`
`Technical Report No. 32-877
`
`DI'g/z‘a/ Video-Data Handling
`
`Roben‘ Nat/Jan
`
`Rm *0 JPL LibraYY.
`
`K. W. Linnes, Manager
`
`Space Insfrumenf Systems Sech‘on
`
`JET PROPULSION LABORATORY
`
`CALIFORNIAINSTITUTEOFTECHNOLOGY
`
`PASADENA. CALIFORNIA
`
`January 5, I966
`
`VALEO EX. 1026_001
`
`VALEO EX. 1026_001
`
`
`
`JPL TECHNICAL
`
`REPORT NO. 32-877
`
`
`
`FIGURES (Cont’dl
`
`Simple notch filter
`
`. Mathematically correct version of simple notch fifter
`
`.
`
`lalI Noisy picture, lb} Two-dimensional frequency
`transform of picture .
`
`10.
`
`11.
`
`12.
`
`13.
`
`Scan—line filter
`
`System frequency-response curve .
`
`Ranger Vlll frame after normal clean—up, (b) Ranger V!”
`frame with sine~wuve frequency correction
`
`Correction frequency-response curve
`
`(a) Ranger V“ Pl frame before (left) and after clean—up,
`lb) Mariner frame I before [leftt and after clean-up
`
`10
`
`10
`
`ll
`
`13
`
`IV
`
`Int-fl“:
`
`VALEO'EX. 1026_002 _
`
`VALEO EX. 1026_002
`
`
`
`
`
`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 statistical analyses.
`
`l. OBJECTIVES
`
`It is the function of the video-data-handling 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
`
`photo-interpretation.
`
`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.
`
`VALEO EX. 1026_003
`
`VALEO EX. 1026_003
`
`
`
`JPL TECHNlCIAL REPORT NO. 32-877___________.__..._______._.———_-————_——-———
`
`ll. PROBLEMS
`
`There are several significant differences lJCtW'OL'll 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 film. 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
`televisiou
`systems which add 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 those 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-prooessing 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-
`rcctions, enhancements, and analyses.
`
`The last step in the sequence was the conversion of
`the digital
`tapes to an accurate 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 (0r 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.
`
`VALEO EX. 1026_004
`
`VALEO EX. 1026_004
`
`
`
`
`
`JF’L TECHNICAL REPORT NO. 32-877
`
`'{O Photometric correction —correction of nonuniform
`
`brightness response of vidicon.
`
`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
`
`response of camera with respect to successive scan
`lines.
`
`6. Sine-wave correction—compensation for attenua—
`tion of higlnfrequency 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 preiiight
`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 reproject the picture to the L
`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 Ranger, 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.
`
`
`-'r£m;f
`nun-u-
`
`Fig. la.
`
`image of a uniform grid as seen by
`an early Ranger camera
`
`
`
`
`
`
`
`
`
`
`
`mun-.1J‘va'II,
`
`n
`
`g
`
`a
`
`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.)
`
`VALEO EX. 1026_005
`
`3
`
`VALEO EX. 1026_005
`
`
`
`JPL TECHNICAL REPORT NO. 32-877
`
`
`
`Fig. 2a. Ranger Vi“ frame reproieded using geometric-correction program
`as it would appear from vertical viewing
`
`.[...ly»|l|‘...4|l-lugrn.Inn.
`
`
`
`
`1—4::
`_,
`,
`,iifiuflp- -
`
`Fig. 2b. Ranger Vi” frame converled to elevations showing contours as
`well as darker—appearing elevated regions
`
`4
`
`-
`
`VALEO EX. 1026_006
`
`VALEO EX. 1026_006
`
`
`
`_._._.._..___.__.—_____—__.___________JPL TECHNICAL REPORT NO. 32-877
`
`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-cainera 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 nonunifornlity in the Ranger VII, VIII and [X 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.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`INTENSITY
`
`
`
`
`
`
`
`
`
`I50
`
`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 iit screen;
`white is down.)
`
`Fig. 4b. Mariner frame 1'] after preliminary,
`experimental field-flattening correction
`and contrast enhancement
`
`VALEO EX. 1026_007 5
`
`VALEO EX. 1026_007
`
`
`
`JPL TECHNICAL REPORT NO. 32~877
`
`
`
`3. Random Noise
`
`4. System Noise
`
`Most of the noise diseovei'ed 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 adiustment, 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 VF 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 Ranger 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 died 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,y)= N0 cos 2m ([13: + icy + A}
`
`{where N is the magnitude of noise at coordinates x and y
`in the picture, n represents the phase shift, and h and k
`are the horizontal and vertical frequency components}
`would match the noise at all times.
`
`The parameters Nu,f1,f<, 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.,i-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
`perfOrrning a cross-correlation of the picture against the
`function N cos 2« (hx + icy), where N is a normalizing
`factor and h and it are chosen approximately by visual
`examination of the picture. The calculation becomes
`
`p(xo.yo) = N Z 2 Bo (xi-x0, y+y.,) cos 21r(hx+ky)
`::—r y=-l
`.
`.
`ii,— = 1:4 EBCOSZ 211' {11x+l<y)
`
`{1)
`
`image brightness and
`the original
`is
`where Bo(xo, y“)
`p(xu, go) 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.
`
`VALEO EX. 1026_008
`
`VALEO EX. 1026_008
`
`
`
`
`
`JPL TECHNICAL REPORT NO. 32-877
`
`
`
`
`Fig. 56. Blown-up portion of film recording from
`Ranger Vii (Notite film grain and
`loss of resolution.)
`
`Fig. 5c. Magnitude of noise
`found in (bi
`
`Fig. 513. Some area from digiiized data but unprocessed
`with respect {a noise removal [Reseau mark has
`been removed; noise from television-camera
`erase cycle is visible.)
`
`'
`
`Fig. 5d. Result of subtraciing
`noise from (bi
`
`VALEO EX. 1026_009 7
`
`VALEO EX. 1026_009
`
`
`
`JPL TECHNICAL REPORT NO. 32-877
`
`
`
`The correction to the picture is simply
`
`Buy) = 13.. (x41) ” p (r. v)
`
`{9)
`
`which is a triangular truncation of a single frequency h",
`and the truncation factor n is related to the sliarpneSs
`ot' cutoll'.
`
`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 transfonn of zero. phase ([10 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
`
`pmn—U, y.,) = N Z Z Bu(x+x.,, y+yu)cos 21(hx-i-lty)
`.r=—r y=—.v
`
`
`
`Xi’?""ii“‘f'i
`% = i: : cos= 2n(hx+ky) (r—lxi) (fl)
`
`.r:—r y=-a
`
`
`
`T
`
`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(x)—->A(h) to a frequency domain h, is
`
`AUI) =f P(:c) cos 21rUiI“i“A)(fI
`
`(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 9. filter will not
`retrieve 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
`
`sin 21r[(h_fln)n]
`21r(h—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
`
`+
`|
`|
`I
`I
`|
`I
`
`-ho
`
`|
`_|_
`|
`|
`I
`I
`I
`I
`
`“0
`
`sinz 2w[(h-h.,)n]
`Liar-'(lll—JIUVII3
`
`(5)
`
`Fig. 7. Mathematically correct version of
`simple notch filter
`
`."'1
`
`VALEO EX. 1026_010
`
`VALEO EX. 1026_010
`
`
`
`MJPL TECHNICAL REPORT NO. 32 877
`
`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
`wiil remove these frequencies can be described as follows.
`Take the average value of the scene brightness in the
`
`OF SCAN
`
`DIRECTION
`.....—__.-..
`
`REAL
`
`Fig. Bo. Noisy picture
`
`-h
`
`0
`
`+15
`
`I. Ho
`SPECTRUM 1!.
`
`-/r
`
`NOISE
`
`region of the point to be corrected. Compare the average
`of the scan line containing this point, and applyr the differ-
`ence between the scene average and the line average as
`a correction to the point. Application of the truncation
`logic of Sectiou 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 300 X 300 elements.
`Preposed improvements of this computer algorithm should
`allow a general reductiou 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 caiculation.
`
`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-
`
`CENTRAL PGlNT [ONLY ONE ELEMENT)
`
` 2| DIGITAL.
`
`ELEMENTS
`
`4
`
`4| DIGITAL
`ELEMENTS
`
`Fig. 9. Scan-line filter
`
`DIRECTION
`-“-'-—-—'—"'-
`OF SCAN
`
`VALEO EX. 1026_011
`
`9
`
`VALEO EX. 1026_011
`
`
`
`JPI. 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 liner 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 h 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 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-
`
`(a)
`
`200 kc +-
`
`(b)
`
`200 kc 4- n
`
`(cl
`
`200 kc -F- f)
`
`(d)
`
`zoo kc + n
`
`.__
`
`I
`
`i
`
`1
`|
`I
`
`:I
`
`i|I
`
`l
`
`:
`il
`
`||
`
`l
`
`THEORETICAL
`RESPONSE
`
`ACI‘UAL RESPONSE
`
`wveese
`
`RESPONSE
`
`CORRECTED
`RESPONSE
`
`I
`
`|
`
`0.2-
`
`5
`
`'
`
`i
`
`D
`
`Fig. 10. System frequency-response curve
`
`Fig. lib. Ranger VIM frame with sine~wuve
`frequency correction
`
`10
`
`VALEO EX. 1026_012
`
`VALEO EX. 1026_012
`
`
`
`
`
`JPL TECHNICAL REPORT NO. 32v877
`
`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. 12. Correction frequency-response curve
`
`B. 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 iunar 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. 1026_013.,
`
`VALEO EX. 1026_013
`
`
`
`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 IPL
`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.
`in 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 significantlyr 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—
`rnodilied} 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. 1026_014
`
`VALEO EX. 1026_014
`
`
`
`JF'L TECHNICAL REPORT NO. 32-877
`
` “hill1
`
`.n:gait“. rf
`
`Fig. 13b. Mariner frame 1 before [left] and offer clean-up
`
`VALEO EX. 1026_015 13
`
`VALEO EX. 1026_015
`
`
`
`JF’L TECHNICAL REPORT NO. 32-877
`
`
`
`REFERENCES
`
`l. Billingsley, F. C., "Digital Video Processing at JPL," Paper No. 15, Seminar Pro-
`ceedings of Electronic imaging Techniques for Engineering, Laboratory, Astronomical
`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. 32-736, Jet Propulsion Laboratory, Pasadena, California,
`September l5, I965.
`
`14
`
`VALEO EX. 1026_016
`
`VALEO EX. 1026_016
`
`
`
`____—_____________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—(Iimcnsionul
`
`high—frequency recovery Iilter.
`
`where l/nl = the number of elements in the filter array
`(u1 = 1,13), and n._. = n1 X the number of rows in the filter
`array (n2 Z :11 X 3 = My).
`
`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 Aadd some scan-line noise N to produce
`received image B.
`
`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:
`
`111
`
`000
`
`5 e
`
`F(x,y)=n1
`
`1
`
`1
`
`1 —n2
`
`1
`
`l
`
`l
`
`111
`
`000
`
`000
`
`+010
`
`000
`
`‘Aaié‘xé
`
`000
`
`=%1/’6‘/9—'1/31/31/3
`
`141/63?)
`
`0-00
`
`000
`
`+010
`
`000
`
`=
`
`‘2/9
`
`IA:
`
`7/9
`
`1/‘3
`
`-%
`
`1/9
`
`or
`
`
`
`
`
`:1
`
`1 2 3 4
`
`34.6431
`
`5732le
`all
`6
`3 2|1
`5|3344|3
`3u3154
`423623
`
` 1
`
`2 —1[:i_"—_1_—1——1 a1
`3
`3|
`3
`3
`3
`3|
`3
`|
`4
`i
`|
`5
`‘lCL‘iijll—l
`
`+
`
`6 V
`
`ALEO EX. 1026_017 _ ‘5
`
`VALEO EX. 1026_017
`
`
`
`JF'L. TECHNICAL REPORT NO. 32-877
`
`
`
`Perform a convolution of filter F and array B to give approximate recovery R
`hack to A:
`
`Herman) = Z Z 13(xu-tmn+y)F(-ny)
`z=—| y=-l
`
`for each
`
`jxo=2t05
`1y0=2t05
`
`The error of recovery is E =
`
`
`
`
`Effectiveness may be measured by comparing average noise [El against error
`matrix [El over the range x = 2 to 5 and y = 2 to 5.
`
`_~
`1
`i
`5
`lNl : T6. 22:; ”Z;
`
`|N(x,y)| = 1.25
`
`I?! = e
`
`WM = 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(x).
`
`23
`
`24
`20
`
`l6
`
`l2
`
`M]!
`
`16
`
`VALEO EX. 1026_018
`
`VALEO EX. 1026_018
`
`
`
`_._._._JPL TECHNICAL REPORT NO. 32-877
`
`Let A be scanned by :1 beam with the response shape S(:c):
`
`St“
`
`The transmitted brightness is a convolution of A and S to form 13(1):
`
`B(x) = '2 A (36..
`fr—i
`
`-|~ x) 3(1')
`
`for each I.. = 11015
`
`There is a visible drop in resolution from A to B.
`
`X
`
`£3
`
`0
`
`‘2
`
`4
`
`-1
`
`-'|
`
`-5
`
`4
`
`-3
`
`|
`
`-4 -2
`
`l0 -7
`
`l
`
`O
`
`(ERROst—A)
`
`The Fourier transform of S(x) is (sin 21rh)2/(21rh)2 = T301).
`
`FREQUENCY f
`
`VALEO EX. 1026_019
`
`17
`
`VALEO EX. 1026_019
`
`
`
`JPL. TECHNICAL REPORT NO. 32-877—-——-——————-——-———.____.______
`
`Now, let us take the reciprocal of Te,
`
`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
`
`5 _TR(”)
`
`We now have an unnormalized correction function C.
`
`
`
`18
`
`'
`
`VALEO EX. 1026_020
`
`VALEO EX. 1026_020
`
`
`
`——___————F——————————___—n—___h____flu.___________——_—————_________———__._——_
`
`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 5 in the frequency domain.
`Two constants, K. and K._., must be determined for the filter.
`
`F{x) = K. 5(0) — KL, C(x)
`
`where 8(0) is a delta function { = 0 for x en’: 0.
`
`=lforx=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 T1? at high
`frequency).
`
`Therefore,
`
`The convolution of F(:c) and a constant brightness of magnitude 1 should give
`an enhancement factor of 1 [see T,,(0)].
`
`1 = :21 F(x) = Z: [5 3(0) - K2 cm]
`
`12—2
`
`=5—K2[—2+7+17+7-2]
`
`Therefore,
`
`
`
`When a convolution is performed between F(x) and B(x), the result R(x) repre-
`sents a reconstruction of A(x) to the degree permitted by the enhancement of the
`
`VALEO EX. 1026_021
`
`19
`
`VALEO EX. 1026_021
`
`
`
`JPL. TECHNICAL REPORT NO. 32-877
`
`
`
`higher frequencies, as indicated by T3; T1:-
`
`l{(x”) = z B (1], + x) F(x)
`::—2
`
`for x" z J. to 15
`
` X
`
`o
`
`ER
`£3
`
`2
`s -|
`0 -z
`
`a
`4
`2 —4
`2 —2
`4 -| —| —5
`
`3
`I —-2
`4 —3
`
`l0
`o —2
`-4 —2
`
`o
`I
`
`[2
`s —4
`lo —7
`
`I4
`2 —2
`I
`o
`
`l6
`(53:8—4)
`(Eg=B-A)
`
`Compare the error 13,, caused by the scanning beam against
`remaining in the reconstructed image.
`
`the error ER
`
`R
`
`151:.
`
`1
`
`‘Ifi
`
`15
`
`30
`
`This is a distinct improvement. Visual com