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Description  |
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FIELD OF THE INVENTION
This invention relates to an apparatus and a method for automatically
detecting cell irregularities such as may be caused by cancer.
SUMMARY OF THE INVENTION
A widely used technique for reliably analyzing smears of body fluids is
described in a publication entitled, Diagnosis of Uterine Cancer by the
Vaginal Smear, by G. N. Papanicolaou and H. F. Trout, published by
Commonwealth Fund, New York, 1943. In brief, Cancer cells which are
exfoliated into body fluids are detectable upon microscopic analysis of
stained smears of the body fluid by highly trained personnel. It has long
been known as the Papanicolaou technique. Such technique involves highly
trained personnel employed in a time consuming and tedious observation
under microscope of a cell's:
(1) Nuclear Diameter,
(2) Cytoplasmic Diameter
(3) Nuclear Shape,
(4) Nuclear Chromatin,
(5) Cytoplasmic Stain Density,
(6) Nuclear Inhomogeneity,
(7) The relative parameters of the cell with respect to others and
(8) Cell Isolation.
The procedure employed was designed by a group of experts in the field of
medicine.
As may be readily appreciated, the benefits of preventive medicine,
especially in the case of cancer where early detection in many cases
determines life or death, has led many to attempt to automate the cell
classification process. One known prior art attempt is found in the U.S.
Pat. No. 3,327,117 issued June 20, 1967 to a Louis A. Kamensky, which is
directed to a means to sense the nucleus and cytoplasm changes that take
place in a cancer cell from that of a normal cell by the use of an
apparatus to probe the cell with an ultraviolet light energy of two wave
lengths of a pre-determined order such that cell classification can be
provided by electrical signals dependant upon the absorbtion profiles of
both wave lengths by the cell under study.
Another prior art attempt of automating cell classification is shown by
U.S. Pat. No. 3,497,690 issued Feb. 24, 1970 to Leon L. Wheeless Jr., et
al. In this attempt the cells are stained by a Fluorochrome, rather than
by the Papanicolaou technique, and subjected to an ultraviolet light
source with subsequent measurement of the fluorescent response of the cell
structure to provide its classification.
A principal object of this invention is to bring to the art of research in
cytology and pathology the investigatorial attributes of Fourier
transformation, i.e the use of the diffracted light from a cell image that
may be collected optically in a single plane and electrically probed to
obtain the spatial intensity in relation to its spectral frequency.
As will be readily appreciated by those skilled in the art of optics the
illumination of an object by a light source will diffract the light into
an optical pattern which has varying intensity at different points in the
pattern. Such a diffraction pattern has no direct resemblence to the
object, as an image, but is a collection of a series of overlapping
diffraction patterns, each pattern due to individual features of the
object. Such diffraction patterns are the result of the modification or
diffraction of the light by the various points or details of the object or
cell image.
While it is conceivable to utilize measuring apparatus to compute and
indicate the spatial frequency of such deflected light it is considerably
lens cumbersome to collect such diffraction pattern by a len or sensors
and transform its various paths of light energy into a single plane. Such
is the function of a Fourier transform apparatus in the art of optics.
This invention was conceived during an investigation that was studying
coherent optical signal processing techniques for cytological
investigations of, for example, exfoliated cells. These investigations
focused directly on the primary morphological features of the cell.
The exfoliated cells are found in body fluids such as secretions from the
female genital track, gastric fluid, sputum, or in various body cavities
such as pleural fluid, peritioneal fluid, urine, cerebrospinal fluids,
punctates expirmates or washings from epitheial surfaces, as were
heretoforth collected from certain body sites for microscopic examination.
In addition, spontaneously exfoliated cells can be supplemented by cells
obtained directly from certain organs by the use of suitable instruments.
Such cells maybe employed for detection and diagnosis of various
pathological conditions.
Actually, as stated before, the invention is concerned with the problem of
automating cytological evaluation by measuring heretofore subtle
distinctions between test cell samples that fall within the capabilities
of machine recognition.
More particularly, this invention relates to a process whereby cells, or
high resolution cell images as by photographs or other means, are
subjected to a coherent light source. The light is scattered, diffracted
and/or refracted into a two dimensional Fourier spectrum of the cell or
cell image. This will provide a variety of transform parameters
functionally related to the cell diameter, nuclear diameter, nuclear
density and other cell features, such as clumping of nuclear
deoxyribonucleic acid (D.N.A.) that in combination greatly enhance the
discriminatory capabilities of cell evaluation.
This invention, therefore, advances the prior art by the disclosure of a
means to use the diffraction and refraction properties of coherent light
for cytological screening and sample enrichment.
Another way of stating the object of this invention is to provide an
apparatus and a process that will afford discrimination or classification
of cytological samples by the computation and evaluation of various
statistical discriminating functions that can be related to cell diameter,
nuclear diameter, and nuclear density - all cytological discriminating
parameters, as for example in tests for malignancy in exfoliated cervical
cells as compared to normal cells, in cytopathology.
A still further object of this invention is to provide an apparatus and a
process for the screening of cytological samples that will accommodate
irregularities in cell shapes in studies of the cells.
Still another object of this invention is to provide apparatus and a
process for screening of cytological samples whereby various statistical
discrimination functions may be calculated, displayed and recorded.
The readers attention is directed to the article, "The Use of Coherent
Optical Processing Techniques for Automatic Screening of Cervical
Cytological Samples," by R. E. Kopp, et al. The Journal of Histochemistry
and Cytochemistry, Volume 22, No. 7, 1974, pp 598-604 wherein a theory and
some results of this invention has been set forth without discussion of
the apparatus and processes to fulfill the above objects and others that
will appear from the following drawings and detailed description of this
invention.
DRAWING DESCRIPTION
With reference to the drawings accompanying this disclosure there is shown
by:
FIG. 1, An isometric schematic illustration of a combination of apparatus
that was used in carrying out the invention hereof;
FIG. 1A, An isometric illustration of a specific form of a combination of
means that has used this invention showing the projection of a collimated
light source to obtain a diffraction pattern for a cell to be classified
by a radial scan.
FIG. 1B, An isometric illustration of an apparatus used in this invention
in companion with the apparatus of FIG. 1A in an angular scan for
measuring selective additional parameters to complete cell classification;
FIG. 2, A frontal view of a solid state electro-optical detector, as may be
utilized in the apparatus and process of this invention,
FIG. 2A, A frontal view of a fiber optic detector as may be utilized in the
apparatus and process of this invention,
FIG. 3, An isometric view of yet another form of a combination of
apparatus, as may be created in a laboratory for carrying out the
procedures of this invention;
FIG. 3A, A cross sectional view of an optical transducer used with the
apparatus of FIG. 3;
FIG. 4, A schematic block illustration of the apparatus of this invention;
FIG. 5, A schematic block form of apparatus to provide computed indication
of cell classification parameters;
FIGS. 6 and 7, Graphical illustrations of measured signature functions from
the apparatus of FIG. 1A for three normal and three malignant cell
structures measured by apparatus according to this invention;
FIGS. 8 and 9, Graphical illustrations of yet another measured signature
function from the apparatus of FIG. 1B, for a normal and a malignant cell
structure according to this invention; and
FIG. 10, A graphical illustration of average measured parameters for two
cell structures computed by apparatus according to this invention.
DETAILED DESCRIPTION
This invention is useful in the classification of cells, and it is
particularly described with respect to the diagnosis of the cancer cells,
whose various structure or morphological features, (sizes, ratio of
nuclear diameter to cytoplasmic diameter, nuclear density, nuclear
irregulatity) differ from that of a normal, non-cancerous, cell structure.
As will be readily appreciated in the performance of this invention, cell
tissue smears are obtained and stained according to the Papanicolaou
technique then fixed on a glass slide. Thereafter, and with particular
reference to the embodiment illustrated in FIG. 1, a photograph is made of
the cell structure, as by the use of a Nikon F camera body mounted onto a
Nikon Su Ke microscope equipped with a trinocular head. It has been found
that photographs bearing a desired contrast can be obtained by use of a
40X objective lens and 10X ocular employed with a 1/2X relay leans to
yield a 200X magnification at the film plane, and by the recording to the
cell measured on K649F emulsion, 35 mm film. The high resolution
capability, large contrast ratio, and large saturation density were found
to be useful film characteristics for this purpose. The film records were
then developed with D-19 developer for 10 minutes at 68 degrees Fehrenheit
to achieve the large contract ratio desired.
The developed film was then mounted within a film transport 10 having an
opening 12 for the exposure of the film 14 to a coherent beam from the
laser 16 expanded to cover the film with a lens 17. The coherent light is
scattered by the cell image forming a two dimensional angular Fourier
Transform spectrum of the cell image 15. The angular spectrum is then
projected by a lens 18 to a transform plane 28.
The Fourier transform or diffraction pattern from the lens 18 is then
collected by a magnifying lens 20 and projected on a face of an optical
detector 22 that is adapted to provide electrical signals for contacts 24
that will be indicative of various measured parameters of the diffraction
pattern on the detector 22, as will be described hereinafter.
This is also shown with reference to FIGS. 1A and 1B which shows an
alternative means of measuring various details of the diffraction pattern
where the laser beam 26 generates the Fourier transform to a diffraction
plane 28 that is expanded by the microscope 20, as shown by the energy
lines 30 and 32 to project a diffraction pattern 34 on a mask 36. The mask
36 and photomultiplier 42 has been substituted in this embodiment for the
optical detector 22 of FIG. 1. As seen, mask 36 has an aperture 38 that
permits the passage of light energy of a portion of the diffraction
pattern to the sensor lens opening 40 of a photomultiplier 42, as will be
readily familiar to those skilled in the art of devices of measuring light
intensity. The photomultiplier 42 is provided with electrical terminals 44
that are the equivalent of terminal 24 for the feeding of the electrical
signals generated thereby, whose amplitude is a function of the intensity
of the light energy transmitted by the mask.
Another means of measuring other specific features of the diffraction
pattern is shown in FIG. 1B. Angular scans of the light intensity in the
diffraction plane we taken using a rotating mask 130 containing a small
hole 132 located at a radial distance from the center of the diffraction
plane. The mask was rotated mechanically by drive 136 of motor 134 through
360.degree. and the light energy passing through the small hole was
collected by a means 131 such as a collector lens and photomultiplier.
One may also combine the feature measuring capability of the two
mechanically activated systems shown in FIGS. 1A and 1B, by a single solid
state electro-optical detector as shown in FIG. 2.
Specifically, there is shown in FIG. 2 a solid-state detector having an
annular plate 208 comprising a plurality of semiconductor fabricated areas
layed out in geometric patterns. More particularly, the plate face is
divided into two semi-circular halves 210 and 212. There is fabricated by
the use of the well known semi-conductor technology a plurality of
individual rings, rings 214, 216, 218 and 220 being specifically called
out by way of example, in the upper half 210. On the face of the lower
half 212 there is similarly provided a plurality of partial wedge shaped
active areas, wedges 222, 224, 226 and 228 being called out by way of
example leaving non-active surfaces 230 and 232 in the lower semi-circular
half 212. Conductors (not shown) lead from each of the rings 214 etc. and
wedges 222, etc. so as to provide for the conducting of an electrical
signal in accordance with the light energy on these rings or wedges, as
will also be readily familiar to those skilled in the art of light
sensitive semi-conductor technology. The detector shown is an improvement
upon the type as disclosed by U.S. Pat. No. 3,689,772. The improvement
being the elimination of unwanted confusion which would be caused by large
area wedges.
It has been found that by this design of the detector 22 it is possible to
automate the process of cell classification to a greater degree than is
possible by the use of the processes involved with apparatus of FIGS. 1A
and 1B. This results from the fact that the rings 214, etc. being each
able to provide an electrical signal indicative of the total energy about
the individual ring will provide a radial scan similar to that permitted
by the mask 36; and the limited areas of the angular position of the
partial wedges 222, etc. will provide an electrical signal indicative of
an angular scan of any light intensity similar to that which will be
provided by the use of the mask 130.
A fiber-optic detector may also be used in place of a photomultiplier or a
solid-state detector. Such a fiber-optic detector is shown by FIG. 2A to
comprise a disc 229 mounting of bundles of individual light conducting
fibers 231, 233, etc. Each bundle of fibers, as will be readily understood
to those skilled in the art, will be connected with individual photo
sensitive means such as phototransistors (not shown) to furnish individual
electrical signals to a computer or similar measuring means, to indicate
in the same fashion as the other detector means the light energy within
the Fourier Transform pattern. Such a bundle of optical fibers can be
connected in the measuring circuit in almost any desired way to provide
analysis of all or any part of the pattern by rendering all or some
bundles effective in providing electrical analysis signals.
With reference now to FIGS. 2 and 3A there is shown a still further form of
apparatus that embodies the principles of this invention. More
particularly, there is shown a stable platform 46 on which is mounted a
laser 48, an expanding lens 49, a Fourier transform lens 50 and a
solid-state electro-optical detector within a housing 52 that is connected
by leads 54 to a minicomputer 58 for taking the measurements of the
detector 52 and providing a computed indication thereof. In this
embodiment a projection microscope 60 is utilized to view the cell tissues
prepared, as aforesaid, and placed on the microscope stage by the glass
slide 62. As schematically shown, the projection microscope 60 has a means
64 to focus light, such as a variable intensity projection bulb, upon the
glass slide 62 in accordance with a variable control 63, whereby a
projection, as by a lens 70, of the cell image may be delivered to a
optical transducer means within a housing 72. At the same time an operator
can also view the glass slide material by means of eyepiece lenses 118.
The contrast of the image on the transducer may be varied by variable
resistance control 66 as shown by indicator 68. The optical transducer is
more particularly described with reference to FIG. 3A to consist of a
sandwich between conductive coated glass flims 74 and 76 of a
photoconductive layers 78 and 82 surrounding a layer 80 of electrically
activated material with variable optical transmission properties. A power
source 84, illustrated as a battery in FIG. 3A and provided by means of an
electrical outlet in FIG. 3 is connected by appropriate conductors to the
transducer shown, as will be readily appreciated by those skilled in the
art. A more particular description of a typical transducer such as may be
required herein is shown by U.S. Pat. No. 3,732,429 issued May 8, 1973. In
brief a photoconductive cadmium sulfide layer 78 functions to convert the
incoherent light image 90 passing through a beam splitter 88 also
projecting the coherent light energy 86 of the laser beam 48 (see FIG. 3)
projected on the conductive coated glass film 74 into a flow of current
through a liquid crystal layer 80. The liquid crystal 80 then responds to
the current flow by changing its optical transmission; in particular, it
becomes translucent such that the image in the liquid crystal layer is
impressed onto the laser beam 86 after the beam passes through the device
to provide an output beam 92 projecting a coherent image of the cell on
slide 62 through the Fourier transform lens 50. Therefore, one may view
the transducer as an instantaneously developed film transparency in that
the projection therefrom is the same as if one exposed a piece of film to
an incoherent light image, placed the developed film transparency in a
path of a laser beam, and observed the outcoming laser beam diffraction
pattern, as by the apparatus illustrated in FIGS. 1 and 1A. Furthermore,
the image transparency (density & contrast) may be varied by adjusting the
exciting voltage applied to it as by control 66.
A schematic illustration of the general means for generating and then
measuring cell diffraction patterns is shown in FIG. 4 and includes the
various previously described system. The laser beam 94 from a laser 96,
such as a Spectra Physics model 124A, is expanded with a lens and a
pinhole combination such as a 4.5 mm lends and 6.8 micron pinhole in a
spatial filter 98, such as a Spectra Physics model 330. A mechanical
shutter 100 is employed between the filter 98 and a collimation lens 102,
such as a Tropel f-4, 200 mm lens, for exposure control. After
collimation, the center portion of the expanded beem is transmitted
through a rectangular aperture (typically 25/32 in..times.1/2 in.) formed
by a light baffle 104, such as a Conductron four-way adjustable aperture
model, to a film holder or optical transducer 106. If a film holder is
used, it has been found that an individual frame of a 35 mm cell image
film strip can be held by clamping it between two optical flats, wetted
with a refractive index matching liquid. Thereafter, the light diffracted
by the cell image is collected with a transform lens 108 to provide a
transform pattern 110. However, as the transform in the back focal plane
of lens 108 may be too small for covenient observation, a short focal
length magnifier 112 is used to enlarge the diffraction pattern image. In
one embodiment of the optical system the magnification factor used thus
far was about 40X, and the equivalent spatial frequency scale in the cell
image plane was about 1000 cycles/mm per cm. The magnified diffraction
pattern 114 (34 in FIG. 1A) is then projected upon appropriate detector
system 116 as described above.
With the aforedescribed measuring equipment there is permitted the
recording of signals from radial and angular information of the Fourier
transform spectrum upon a magnetic tape for data storage and handling.
Reference should now be made to FIG. 5 showing that subsequent to the
recording on the magnetic tape such tapes may be digitized by an
instrument 190.
Final processing of the raw, digitized data is achievable by a computer 204
and at the same time provided to a magnetic tape machine 206 to permit
retention of the digitized data for subsequent checking of the
computation, if necessary.
As will appear hereinafter, the aforesaid apparatus will permit the
generation of the graphical illustrations of FIGS. 6 through 10 from
measured data for the comparison of a normal cell with a malignant cell.
At the same time the apparatus provides signals that may be utilized in a
statistical analysis that will utilize the fundamentals of various
statistical decision procedures such as the Baysian decision process in
pattern classification.
Now in particular regard to the process that is only permitted by the
aforedescribed apparatus in the classification of cell tissue, and more
particularly exfolitated samples such as are presently subjected to
microscopic examination in the screening of cervical cell samples for
determination of cancer, the normal process hereof involves first the step
of the optical generation of a two dimensional Fourier transform. This
involves the use of the cell image 15 (see FIG. 1) to spatially modulate
the collimated laser beam thereby causing a diffraction of coherent light
which is then collected by a Fourier transform lens located one focal
length behind the image plane.
At a distance of one focal length behind the lens, the transverse spatial
distribution of optical energy is functionally related to the modulated
light immediately behind the film. This relationship is the
two-dimensional Fourier transform given by:
##EQU1##
where transform size scaling is determined by the wavelength (.lambda.) of
the coherent light and the focal length (f) of the lens:
w.sub.x =2.pi.x.sub.f /.lambda.f, w.sub.y =2.pi.y.sub.f /.lambda.f (2)
where F is the Fourier transform of the cell image f, and the variables
x.sub.f and y.sub.f are the cartesian coordinates in the transform plane.
There are several properties of the Fourier transform relationship which
prompt the use of this approach as a screening device. The distribution,
F(w.sub.x, w.sub.y), is centered on the optical axis of the lens, with
180.degree. symmetry in the transform plane, and its amplitude is
independent of the location of the cell image on the film. This
circumvents the problem of search for a particular image or feature of the
image within the field of view of an instrument. Similar sized features in
the cell contribute energy over the same region of the spectrum with small
sensitivity to their precise shape and independent of their location
within the image. Although it is not readily apparent from Eq. (1), there
is an inverse relationship between the size of the image and the region of
the Fourier spectrum containing the energy diffracted by the image--that
is, small objects have large spectra and large objects have small spectra.
These properties are attractive from an instrumentation point of view when
considering a screening device. It is again worth mentioning that the
relationship given in Eq. (1) is not highly sensitive to cell image motion
along the optical axis, as in the case in scanning systems which require
elaborate automatic focusing systems.
A more complete discussion and analysis of the optical generation of two
dimensional Fourier transform can be found by reference to the books
INTRODUCTION TO FOURIER OBJECTS by J. W. Goodman, McGraw Hill, N.Y. 1968,
pp. 77-83 and AN INTRODUCTION TO COHERENT OPTICS AND HOLOGRAPHY by G. W.
Stroke, Academic Press, N.Y. 1966, pp. 70-96.
The Fourier transform pattern of all the cells classified to date were
subsequently analyzed quantitatively by measuring both the average radial
distribution of light energy in the transform and also the angular
variation at selected radial positions in the transform plane. The average
radial energy distribution was measured using the apparatus shown
schematically in FIGS. 1A and 1B. A spectrum sampling mask was made
consisting of an open annulas 38 of radius r.sub.o and width .DELTA.r.
This mask was located after the Fourier transform lens 18 and in front of
a photomultiplier tube 42 which measured the integrated light intensity
within the annulus. The mask and photomultiplier were then moved in unison
along the optical axis of the transform lens, i.e., along the x-axis in
FIG. 1A, and the outputs recorded as a function of x. As the origin of the
x-axis is located at the point where the rays of light constituting the
transform have an apparent focus, the spreading bundle of these rays has a
distribution of intensity along any plane (defined by x-x.sub.o) that is
given approximately as
##EQU2##
where F (.rho.,.theta.) is the Fourier transform expressed in polar
coordinates .rho.,.theta. and .rho..sup.2 =w.sub.y.sup.2 +w.sub.y.sup.2 ;
r the radial position in the spreading bundle of rays; and the factor
ar/xo contains the scale factor "a" of the optical system indicating the
linear dilation of the beam, and the factor 1/x.sub.o.sup.2 r.sup.2
accounds for the usual squarelaw fall-off of the light intensity. The
output of the photomultiplier M.sub.out is proportional to the integrated
light coming through the annulus in the mask when it is located at an
artitrary position, or explicitly:
##EQU3##
It may be necessary to have webs to support the annulus in the mask. The
webs will block some of the light. (However, the webs are useful in
obscuring light in the diffraction pattern due to the rectangular aperture
geometry).
To gain some insight into the nature of this measurement we will assume
that the annulus width .DELTA.r is sufficiently small so that:
##EQU4##
where the average pertains to the average taken over the angular
variations. If r.sub.o and .DELTA.r are fixed and x is varied we may
sample the average .vertline.F.vertline..sup.2 at different values of
radial spatial frequency, .rho.. Thus assuming that the optical scale
factor "a" is selected so that:
ar.sub.o /x=.rho. (6)
we find that:
##EQU5##
Finally, with a spatial frequency satisfying a we have:
##EQU6##
or an output that a proportional to .rho..sup.2 times the intensity
squared of the transform.
Different masks were constructed having .DELTA.r/r.sub.o ratios of 0.25 and
0.1 and were used to measure .rho..sup.2
.vertline.F.vertline..sub.avg.sup.2 over two spatial frequency ranges: 10
to 100 cycles/mm; and 100 to 1000 cycles/mm, respectively referred back to
the microscope slide. The data was reduced further and normalized by
dividing each output by the total light energy E in the Spectrum to
complete the step of conducting a radial scan of the diffraction pattern.
In such scan runs data from one of the masks produced the curves of FIGS.
6 and 7. These curves are measures of the average radial distribution of
normalized energy in the transforms and one may regard them as measures of
.rho..sup.2 .vertline.F.vertline..sub.avg.sup.2, bearing in mind the
above, particularly the fact that the width of the annulus is not
arbitrarily small but in fact .DELTA.r/r.sub.o .apprxeq.0.25 or 0.1 with
the greatest error appearing in the low frequencies. Such curves may be
regarded as a signature functions for the particular cell.
In addition to the annulus data, angular scans of the light intensity in
the Fourier transform were made with a mask containing a small hole 132
located at a radial distance from the center of the transform. Actually
this step includes placing the hole at four different radial distances
corresponding to spatial frequencies of 430, 485, 565 and 630 cycles/mm.
The hole diameter corresponds to 65 cycles per millimeter. The mask was
rotated through 360.degree., measuring the optical energy passing through
the small hole as a function of the angular position in the Fourier
transform. This was done for each of the four radial distances mentioned.
The curves of the angular variations are also shown for the cells by FIGS.
8 and 9 and may be regarded as another signature function for the cell.
The ordinate in each case is in arbitrary relative scale, nevertheless the
results can be compared from curve to curve since the maximum value on
each scale is related to the others in the set.
It should be noted that the curves of FIG. 6 are the result of the use of
the apparatus of this invention in screening normal cell tissue; whereas
the curves of FIG. 7 are a similar result in the screening of malignant
cell tissue. The concave shape of the curves of FIG. 6 for the normal
cells is readily contrasted with the convex shape of the curve for the
malignant cells, whereby providing a means to distinguish normal and
malignant cells by the slope of their radial distribution curve in a low
frequency region, such as 10 cycles/mm, with normal cells having smaller
slopes than the malignant cells.
With more particular regard to FIGS. 8 and 9, angular scans of malignant
cells (shown by FIG. 9) tend to have larger variations than the scans for
the normal cell as shown by FIG. 8. This was investigated further by means
of a power spectral analysis of the angular scan curves. With reference to
FIG. 10 there is shown the average power spectrum for a group of malignant
cells (trace 236) and a group of normal cells (trace 238). It should be
noted from FIG. 10 that there is a range illustrated between the dotted
lines 240 and 242 where one can find a wide separation of the average
power spectrum density for malignant and normal cells within which machine
measureable features would be less subject to classification errors than
in other areas of the average power spectrum density for these cells.
Data collected from a group of cells was examined extensively and various
parameters were abstracted from this data to be used for discriminating
cell features. These parameters or features included the total light
energy in the transform of the cell, the slope of .rho..sup.2
F.sup.2.sub.avg (the slope of the product of the square of the radial
frequency times the average radial distribution of light energy in the
transform), the variance of .rho..sup.2 F.sup.2.sub.avg over a range of
valves of .rho., the variance of .vertline.F.vertline..sup.2 over angular
coordinates, and the total energy in a portion of the power spectrum of
the angular variation of .vertline.F.vertline..sup.2, etc. To be explicit,
some of the parameters are given by the expressions:
1. Total energy:
##EQU7##
where (.rho. represents the radial spatial frequency coordinate, .theta.
the angle, and F(.rho.,.theta.) the Fourier transform distribution in
polar coordinates):
2. Slope of .rho..sup.2 F.sup.2.sub.avg in the range a thru d (cycles/mm)
normalized to total energy:
##EQU8##
where a, b, c and d are specific radial positions of the selected range of
radial s | | |
