness of the crushable aluminum honey-
`comb blocks 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 methods re-
`quires knowledge of the video system. Therefore, a careful
`and extensive program of calibration measurements to
`determine the photometric, geometric, and frequency
`responses of each camera had to be undertaken. These
`measurements were recorded on magnetic tape at PL
`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 rccorrect
`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.
`in addition, each
`color filter (for missions such as i‘ifariner) 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 brightnesa 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-
`modilied) 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 geometric~correction 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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`JF’L TECHNICAL REPORT NO. 32-877
`
`
`
`Fig. 13b. Mariner frame 1 before [leftl and after clean—up
`
`VALEO EX. 1024_015
`VALEO EX. 1024_015 13
`
`
`
`JPL TECHNICAL REPORT NO. 32-877
`
`
`
`REFERENCES
`
`l. Billingsley, F. C., "Digital Video Processing at JPL," Paper No. 15, Seminar Prod
`ceedings of Eiectronic imaging Techniques for Engineering, Laboratory, AstrOnomicoi
`and Other Scientific Measurements, Society of Photo-Optical Instrumentation Engi-
`neers, April 26—27, 1965.
`
`2. Rindfleisch, T. C., A Photometric Method for Deriving Lunar Topographic informa-
`tion, Technical Report No. 32-786, Jet Propulsion Laboratory, Fosadena, California,
`September 15, I965.
`
`14
`
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`______—fl_______________JPL TECHNICAL REPORT NO. 32-877
`
`APPENDIX
`
`The following are simplified examples of (l) a two-
`dimensional scan-noise line filter and (2) a one—(Iimensionnl
`
`high—frequency recovery filter.
`
`where l/n1 = the number of elements in the filter array
`(u1 = 1,3), and n._. = n. X the number of rows in the filter
`_|/
`array (n3 : 111 X 3 — me)-
`
`As a test application of filter F on a received noisy
`signal B, consider a 6 X 6 array of numbers representing
`brightness A. To A add some scan-line noise N to produce
`received image B.
`
`
`
`346431
`
`57:52le
`6116 3 2[1
`5|3344|3
`Suiifl4
`423623
`
` 1
`
`2 —1[:1—‘:i“:i‘—1 —1
`3
`3|
`3
`3
`3
`3|
`3
`|
`4
`l
`|
`s —1L:1__—r—_1_—r1—1
`
`+
`
`6 3
`
`46481
`
`1 2
`
`45—2—1-FI1
`3 9|4965|4
`4 5[3344|3
`ZBLLHS
`
`5 6
`
`VALEO EX. 1024_017
`VALEO EX. 1024_017 , ‘5
`
`y 1 2 3 4
`
`5 6
`
`The computer presently uses a 21 X til-element array;
`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 a 3 X 3
`array:
`
`F(x,y)=n1
`
`1
`
`1
`
`l
`
`1
`
`1
`
`1
`
`1
`
`1 —n2
`
`l
`
`=
`
`1%;
`
`‘4:
`
`Va
`
`1x15:
`
`56
`
`V9
`
`1261/63?)
`
`+
`
`0
`
`Vs
`
`0
`
`0
`
`0
`
`0
`
`“‘
`
`+
`
`0
`
`l
`
`0
`
`0
`
`0
`
`0
`
`0
`
`1
`
`0
`
`0
`
`0
`
`0
`
`0
`
`1%;
`
`‘0
`
`0
`
`l
`
`0
`
`O
`
`1
`
`O
`
`0
`
`l
`
`0
`
`0
`
`1/3
`
`0
`
`O
`
`0
`
`0
`
`1/9
`
`=
`
`‘25
`
`56
`
`1A:
`
`3%
`
`1A1
`
`1/9
`
`*7/9
`
`1/9
`
`or
`
`F
`
`_].
`
`O
`
`1
`
`y
`
`
`
`JF'L TECHNICAL REPORT NO. 32-877
`
`Perform a convolution of filter F and array B to give approximate recovery R
`back to A:
`
`H(xo,yn)= Z ZB(x.,-I—,xr0+y))F(:r y)
`z=-1y=-l
`
`for each 13:0 2 2' to 5
`{yo = 2t05
`
`The error of recovery is E =
`
`Effectiveness may be measured by comparing average noise [Nl against error
`matrix |E| over the range x—~ 2 to 5 and y = 2 to 5.
`
`——.
`1
`fi
`5
`[Nizfigg l xyl—125
`
`IE] T16; W I xy)| —075
`
`Hence, a decided improvement is shown for a very small filter.
`
`Example 2
`Let us consider a one—dimensional scene in x with brightness A(:'c).
`
`29
`
`24
`20
`
`l6
`
`IE
`
`(A):
`
`16
`
`"
`
`'
`
`VALEO EX. 1024_018
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`
`
`__._._JF’L TECHNICAL REPORT NO. 32-877
`
`Let A be scanned by a beam with the response shape S(x):
`
`EU)
`
`The transmitted brightness is a convolution of A and S to form B(.r):
`
`13(x) = '2 A(x.. + 1‘) 8(1')
`J':—!
`
`forenc]1:c.. = 1m 15
`
`There is a visible drop in resolution from A to B.
`
`X
`
`£5
`
`0 —a
`
`4
`
`-1
`
`--l —5
`
`4
`
`-3
`
`I
`
`-4 -2
`
`l0 —7
`
`l
`
`o
`
`(ERROR=B-A)
`
`The Feurier transform of S(x) is (sin Ewle/(Zarh)? = T301).
`
`FREQUENCY f
`
`VALEO EX. 1024_019
`VALEO EX. 1024_019
`
`17
`
`
`
`JF’L. TECHNICAL REPORT NO. 32-877———-———————-———-———__._.___
`
`Now, let us take the reciprocal of TR,
`
`but Tn g 5 is an arbitrary upper bound to avoid noise enhancement.
`
`Let us subtract T“ from 5 and take an inverse Fourier transform to real space.
`
`4.0
`
`s—rflw
`
`We now have an unnormalized correction function C.
`
`
`
`18
`
`'
`
`VALEO EX. 1024_020
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`
`
`———————————————-————————ha—a~_uu.dhd.y_.____________.___u__.____________._____._____
`
`JPL TECHNICAL REPORT NO. 32-877
`
`'
`
`In order to convert C into a filter, an adjustment must he made for the fact that
`the transform of this function was subtracted from 5 in the frequency domain.
`Two constants, K. and K._., must be determined for the filter.
`
`m) = K, 5(0) — K2 C(x)
`
`where 8(0) is a delta function { = 0 for x % 0.
`
`=1forx=0
`
`The convolution of F(:c) and a brightness of very high frequency will cause
`C(x) to drop out, and an enhancement factor of 5 will result (see Tn 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)].
`
`1 = :21 F(x) = 2293(0) - K2 cm]
`
`12—2
`
`=5—K2[—«2+7+17+7-2]
`
`Therefore,
`
`
`
`Ft x)
`
`o
`
`0.3
`
`-l.0
`
`2.4
`
`-u.o
`
`0.3
`
`0
`
`When a convolution is performed between F(x) and B(x}, the re5ult R(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
`
`
`
`JF’L. TECHNICAL REPORT NO. 32-877
`
`
`
`higher frequencies, as indicated by T3; Tr:-
`
`1{(x”) = E: B {1], + x) F(x)
`::—2
`
`for x” I J. to 15
`
` X
`
`o
`
`ER
`53
`
`2
`s -|
`o -z
`
`4
`2
`2 —2
`4
`-l —|
`
`a
`-—4
`-5
`
`3
`-2
`r
`4 —3
`
`l0
`o —2
`-4 -2
`
`o
`I
`
`[2
`-4
`5
`l0 —7
`
`:4
`2 —2
`I
`o
`
`15
`(ER=R—A)
`(Eg=B-A)
`
`Compare the error 13,; caused by the scanning beam against
`remaining in the reconstructed image.
`
`the error ER
`
`This is a distinct improvement. Visual comparison of the plots of A vs 13 and
`A vs R also shows that R matches A much better than does B.
`
`20
`
`VALEO EX. 1024_022
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`___.__.JF’L TECHNICAL REPORT NO. 32-877
`
`ACKNOWLEDGMENTS
`