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Claims  |
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The embodiments of the invention in which an exclusive property or
privilege is claimed are defined as follows:
1. A method of recognizing and counting randomly sized, randomly located
and randomly oriented objects of a distinct geometrical shape in a mass of
objects of varying geometrical shapes, said method comprising the steps
of:
arraying said mass of objects in a non-overlapping field;
passing a beam of coherent light through said non-overlapping field such
that said field scatters said beam of coherent light;
positioning a Fourier transform lens such that the lens collects light
scattered by said non-overlapping field and forms a composite Fourier
spectrum of said non-overlapping field;
measuring the intensity of the light at selected points in said composite
Fourier spectrum; and,
combining said light intensity measurements by nonuniformly weighting each
light intensity measurement made by a predetermined weighting factor, B;
and, summing said nonuniformly weighted light intensity measurements to
provide an estimated count of the number of objects of a distinct
geometrical shape located in said non-overlapping field.
2. A method of recognizing and counting randomly sized, randomly located
and randomly oriented objects of a distinct geometrical shape in a mass of
objects of varying geometrical shapes as claimed in claim 1 wherein:
said non-overlapping field is positioned orthogonal to said beam of
coherent light; and,
said Fourier transform lens is positioned a focal length's distance from
said non-overlapping field on the side thereof remote from the side
receiving said beam of coherent light, whereby said Fourier spectrum is
formed a focal length's distance from said Fourier transform lens.
3. A method of recognizing and counting randomly sized, randomly located
and randomly oriented objects of a distinct geometrical shape in a mass of
objects of varying geometrical shapes as claimed in claim 2 wherein:
said objects of a distinct geometrical shape produce a Fourier spectrum
having hills and valleys; and,
at least some of the selected positions at which said light intensity
measurements are made are located at some of the hills and valleys of the
Fourier spectrum produced by said objects of a distinct geometrical shape.
4. A method of recognizing and counting randomly sized, randomly located
and randomly oriented objects of a distinct geometrical shape in a mass of
objects of varying geometrical shapes as claimed in claim 3 wherein said
weighting factors, B, are determined by using regression techniques based
on measurements made using training non-overlapping fields wherein the
number of objects of said distinct geometrical shape is known.
5. A method of recognizing and counting randomly sized, randomly located
and randomly oriented objects of a distinct geometrical shape in a mass of
objects of varying geometrical shapes as claimed in claim 2 wherein said
selected points at which said light intensity measurements are made and
said weighting factos, B, are determined by using regression techniques
based on measuremens made using training non-overlapping fields wherein
the number of objects of said distinct geometrical shape is known.
6. A mehod of recognizing and counting randomly sized, randomly located and
randomly oriented objects of varying geometrical shapes as claimed in
claim 2 wherein said weighting factors, B, are determined by using
regression techniques based on measurements made using training
non-overlapping fields wherein the number of objects of said distinct
geometrical shape is known.
7. A method of recognizing and counting randomly sized, randomly located
and randomly oriented objects of a distinct geometrical shape in a mass of
objects of varying geometrical shapes as claimed in claim 1 wherein said
selected points at which said light intensity measurements are made and
said weighting factors, B, are determined by using regression techniques
based on measurements made using training non-overlapping fields wherein
the number of objects of said distinct geometrical shape is known.
8. A method of recognizing and counting randomly sized, randomly located
and randomly oriented cells of a distinct morphology, such as
reticulocytes, in a mass of cells of varying morphology, such as a blood
sample, said method comprising the steps of:
arraying said mass of cells on a slide so as to form a non-overlapping
field;
passing a beam of coherent light through said non-overlapping field of
cells such that said field scatters said beam of coherent light;
positioning a Fourier transform lens such that the lens collects light
scattered by said non-overlapping field of cells and forms a composite
Fourier spectrum of said non-overlapping field;
measuring the intensity of the light at selected points in said composite
Fourier spectrum; and,
combining said light intensity measurements by nonuniformly weighting each
light intensity measurement mode by a predetermined factor, B; and summing
said nonuniforly weighted light intensity measurements to provide an
estimated count of the number of cells of said distinct morphology located
in said non-overlapping field of cells.
9. A method of recognizing and counting randomly sized, randomly located
and randomly oriented cells of a distinct morphology in a mass of cells of
varying morphology as claimed in claim 8 wherein:
said slide containing said non-overlapping field of cells is positioned
orthogonal to said beam of coherent light; and,
said Fourier transform lens is positioned a focal length's distance from
said non-overlapping field of cells on the side thereof remote from the
side receiving said beam of coherent light, whereby said Fourier spectrum
is formed a focal length's distance from said Fourier transform lens.
10. A method of recognizing and counting randomly sized, randomly located
and randomly oriented cells of a distinct morphology in a mass of cells of
varying morphology as claimed in claim 9 wherein:
said cells of a distinct morphology produce a Fourier spectrum having hills
and valleys; and,
at least some of the selected points at which said light intensity
measurements are made are located at some of the hills and valleys of the
Fourier spectrum produced by said cells of a distinct morphology.
11. A method of recognizing and counting randomly sized, randomly located
and randomly oriented cells of a distinct morphology in a mass of cells of
varying morphology as claimed in claim 10 wherein said weighting factors,
B, are determined by using regression techniques based on measurements
made using training slides wherein the number of cells of said distinct
morphology is known.
12. A method of recognizing and counting randomly sized, randomly located
and randomly oriented cells of a distinct morphology in a mass of cells of
varying morphology as claimed in claim 9 wherein said selected points at
which said light intensity measurements are made and said weighting
factors, B, are determined by using regression techniques based on
measurements made using training slides wherein the number of cells of
said distinct morphology is known.
13. A method of recognizing and counting randomly sized, randomly located
and randomly oriented cells of a distinct morphology in a mass of cells of
varying morphology as claimed in claim 8 wherein said weighting factors,
B, are determined by using regression techniques based on measurements
made using training slides wherein the number of cells of said distinct
morphology is known.
14. A method of recognizing and counting randomly sized, randomly located
and randomly oriented cells of a distinct morphology in a mass of cells of
varying morphology as claimed in claim 8 wherein said selected points at
which said light intensity measurements are made and weighting factors, B,
are determined by using regression techniques based on measurements made
using training slides wherein the number of cells of said distinct
morphology is known.
15. Apparatus for recognizing and counting randomly sized, randomly located
and randomly oriented objects of distinct geometrical shape in a mass of
objects of varying geometrical shapes, said appratus comprising:
light means for producing a collimated coherent light beam;
support means for supporting, in a non-overlapping field, a mass of objects
of varying geometrical shapes in said coherent light beam;
transform lens means, mounted on the side of said support means remote from
the side receiving said coherent light beam, for collecting light
scattered by the mass of objects supported by said support means in a
non-overlapping field and forming said collecting light into a composite
Fourier spectrum of the mass of objects forming said non-overlapping
field;
light detecting means mounted so as to detect the intensity of the light at
selected points in the Fourier spectrum produced by said transform lens
means and produce output signals having a parameter related to the
intensity of the light detected at said selected points in said Fourier
spectrum; and,
combining means connected to said light detecting means for receiving said
output signals having a parameter related to the intensity of the light
detected by said light detecting means, nonuniformly weighting selected
ones of said received output signals and summing the resultant
nonuniformly weighted signals to produce a combined output signal having a
parameter related to the number of objects of a distinct geometrical shape
located in said non-overlapping field.
16. Apparatus for recognizing and counting randomly sized, randomly located
and randomly oriented objects of a distinct geometrical shape in a mass of
objects of varying geometrical shapes as claimed in claim 15 wherein said
transform lens means is located a focal length's distance from said
support means and wherein said composite Fourier spectrum is formed at the
focal plane of said transform lens means located on the side of said lens
means remote from the side on which said support means is located.
17. Apparatus for recognizing and counting randomly sized, randomly located
and randomly oriented objects of a distnct geometrical shape in a mass of
objects of varying geometrical shapes as claimed in claim 16 wherein:
said transform lens means defines an optical axis;
said support means and said light detecting means lie in planes orthogonal
to said optical axis; and,
said selected points at which said light detecting means detect light in
the Fourier spectrum produced by said transform lens means are located at
predetermined radial positions in the plane in which said light detecting
means lies.
18. Apparatus for recognizing and counting randomly sized, randomly located
and randomly oriented objects of a distinct geometrical shape in a mass of
objects of varying geometrical shapes as claimed in claim 17 wherein:
said light detecting means produce analog signals whose magnitude is
related to the intensity of the light detected by said light detecting
means;
said combining means includes analog-to-digital converting means connected
to said light detcting means for converting said analog signals into
digital signals; and,
said combining means also includes calculating means connected to said
analog-to-digital converting means for nonuniformly weighting said digital
signals and summing the resulting nonuniformly weighted digital signals.
19. A method of determining the vector positions, X.sub.ij, at which light
intensity measuremments are to be made in a pattern recognition system for
recognizing geometrically distinct objects that includes a source of
coherent energy positioned so as to direct a beam of coherent energy
through a mass of objects located in a monolayer field and a fourier
transform lens positioned so as to collect energy scattered by the objects
forming said monolayer field and form a composite fourier spectrum
thereof, said method comprising the steps of:
assuming a set of vector positions x'.sub.ij ;
making energy intensity measurements at each assumed vector position
x'.sub.ij, for each one of a training set of monolayer fields having a
known parameter related to the objects to be recognized;
performing a partial F-value test using the results of said measurements
for each assumed vector position, x'.sub.ij ; and,
testing the results of each partial F-value test to determine if the result
is greater than F.sub.1,N-k-1; .gamma. where .gamma. is the gamma
distribution point of Fisher's F distribution of 1 and N-k-1 degrees of
freedom, N is equal to the number of samples used in the training set and
k is the total number of vector positions x.sub.ij to be determined; and,
choosing the assumed vector positions, x'.sub.ij, to be vector positions,
x.sub.ij, at which measuremens are to be made if the result of their
related partial F-value test is greater than F.sub.1,N-k-1;.gamma..
20. A method of choosing the vector positions, x.sub.ij, at which
measurements are to be made in a pattern recognition system as claimed in
claim 19 including the further step of determining if each assumed
variable, x'.sub.ij, that has a partial F-value test result greater than
F.sub.1,N-k-1;.gamma., has a large probability of having a null value and
rejecting the assumed variables, x'.sub.ij, that have a large probability
of having a null value prior to choosing which assumed vector positions
x'.sub.ij are to be vector positions x.sub.ij.
21. A method of choosing the vector positions, x.sub.ij, at which
measurements are to be made in a pattern recognition system comprising the
steps of:
assuming a set of vector positions, x'.sub.ij,
making energy intensity measurements at each assumed vector position,
x'.sub.ij, for each one of a training set of items;
performing a partial F-value test using the results of said measurements
for each assumed vector positions, x'.sub.ij ; and,
testing the results of each partial F-value test to determine if the result
is geater than F.sub.1,N-k-1;.gamma. where .gamma. is the gamma
distribution point of Fisher's F distribution with 1 and N-k-1 degrees of
freedom, N is equal to the number of samples used in the training set and
k is the total number of vector positions x.sub.ij to be determined; and,
choosing the assumed vector positions, x'.sub.ij, to be vector positions,
x.sub.ij, at which measurements are to be made if the result of their
related partial F-value test is greater than F.sub.1,N-k-1;.gamma..
22. A method of choosing the vector positions, x.sub.ij, at which
measurements are to be made in a pattern recognition system as claimed in
claim 21 including the further step of determining if each assumed
variable, x'.sub.ij, that has a partial F-value test result greater than
F.sub.1,N-k-1;.gamma., has a large probability of having a null value and
rejecting the assumed variables, x'.sub.ij, that have a large probability
of having a null value prior to choosing which assumed vector positions
x'.sub.ij are to be vector positions x.sub.ij. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
This invention is directed to object recognition and counting and, more
particularly, to recognizing and counting geometrically distinct located
objects in a field of objects of varying types.
While this invention was developed for use in detecting and counting
particular types of biological cells located in a field of cells of
varying types, specifically reticulated red blood cells in a blood sample,
and is primarily described in such an environment, it will be appreciated
by those skilled in the art and others from the following description that
the invention is also useful in other environments. Generally, the
invention is useful in any environment where it is desired to recognize
and count the number of geometrically similar objects, located in a mass
of objects having various geometrical shapes, where the mass of objects
can be arrayed in a non-overlapping monolayer. The invention is
particularly useful where the objects are small, e.g., cellular in size,
but range in equivalent size from 0.01 .mu. to 100 .mu. for common
objects. It should be recognized that larger objects can be imaged to this
equivalent size.
For nearly the last two decades biomedical research has focused on
automating the acquisition and interpretation of data in cytology and
microscopy. A variety of techniques has been proposed and, in some cases,
implemented. In many such proposals the optical characteristics of the
objects (e.g., cells) have formed the basis of the proposed technique. For
example, techniques depending on the optical absorption, fluorescence and
scattering properties of cells have been proposed and in some cases used
to separate and classify cells. One difficulty with using cellular optical
properties to distinguish between cell types is that, since a single cell
is examined at a time, chemical reactions are often needed to create or
enhance the optical characteristics upon which these techniques depend. As
a result, these techniques rely heavily on the ability to create the
needed chemical reactions, rather than solely on optical properties. Thus,
although continuous flow systems based on optical information can analyze
up to several thousand cells per second with a high degree of
repeatability, because cell classification depends on external factors
(e.g., chemical reactions), the possibility of error is higher and more
empirical. Moreover, many of these systems are very dependent on the use
of electronic digital computers to perform a variety of time-consuming,
and therefore expensive, processing steps. This expense has made such
systems particularly undesirable for use in general clinical environments.
As a result of the foregoing difficulties, consideration has been given to
the use of optical data processing techniques (as opposed to electronic
data processing techniques) to identify and count objects. Optical data
processing techniques are based on the knowledge that geometrically
distinct objects will scatter light in a distinct manner, and that each
geometrically similar object will scatter light in a similar manner.
As will be recognized by those skilled in the data processing art, optical
data processing techniques function in an analog, as opposed to a digital,
manner. Further, because of the parallel nature of the data processing
analog operations can be performed at substantially higher processing
rates and with higher data capacity, than can digital operations,
particularly in the area of summing data for subsequent analysis.
One of the difficulties in applying optical data processing techniques, as
well as other techniques, to the recognition and counting of objects, such
as biological cells, is the inherent requirement that the resultant system
exactly and unambiguously identify and count the particular cell
population desired.
In the past, attempts to meet the foregoing constraint have involved
applying matched filter concepts to provide a system wherein only the
light scattered by the objects to be recognized and counted is passed. The
problem with the use of matched filters is that they suffer from
rotational alignment dependencies and, require an unambiguous description
of the Weiner spectrum of the cell or object to be recognized and counted.
In many environments the need for an unambiguous or exact count can be met
using an estimated count, depending upon the required degree of
"exactness." An estimation approach is particularly attractive when the
resultant count is to be used for threshold or screening purposes. But,
estimation optical data processing systems also have the problem that they
require the Weiner spectrum of the desired cell be identified. However, in
an estimation system this requirement can be dealt with by using a
statistical approach. Specifically, instead of attempting to isolate a
single cell for use in identifying or determining the Weiner spectrum of
the cells to be counted, an ensemble of cells can be used to form an
average spectrum. In this regard, attention is directed to U.S. Pat. No.
3,947,123, issued Mar. 30, 1976 to F. Paul Carlson, et al., for "Coherent
Optical Analyzer."
While the optical data processing method and apparatus described in the
foregoing patent is an advance over prior methods and apparatus and lends
itself to studies of cell types, groups, or subclasses, by simply varying
the ensemble selected to develop the average spectrum, it has certain
disadvantages. For example, the system is limited by its need to
continually fabricate a new Weiner filter for each new class or group to
be examined. Further, the method and apparatus implicitly requires that an
ensemble of the particular cell to be identified and counted be
unambiguously isolated. Obviously, this inflexible filter fabrication
requirement significantly limits the extension of this method and
apparatus to other environments.
Another previous problem with applying optical data processing tehniques to
cell recognition and counting is that of interfacing a coherent optical
system to the cells to be counted, both in an input and output sense. In
the case of cells on a film slide, the input problem can be readily
resolved by creating a monolayer of the cells. However, the output problem
remains unless indirect measurements, such as integrating the total
output, is acceptable. In many cases, such an indirect measurement is
unacceptable or, at best, is less acceptable than desired.
Therefore, it is an object of this invention to provide a new and improved
optical data processing method and apparatus for identifying and counting
objects.
It is a further object of this invention to provide a new and improved
optical data processing method and apparatus for recognizing and counting
the number of objects of a particular type in a field of objects of
varying types that is based on the geometrical distinctness of the
objects.
It is a still further object of this invention to provide an uncomplicated
optical data processing method and apparatus suitable for recognizing and
counting the number of biological cells of a particular morphological type
in a field of biological cells of varying types.
It is also an object of this invention to provide a method of determining
the vector positions at which measurements are to be made in a pattern
recognition system.
SUMMARY OF THE INVENTION
In accordance with this invention, a method of recognizing and counting
geometrically distinct objects located in a field of objects having
varying geometrical shapes is provided. The preferred form of the method
generally comprises the steps of: directing a beam of coherent light
through a monolayer field of objects, including objects of the type to be
recognized and counted, such that the objects located in the field scatter
the coherent light beam; collecting the scattered light using a Fourier
transform lens positioned such that the field is positioned in the focal
plane located on one side of the lens; detecting the intensity of the
light present at discrete points in the focal (Fourier transform) plane
located on the side of the lens opposed to the field side; and, weighting
and summing the resultant measurements to obtain an estimate of the number
of the objects to be recognized that are located in the field.
In accordance with further principles of this invention, an apparatus for
recognizing objects of a particular type located in a monolayer field of
objects of varying types is provided. The preferred form of the apparatus
of the invention comprises: a source of coherent collimated light forming
a beam oriented so as to pass through said field; a collecting lens
positioned so as to collect the light scattered by said field, said lens
being located a focal length's distance from said field; detecting means
for detecting the scattered light collected by said lens at the focal
plane of said lens opposite from the focal plane at which said field is
located; and, weighting and summing means for weighting and summing the
light detected by the detecting means. The detecting means preferably
comprises a plurality of light-detecting elements located at equally
spaced (discrete) radial positions, i.e., positions that, if located along
a common radius extending orthogonally outward from the optical axis
defined by said lens, would be equally spaced. This arrangement is
particularly useful when the radial positions at which measurements are to
be made are initially unknown. Even if known, this arrangement can be
utilized merely by using zero weighting factors to eliminate any light
measurements made at undesired radial positions. Alternatively, the
light-detecting elements may be unequally spaced. This arrangement, i.e.,
unequal spacing, is particularly useful if the radial measuring positions
(which relate to object-identifying frequency points) are known.
It will be appreciated from the foregoing summary that the method and
apparatus of the invention does not require the inclusion of a Weiner
filter. While an apertured mask may be located at the Fourier transform
plane of the lens, such a mask need not have the characteristics of a
Weiner filter. Further, while useful in some instances, a mask is not
required.
Preferably, the weighting factors applied to the detected light are
obtained by regression techniques. The regression techniques are based on
the assumption that the objects to be recognized and counted are
geometrically distinct from the other objects in the field, whereby each
type of object scatters light in a different manner and thus has a
different Fourier spectrum. The regression techniques are based on the
knowledge that, given enough sampling characteristics of the objects to be
recognized and counted, a vector space of the weighting factors can be
developed that will adequately describe the particular object space. The
regression technique preferred is a least-squares regression technique. In
the situation where the radial positions (e.g., frequencies at which
measurements to be made) are known, the least-squares regression technique
is used to develop weighting factors that allow electronic or digital
methods to be utilized to estimate the number of objects to be recognized
and counted. In the case where the radial positions are unknown, the
regression technique is used to develop both the radial positions and the
weighting factors. In the latter situation, if equally spaced detectors
are actually included in a physical implementation of the invention, as
noted above, selected weighting factors may be made equal to zero, whereby
only selected radial positions actually produce the resulting recognition
and counting information.
BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing objects and many of the attendant advantages of this
invention will become more readily appreciated as the same becomes better
understood by reference to the following detailed description when taken
in conjunction with the accompanying drawings, wherein:
FIG. 1 is a partially block and partially pictorial diagram illustrating an
apparatus, formed in accordance with the invention, wherein light is
measured at unequally spaced radial positions located in the Fourier
transform plane of a lens;
FIG. 2 is a waveform diagram illustrating the light spectrum formed along a
radius in the Fourier transform plane of a lens for both a single object
and for a field of objects;
FIG. 3 is a plan view of a window suitable for use in the apparatus
illustrated in FIG. 1;
FIG. 4 is a flow diagram illustrating a sequence of steps used to determine
weighting factors and radial positions, all in accordance with the
invention; and,
FIG. 5 is a partially block and partially pictorial diagram illustrating an
apparatus, formed in accordance with the invention, wherein light
measurements are made at equally spaced radial positions located in the
transform plane of a lens.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Prior to describing the invention in detail, a brief discussion of certain
background information is presented. As will be readily understood by
those skilled in the optical data processing arts, a collimated, coherent
light beam passing orthogonally through a monolayer field of objects is
scattered by the objects. If this scattered light is collected by a
Fourier transform lens, mounted such that the field is located at one
focal plane of the lens, a composite Fourier spectrum is formed at the
other focal plane of the lens. The composite spectrum includes, in an
additive sense, the Fourier spectrum of each object in the field. This
result is based in part on the fact that the only change in the spectrum
of an object not on the optical axis is a non-measurable phase factor that
is lost in the hereinafter described intensity measurement process. The
present invention analyzes the composite spectrum and produces an output
related to the number of objects of a particular type contributing to the
composite spectrum. Thus the invention "recognizes" and "counts" the
number of objects of a given type in a field of objects of varying types.
FIG. 1 illustrates an apparatus formed in accordance with the invention for
forming and analysing the composite spectrum. The apparatus illustrated in
FIG. 1 includes a monolayer of objects, e.g., blood slide 11, mounted
orthogonally in a collimated laser light beam 13 created by a collimated
laser light source 14. Located on the side of the blood slide 11, remote
from the side receiving the collimated light beam 13, is a Fourier
transform lens 15. The distance between the blood slide and the Fourier
transform lens 15 is equal to the focal length (f) of the transform lens.
Located on the opposite side of the Fourier transform lens 15 from the
blood slide 11 is a window 17. While in most circumstances the inclusion
of a window is not necessary, if included, the window is located at the
Fourier plane of the transform lens 15, i.e., in a plane orthogonal to the
optical axis 21 defined by the transform lens and spaced from the lens by
a distance equal to the focal length (f) of the transform lens 15. A
suitable window is illustrated in FIG. 3 and hereinafter described.
Located on the side of the window 17 remote from the transform lens 15, but
still at the lens focal plane, are a plurality of photodetectors 19. The
photodetectors, as will be better understood from the following
description, are located along one or more radii extending orthogonally
outward from the optical axis 21 of the transform lens 15, at different
radial distances. Alternatively, an approximately mounted mirror may be
used to direct the light to detectors located off of the optical axis 21.
In the apparatus illustrated in FIG. 1, the radial distance between
adjacent detectors is different; however, it may be the same, as will be
better understood from the following discussion. In any event, it is to be
understood that the light sensitive surfaces of the detectors lie in the
focal plane of the lens, or receive light reflected from the focal plane.
A multiple-pole switch 23 is connected such that each photodetector can be
selectively connected to a current-to-voltage converter 25. The output of
the current-to-voltage converter is connected to the input of a digital
voltmeter 27. The digital voltmeter is adapted to produce individual data
cards 29 for each measurement made by a photodetector. The data on the
data cards (which could also be recorded on some other memory media) is
processed by a batch process computer 31 in combination with known count
data, obtained for example by manual counting, to first develop weighting
factors. Thereafter the developed weighting factors are used in
combination with card data to produce estimated counts, all in the manner
hereinafter described.
It is pointed out here that the blood slide is only an example of one type
of monolayer object field with which the invention is useful, and that the
invention is equally suitable for use with other types of object fields.
The only requirement to be met is that different types of objects in the
field have different geometrical shapes and that the field be a
non-overlapping monolayer field. In the case of a blood slide, the objects
include mature red blood cells (erythrocytes), immature red blood cells
(reticulocytes), white blood cells (leukocytes), and artifact.
As will be readily appreciated by those skilled in the art, the objects on
the blood slide scatter the collimated laser light 13. The light scattered
by the objects is collected by the Fourier transform lens 15 and a
composite Fourier spectrum is created at the plane of the window 17. The
composite Fourier spectrum includes the Fourier spectrum of each of the
objects.
FIG. 2 is a waveform diagram illustrating both a typical composite Fourier
spectrum S.sub.1 and a single object Fourier spectrum S.sub.2, taken along
one of the radii of the transform plane. The vertical axis denotes beam
intensity and the horizontal axis denotes radial or vector positions. As
will be readily understood by those familiar with optical Fourier
transformation, radial positions are frequency-related.
In accordance with the invention, if light intensity measurements made at
suitable radial positions (i.e., X.sub.1, X.sub.2, etc.) are suitably
weighted and, the resultant weighted measurements summed, the result is
related to the number of objects of a particular type (e.g.,
reticulocytes) located in a field of objects of varying types (e.g., a
blood slide field). The key, of course, is to appropriately choose the
radial positions and correctly weight the measurements made at those
positions. In most instances, a particular object creates a wave having
hills and valleys (see object spectrum S.sub.2 illustrated in FIG. 2). It
has been found that if measurements are made at these hills and valleys,
i.e., if X.sub.1, X.sub.2, X.sub.3, etc., are located at the hills and
valleys of the spectrum of the object to be recognized and counted, and
these measurements are appropriately weighted, an accurate estimated count
of the number of such objects is provided. In other words, while other
radial positions are acceptable in many circumstances, the hills and
valleys are acceptable in almost all, if not all circumstances. In some
instances, the hill and valley positions are known. For example, prior art
devices, such as the one described in U.S. Pat. No. 3,947,123, referenced
above, can be used to develop information about the radial position of the
hills and valleys of certain cell spectrums, such as a reticulocyte
spectrum. When this information is known, obviously the photodetectors are
placed at these desired radial positions initially, or if the
photodetectors are fixed in position only measurements made by
photodetectors located at the desired positions are chosen for use in the
weighting and summation steps.
Prior to describing the invention further, a brief discussion of the theory
of operation of the invention as best understood is next set forth.
In accordance with the present invention, a model of the vector space
defining the objects to be counted is constructed. The model is
constructed adaptively through a least-squares procedure by defining a
dependent variable y.sub.i, which is directly proportional to an observed
count of the cells or objects to be counted in terms of a set of
independent variables x.sub.ij, which are proportional to the intensity at
certain spatial frequencies (radial positions) of the spectrum, and a set
of coefficients .beta..sub.j (weighting factors), which weight the
contribution from each x.sub.ij, such that the resulting sum of the terms
is proportional to the desired count. More specifically,
y.sub.i = .beta..sub.0 + .beta..sub.1 x.sub.il + . . . + .beta..sub.J
x.sub.iJ + .epsilon..sub.i, (1)
where i = 1, 2, . . ., N, and where .epsilon..sub.i is some random noise or
error associated with the observed count, y.sub.i. From this model, an
unknown y.sub.i can be predicted from measurements of x.sub.ij, when the
appropriate .beta..sub.j are known.
Obviously, development of this model depends upon a determination of the
coefficients, .beta..sub.j. While the true values of the coefficients or
weighting factors cannot be determined without full knowledge of all
possible occurrences of y.sub.i and x.sub.ij, they can be estimated using
a least-squares technique based on a set of N observations of y.sub.i and
x.sub.ij. That is, counts made of the number of objects to be recognized
and counted located in a random field of objects, made either manually by
a technician or by prior art techniques at the same time intensity
measurements (x.sub.ij) are made, can be used to develop B.sub.j. More
specifically, a term denoting the sum of the squares, S, can be defined by
the following equation:
S = .SIGMA. [y.sub.i - (.beta..sub.0 + .beta..sub.1 x.sub.il + . . . +
.beta..sub.J x.sub.iJ)].sup.2 (2)
this equation can be rewritten in matrix form as:
S = (Y - X.beta.).sup.T (Y-X.beta.) (3)
where .beta..sup.T = (.beta..sub.0,.beta..sub.1, . . . , .beta. .sub.J),
Y.sup.T = (y.sub.1,y.sub.2, . . . ,y.sub.N) and X is a Nx(J+1) matrix. The
criterion for selection of the .beta..sub.j elements is to require that S
be a minimum, which is equivalent to saying that the sum of the squares of
the differences between the observed values and the true values be the
least. The least-squares estimates, B, where B.sup.T = (b.sub.o,b.sub.1, .
. . ,b.sub.J), are those which minimize the quadratic form of Equation (3)
with respect to .beta.. The procedure to be followed is described in
detail in "Applied Regression Analysis" by N. Draper and H. Smith,
published by John Wiley & Sons, Inc., New York, 1966, and "The Analysis of
Variance" by H. Scheffe, also published by John Wiley & Sons, Inc., 1959,
pp. 68-70, and comprises taking the partial derivatives of S with respect
to .beta..sub.j, setting the resultant matrix equation equal to zero, and,
then, replacing .beta..sub.j with the resulting B.sub.j. This procedure
yields the equation:
(X.sup.T X)B = X.sup.T Y, (4)
the solution of which can be written as:
B = (X.sup.T X).sup.-1 X.sup.T Y (5)
thus, the least-squares technique results in the following model for the
predicted count
y.sub.i = b.sub.0 + b.sub.1 x.sub.il + b.sub.2 x.sub.i2 + . . . + b.sub.j
x.sub.ij (6)
where the estimated cell count is represented by y.sub.i and the Weiner
spectrum intensity measurements are represented by the x.sub.ij, taken at
specific vector points in the Fourier transform plane (i.e., the focal
plane of the lens). For slide N+1 (i.e. the first slide after the
weighting factors, b.sub.j, have been determined) from the same class of
cells, the estimated cell count is given by:
y.sub.N+1 = b.sub.0 + b.sub.1 x.sub.N+1,1 + b.sub.2 x.sub.N+1,2 + . . . +
b.sub.J x.sub.N+1,J (7)
which can be written in matrix notation as
Y.sub.N+1, = X.sub.N+1 B (8)
where X.sub.N+1, = (1, X.sub.N+1, . . . ,X.sub.N+1,J).
Since the count represented by Equations (7) and (8) is just an estimate,
there is an inherent error. This error can be described by the variance of
the estimation (see the "Applied Regression Analysis" reference cited
above) as:
V(Y.sub.N+1) = X.sub.N+1 V(B)X.sub.N+1,= X.sub.N` (X.sub.T X).sup.-1
X.sub.N+1 .sigma..sup.2 (9)
where .sigma..sup.2 represents the variance of the original count, y. If an
estimated variance (see "Statistics: With a View Toward Applications" by
L. Brieman, published by Houghton Mifflin, Boston, 1973), .sigma..sup.2,
is now used to describe the variance, .sigma..sup.2, where:
.sigma..sup.2 = (Y-Y).sup.T (Y-Y)/N-J-1 (10)
then the estimated variance of the N+1 estimated count, y.sub.N+1, will be
given by:
##EQU1##
Since the prediction model, Equation (6), is constructed from a finite set
of training samples, y.sub.i, the statistical estimates might be far from
being the true values. This is equivalent to saying that the coefficients
b.sub.j may vary if the size of the set of "training " samples is changed,
or if another set of "training" samples is used. Some way of indicating
the accuracy of the estimation is thus necessary. To do this, a 100
.gamma.% confidence region is used. Inside this region the true prediction
model, and hence the true value of the estimates, are all expected to lie
in 100 .gamma.% of the cases. This range of confidence is given by:
##EQU2##
where F.sub.J+1,N-J-1; .gamma. is the .gamma. distribution point of
Fisher's F distribution with (J+1) and (N-J-1) degrees of freedom. (See
"Statistics: With a View Toward Applications" and "The Analysis of
Variance", both referenced above.) This approach provides a more
reasonable measurement of the estimation error because it simultaneously
adjusts for the variability of all the coefficients b.sub.j that are due
to the random observation errors, .epsilon..sub.i.
As will be readily appreciated by those skilled in the art, the above
analysis is based on the assumptions that: (1) a scheme of selecting and
obtaining the independent variables, x.sub.ij, is known; and, (2) the
model formed with these variables is correct. If the model is correct, the
estimates, y.sub.i, will be unbiased and correct.
To implement this model in a coherent optical processor of the type
illustrated in FIG. 1, the problem to be resolved is the selection of the
spatial frequency vector components, i.e., the position (or selection) of
the detectors whose outputs are to be used, when this information is
unknown. Prior to discussing the resolution of this problem a further
point is first discussed. Specifically because even particular cells
(objects) within a class have a morphological (geometrical shape)
variability associated with their size, their spectral amplitudes differ
over a range of radial positions. To minimize the variance associated with
this amplitude difference, smoothing of the irradiance spectral values is
accomplished by using either: (1) a window 19 having finite-sized sampling
openings; or, (2) finite-sized detectors, if the window is eliminated.
When either of these techniques is used, objects of similar quasicircular
morphology, e.g., shape or form, but with variations in azimuthal
amplitude, e.g., size, will have a finite dimension in azimuth. In other
words, X.sub.1, X.sub.2, X.sub.3, etc., (FIG. 2) will have a finite width
determined by size variations. Measurements made over these width
variations provide the desired smoothing.
In summary, the sampling system must not only perform discrete sampling in
the focal plane, it must also have a smoothing or aperture-averaging
effect to compensate for size (but not shape) variations. Either a window
of the type illustrated in FIG. 3, or finite sized photodetectors, can be
used to achieve this result.
The data obtained by making intensity measurements at each sampling
aperture or sampling point from a training set of slides, together with a
knowlege of the values of the dependent variables (counts of the desired
objects), y.sub.i, are used to find the weighting coefficients, B, in
accordance with Equation (5). This knowledge is then used in accordance
with Equation (8) to subsequently predict or estimate the number of
objects, Y.sub.N+1.
Turning now to the spatial frequency vector component problem denoted
above, in the foregoing discussion, the x.sub.ij sampling points (vector
components) were assumed t | | |
