Image gradation processing method and apparatus for radiation image recording system

Abstract

A method and apparatus for processing a radiation image in a radiation image recording system in which a stimulable phosphor is stimulated with a scanning stimulating ray and the light emitted from the stimulable phosphor upon stimulation by the stimulating ray is detected by a photodetector which gives an output to be processed and used for recording a visible image on a recording medium. The radiation image of the frontal chest is gradation processed. The gradation processing is characterized in that the density at the boundary of the heart and the lungs of the image on the recording medium is lowered to lower the contrast of the heat and raise the contrast of the lungs.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a method of processing a radiation image in a radiation image recording system used for medical diagnosis and apparatus therefor. This invention particularly relates to an image gradation processing method and apparatus in a radiation image recording system in which a stimulable phosphor is used for recording radiation image information as an intermediate recording medium and the image recorded therein is read out for reproduction and finally recorded on a recording medium.

2. Description of the Prior Art

The radiation image recording system as mentioned above is disclosed, for instance, in U.S. Pat. No. 3,859,527 and Japanese patent application No. 53(1978)-84741, the latter being filed in the name of the same applicant. In this system, radiation image information is recorded in a stimulable phosphor by exposing the phosphor to a radiation transmitting through an object like a human body, then the recorded information is read out by use of a photodetector by stimulating the phosphor with a stimulating ray like a laser beam or the like, and the read out information is recorded on a recording medium by modulating a recording laser beam or the like with the information read out by the photodetector.

The above-described radiation image recording system is far more advantageous that the conventional radiography using a silver halide photographic film in that the image is recorded over a very wide dynamic range of radiation exposure. Therefore, this system is particularly valuable when it is applied to the radiographic diagnosis of the human body. By using this system for such purposes, it becomes possible to obtain the information which cannot be obtained in the conventional radiography because of the limited exposure range that can be recorded and observed on the conventional X-ray film.

Further, since the X-rays do harm to the human body, it is impossible from the viewpoint of safety to expose the human body to X-rays of high dose. Therefore, it is desired that the necessary information in the radiography can be obtained by exposing the human body only once to the X-ray of comparatively low dose. On the other hand, radiographs should preferably have both a wide exposure latitude and high image quality of high contrast, high sharpness, low noise etc. for viewing and diagnosis purposes. Unfortunately, since the conventional radiography is designed so as to satisfy all the required conditions to some extent, the range of recording density or the ability to record various levels of information and the image quality are both insufficient and neither of these properties are completely satisfied.

The present invention is particularly directed to an improvement in the radiation image recording system of the above-described type in which the image gradation of a radiation image of the chest is improved.

In the conventional chest radiography, an X-ray film is used for recording the X-ray transmission image of the chest and recorded image is observed with the naked eyes for diagnosis. In the chest radiography, there are recorded lungs, a heart and a spine. The spine has the lowest density since the transmittivity thereof to the X-rays is low. The heart has the second lowest density since the transmittivity thereof to the X-rays is comparatively low. The lungs has high density since the transmittivity thereof to the X-rays is high. Further, since the lungs have complex trachea/bronchus and blood vessels, the image of the lungs is very complicated. The part outside the substantial image of the human body has the upmost density since this part of the X-ray film is exposed to X-rays directly coming from the X-ray source.

As mentioned above, the chest radiography has various information of various parts of the human body which is recorded in the density having a wide range of levels. Sometimes, the density ranges from 0 to 3.5 in terms of optical density. Further, since the various parts are not recorded in the desirable contrast respectively, it is very difficult and necessary to have a great skill to make proper diagnosis from the radiograph in which the disease must be found out from a very slight variation in density in the image.

It is generally known in the art that the image properties can be changed by processing the image by use of an electronic signal or information processing method. For instance, even in radiography, it is possible to read the image recorded on the X-ray film by an optical scanning means and process the read out signal by a signal processing means to change the various image properties such as contrast and the density level and then record a visible image on a recording film or the like based on the processed signal.

In the radiography, however, the recorded image is used for the purpose of "diagnosis" and the diagnostic efficiency and accuracy (the level of easiness for diagnosis or adaptability to diagnosis) are not simply enhanced by simply making so-called "good" image from the point of the ordinary image quality factors such as sharpness, granularity and contrast. Rather than these factors, the diagnosis efficiency and accuracy are influenced by other complex factors such as reference with the normal shade, reference with the anatomical structure and utilization of other diagnostic view or records.

On the other hand, it has been known in the art as one example of image processing to record the radiograph on a microfilm in a reduced size. For instance, as shown in Japanese Patent Laid Open No. 48(1973)-25523, it is known to use a photographic film having a modefied gradient contrast in which the contrast (gamma) is lowered in the high density area to compress the density range at the time of copying, and further conduct an unsharp masking process to compensate the lowering of sharpness caused by image size reduction and copying. This process, however, is effective only for preventing the lowering of the image quality in the image size reduction and copying steps and is not made for the purpose of enhancing the diagnostic efficiency and accuracy.

SUMMARY OF THE INVENTION

The primary object of the present invention is to provide a method of and apparatus for gradation processing the chest radiograph or a radiation image of the chest.

Another object of the present invention is to provide a method of and apparatus for processing a radiation image in a radiation image recording system using a stimulable phosphor which is capable of obtaining a radiation image having high diagnostic efficiency and accuracy.

The method of and apparatus for gradation processing the radiation image of the chest are characterized in that the density at the boundary of the heart and the lungs of the image on the recording material is lowered to lower the contrast of the heart and thereby raising the contrast of the lungs in the radiation image finally recorded on a recording medium.

In accordance with the gradation process as mentioned above, the density range of the heart becomes narrow and the lower density of lungs is more lowered and the contrast of the lungs is enhanced, and consequently the image thus gradation processed is improved of its diagnostic efficiency and accuracy. It should be noted that, though the contrast of the heart is lowered it does not affect the diagnostic efficiency and accuracy since this part is the brightest part and human eyes have high gradational response to such a part. Since the spine has substantially the same density as the heart, this part does not affect the diagnostic efficiency and accuracy either.

In general, most of the chest radiographs are made for the purpose of mainly observing the lungs. Therefore, in accordance with the present invention in which the contrast and the density of the lungs are particularly improved, the diagnostic efficiency and accuracy of the lungs are markedly enhanced without substantially lowering the diagnostic efficiency and accuracy of the spine and the heart.

The stimulable phosphor referred to in this invention means a phosphor which is able to store radiation energy upon exposure thereof to a radiation as of light or high energy radiations and then emits light according to the stored energy upon optical stimulation. The stimulable phosphor is desired to emit light having a wavelength within the range of 300 to 500 nm. For example, rare earth activated alkaline earth metal fluorohalide phosphor is preferred. On example of this phosphor is, as shown in Japanese patent application No. 53(1978)-84742, a phosphor represented by the formula (Ba.sub.l-x-y' Mg.sub.x' Ca.sub.y)FX:aEu.sup.2+ wherein X is at least one of Cl and Br, x and y are positive numbers which satisfy 0<x+y.ltoreq.0.6 and xy.noteq.0, and a is a number satisfying 10.sup.-6 .ltoreq.a.ltoreq.5.times.10.sup.-2. Another example of this phosphor is, as shown in Japanese patent application No. 53(1978)-84744, a phosphor represented by the formula (Ba.sub.l-x' M.sub.x.sup.II)FX:yA wherein M.sup.II is at least one of Mg, Ca, Sr, Zn and Cd, X is at least one of Cl, Br and I, A is at least one of Eu, Tb, Ce, Tm, Dy, Pr, Ho, Nd, Yb and Er, x is a number satisfying 0.ltoreq.x.ltoreq.0.6, and y is a number satisfying 0.ltoreq.y.ltoreq.0.2. Further, as the stimulable phosphor to be used in this invention can be used ZnS:Cu,Pb; BaO.xAl.sub.2 O.sub.3 :Eu wherein 0.8.ltoreq.x.ltoreq.10; and M.sup.II O.xSiO.sub.2 :A wherein M.sup.II is Mg, Ca, Sr, Zn, Cd or Ba, A is Ce, Tb, Eu, Tm, Pb, Tl, Bi or Mn, and x is a number satisfying 0.5.ltoreq.x.ltoreq.2.5, as shown in Japanese patent application No. 53(1978)-84740. Furthermore, as the stimulable phosphor can be used LnOX:xA wherein Ln is at least one of La, Y, Gd and Lu, X is at least one of Cl and Br, A is at least one of Ce and Tb, x is a number satisfying 0<x<0.1, as shown in Japanese patent application No. 53(1978)-84743. Among the above numerated phosphors, the rare earth activated alkaline earth metal fluorohalide phosphor is the most preferable, among which barium fluorohalides are the most preferable in view of the high intensity of emission of light.

Further, it is desirable to color the phosphor layer of the stimulable phosphor plate made of the above phosphor by use of pigments or dyes to improve the sharpness of the image obtained thereby as disclosed in Japanese patent application No. 54(1979)-71604.

As for the stimulating rays for stimulating the phosphor after the phosphor is excited with the radiation energy in an image pattern, a laser beam having high directivity is used. As the laser beam, a laser having a wavelength within the range of 500 to 800 nm, preferably of 600 to 700 nm is preferred. For example, a He-Ne laser (633 nm) or a Kr laser (647 nm) can be used. If a color filter which cuts the light having a wavelength beyond the range of 500 to 800 nm is used together with a light source, a light source having a wavelength distribution beyond said rante can be used.

The radiation image information read out by use of the device of this invention is used to reproduce a radiation image on a recording medium such as a silver halide photographic film, a diazo film or an electrophotographic recording material. Further, it is possible to reproduce the radiation image on a cathode ray tube.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a schematic view of a chest radiograph to be processed in accordance with the present invention,

FIG. 2 is a flow chart which shows the steps of the method of processing the chest radiograph in accordance with the present invention,

FIG. 3 is a graph showing an embodiment of the gradation processing in accordance with the present invention,

FIGS. 4 and 5 are graphs showing other embodiments of the gradation processing in accordance with the present invention,

FIG. 6 shows various embodiments of the gradation processing in accordance with the present invention and some examples of the gradation processing which are not included in the present invention,

FIG. 7 is a block diagram of a radiation image recording system in which the image processing apparatus of the present invention is employed,

FIGS. 8 and 9 are histograms of the densities respectively of the heart and the lungs, and

FIGS. 10A to 10C show the density measured and the differential waveform obtained when the central part of the heart is horizontally scanned.

DESCRIPTION OF PREFERRED EMBODIMENTS

Now the present invention will be described in detail with reference to the drawings.

Referring to FIG. 1, a frontal chest radiograph has images of lungs 1, heart 2 and spine 3. Since the conventional chest radiograph does not have desirable density and contrast, the accurate diagnosis is not easy from the radiograph as it is. In accordance with the present invention, therefore, the X-ray image information is read out from the image recorded in the stimulable phosphor (hereinafter referred to as "original image") and the read out information is processed by a signal conversion system for varying the gradation when the image is finally recorded on a recording medium like a photographic film.

FIG. 2 shows the steps of the method of processing the radiation image in accordance with the present invention which is particularly applied to an X-ray image recording system. At first, a stimulable phosphor is exposed to X-rays transmitting through a human body. Thus, the X-ray image is input into the stimulable phosphor and memorized therein as radiation energy stored at its trap level.

Then, after the X-ray image input, the stimulable phosphor is stimulated with a scanning stimulating light beam having a wavelength within the range of 500 to 800, preferably 600 to 700 nm. Upon stimulation, the stimulable phosphor emits light having a wavelength within the range of 300 to 500 nm. The emitted light is detected by a photodetector like a photomultiplier or a photodiode which receives only the light within this range of wavelength. Thus, the radiation image information is read out.

The output of the photodetector is amplified and then A/D converted to a digital signal and recorded in a magnetic memory tape. The digital signal memorized in the magnetic memory tape is processed by a processing means like a mini-computer to conduct the gradation processing.

Among the signals representing the original image, the signal corresponding to the lungs 1 has the highest level excluding the area outside the object human body, and the signals for the spine 3 and the heart 2 have the lowest level. The difference between the signal for the spine 3 and the signal for the heart 2, the latter being a little higher than the former, is very small and accordingly both signals can be represented by one of the signals practically. These signals will hereinbelow be represented by the signal for the heart 2. Therefore, by obtaining the minimum value Smin of the signal for the spine and the heart and the maximum value Smax of the signal for the lungs and performing the signal conversion only on the signals having a level between these values, it is possible to conduct the gradation processing on the necessary image to obtain a radiation image having high diagnostic efficiency and accuracy.

In the present invention, the density at the boundary of the lungs 1 and the heart 2 is lowered to lower the contrast of the heart 2 and raise the contrast of the lungs 1. By lowering the density at the boundary of the lungs 1 and the heart 2, the diagnostic efficiency and accuracy are enhanced.

FIG. 3 is a graph showing the gradation processing, in which the chain line 4 represents a linear signal conversion shown by a straight line extending between the maximum density point at the maximum value of the original signal Smax and the minimum density point at the minimum value of the original signal Smin.

It should be understood here that the photographic film used for recording the final radiation image does not usually have such a linear characteristic, and accordingly, in order to effect such a linear signal conversion on the photographic film it is necessary to perform a well known "gamma correction". Therefore, it should be noted that the gamma correction should be performed together with the gradation processing. In the description hereinbelow, the description will be made only with respect to the gradation processing on the assumption that the signals are to be subjected, if necessary, to the gamma correction.

Referring now back to FIG. 3, the solid line 5 shows an example of the signal processing conducted in accordance with the present invention. The signal level corresponding to the density at the boundary between the lungs 1 and the heart 2 is indicated with the reference character So and the lowered density from the original level at the boundary level So is indicated with .DELTA.D. In the embodiment as shown in FIG. 3, the degree of lowering the density is made maximum at the boundary level So. Therefore, the contrast between the heart 2 and the spine 3 within the signal range between Smin and So is lowered, and the contrast of the lungs 1 within the signal range between So and Smax is raised as shown by the gradient of the curve 5 in FIG. 3.

The maximum density Dmax and the minimum density Dmin on the final image recorded on the film or the like are somewhat changed by the contrast of the object, the conditions of observation and the ratio of Smin to Smax for example. In general, however, the minimum density Dmin is preferred to be equal to the fog density +0.01 to +0.1 represented by the optical density and the maximum density Dmax is preferred to be within the range of about 1.2 to 2.5.

The preferred degree of lowering of the density at the boundary level So depends upon the observer who conducts the diagnosis based on the radiation image recorded on the film and also upon the characteristics of the radiation image itself such as the difference in density between the heart and the lungs. In general, when the degree of lowering of the density .DELTA.D is small, the gradation image is small, and, therefore, improvement of diagnostic efficiency and accuracy is too small. When .DELTA.D is too large, the contrast of the heart is too much lowered and the diagnostic efficiency and accuracy in the heart are lowered. As the result of tests, it was proved that the diagnostic efficiency and accuracy were improved when .DELTA.D was within the range of 0.1 to 0.5.

In the embodiment shown in FIG. 3, since the gradation variation is made discontinuous at the boundary level So. Therefore, the variation in density is also made discontinuous at the boundary and the image appears unnatural because of the discontinuity. Accordingly, it is desirable that the variation of the density be made continuous or smooth at the boundary level So as shown in FIGS. 4 and 5. In FIG. 4, the angled point at the boundary level So is rounded. In FIG. 5, the whole curve is changed continuously. With these embodiments as shown in FIGS. 4 and 5, the gradation variation is made smooth and natural.

The results were evaluated by four radiologists since it was impossible to evaluate the diagnostic efficiency and accuracy by the objective physical evaluation by use of sharpness, contrast and granularity.

The standard evaluation was as follows.

+2: The diagnostic efficiency and accuracy were greatly enhanced and improved. For instance, the diseased portions which were not recognized in the conventional radiograph have become recognizable, or the diseased portions which were very difficult to recognize have become clearly recognizable.

+1: The diagnostic efficiency and accuracy were improved. For instance, the diseased portions which were difficult to recognize have become recognizable.

0: The diagnostic efficiency and accuracy were not so improved, though the image has become somewhat clearer.

-1: The diagnostic efficiency and accuracy were lowered in some parts even though they were somewhat improved in other parts.

-2: The diagnostic efficiency and accuracy were lowered with no parts where they were improved.

Under the above standard, original images of ten samples of chest radiograph including the normal pattern, cancer pattern, pneumonia pattern and so forth which were subjected to the gradation processing of various types as shown in FIG. 6 were presented to four radiologists and the diagnostic efficiency and accuracy were evaluated for these samples. In FIG. 6, the curves 6, 7, 8 and 9 are examples of the gradation processing in which the density at the boundary between the heart and the lungs were lowered by 0.05, 0.2, 0.4 and 0.6, respectively. The curve 10 represents the density variation without any gradation processing, and curve 11 shows an example of the gradation processing made in the opposite direction, i.e. the density at the boundary level So was increased. (.DELTA.D=-0.3)

The results of the evaluation are shown in Table 1.

TABLE 1______________________________________Gradation Evaluation PointProcessing (average value) General Evaluation______________________________________Curve 6 +0.4 No particular improvementCurve 7 +1.5 ImprovedCurve 8 +1.6 ImprovedCurve 9 -1.8 Degraded particularly at heartCurve 10 +0.1 No changeCurve 11 -1.8 Degraded______________________________________

According to the tests conducted by the present inventors, the degree of lowering .DELTA.D of the density at the boundary level So was within the range of 0.1 to 0.5 in order to effectively enhance the diagnostic efficiency and accuracy.

FIG. 7 is a block diagram showing the outline of the radiation image recording system in which the method and apparatus of this invention are embodied. A stimulable phosphor plate 20 on which an X-ray image is recorded by the chest radiography is mounted on a drum 21. The drum 21 is moved in the axial direction as well as rotated about its axis so that the phosphor plate 20 is exposed to a light beam from a read-out light source 22 which is located outside the drum 21. Thus, the light beam scans the phosphor plate 20 in the two dimensional scanning mode. As for the light source 22 is used a He-Ne laser source.

The light emitted from the stimulable phosphor plate 20 upon stimulation by the scanning light beam from the light source 22 is received by a photodetector 23 and converted to an electric signal, which is amplified by an amplifier 24 and converted to a digital signal through an A/D converter 25. The digital signal thus obtained is memorized in a magnetic memory tape 26. The date memorized in the magnetic memory tape 26 is input into arithmetic and logical units or processer 27 like a computer, wherein the Smin, So and Smin of the original image signal are analyzed.

In the normal chest radiograph, a histogram as shown in FIG. 8 can be obtained for the whole chest image. In the histogram shown in FIG. 8, the signal for the area outside the object is not included. This histogram has two peaks the lower one thereof representing the frequency distribution for the heart and the higher one thereof representing that of the lungs. The height of the two peaks and the width thereof are different depending upon the range of the part of the human body for which the histogram was made, the shape of the chest and so on. The minimum and maximum values Smin and Smax are calculated as the points where the frequency of the histogram falls to zero or a predetermined small value, e.g. 5% of the maximum frequency. The boundary level So corresponding to the density at the boundary of the heart and the lungs can be determined as the level of the signal at the bottom of the valley of the histogram between the two peaks as shown in FIG. 8 or as the average value of the two signals Sh and Sf corresponding to the two peaks, i.e. (Sh+Sf)/2.

When two histograms 28 and 29 are separately made for the heart and lungs as shown in FIG. 9, the boundary level So can be determined as the average value of the two peaks, i.e. (Sh+Sf)/2, or as the level of the signal at the crossing point of the two histograms. It will be mentioned hereinafter how to designate the heart and the lungs in the image.

In view of the simplicity of calculation, the above mentioned methods of determining the boundary level So are advantageous in practice, though there are various other methods possible for determining the boundary level So. Though it is practically very difficult to obtain the true boundary level So from the histogram, it has been confirmed that favorable results were obtained even with the abovementioned approximate value of the boundary level So.

The designation of the heart and the lungs can be conducted as follows.

The first method is a statistical method in which the boundary level is statistically presumed from a number of radiographs. This method is able to obtain a sufficiently accurate boundary level for practical use by making a proper compensation for the characteristics of the human body to be the object of the radiation image as desired.

The second method is a direct searching method in which the instantaneous light emission observed at the time of the initial image recording step for recording the radiation image in the stimulable phosphor is utilized for searching the position of the boundary between the heart and the lungs. In other words, as proposed in Japanese patent application No. 53(1978)-122882 filed by the same applicant, the instantaneous emission of light upon exposure of the stimulable phosphor to the recording radiation is detected to confirm the position of the boundary by making the histogram as shown in FIG. 9. By making the histogram as shown in FIG. 9, it is possible to know the boundary level So as the level at the crossing point of the two histograms 28 and 29 or to calculate the boundary level So as the average value of the two peaks of the histograms (Sh+Sf)/2 as mentioned hereinbefore.

Further, it is also possible to determine the boundary level So by use of a signal obtained by scanning the original image as shown in FIGS. 10A to 10C. Referring to FIG. 10A, the central part of the chest radiograph is scanned by a read-out light beam and the signal waveform obtained thereby along the scanning line is used in combination with a differentiated waveform of the signal as shown in FIGS. 10B and 10C. Referring to FIGS. 10A to 10C, when the chest radiograph is horizontally scanned at the center thereof, four pulses are obtained as shown in FIG. 10C at the boundaries between the lungs 1 and other portions. The area between the first pulse and the fourth pulse corresponds to the chest itself. Therefore, from the maximum value and the minimum value within this area, Smax and Smin can be obtained. The second pulse and the third pulse correspond to the boundaries between the lungs 1 and the heart 2. Therefore, the value of the original image signal So at these points is the boundary level. When the values at these points are different from each other, the average value of these two values can be used as the boundary level So.

After these values, Smin, So and Smax, have been obtained, the data recorded in the magnetic memory tape 26 are processed to perform the signal conversion of gradation processing as shown in FIGS. 3 to 6 so that the radiograph may be reproduced on the final recording medium in the desirable gradation. The processed data are returned to the magnetic memory tape 26 for memorization of the data after processing. The operation of the signals can also be performed in the form of analog signals. Further, the signal processing may include the process for compensation for the gradation of the final recording medium such as a photographic film. Furthermore, an unsharp masking process and/or a frequency filtering can be conducted to control the sharpness of the image.

The gradation processed data are read out from the magnetic memory tape 26, converted to an analog signal by a D/A converter 30 and input into a recording light source 32 after amplified by an amplifier 31.

The light emitted from the light source 32 is focused on a copy film 34 by means of a lens 33 to record an image thereon. The copy film 34 is mounted on a recording drum 35 which is rotated and axially moved for causing the copy film mounted thereon to be exposed to the light from the light source 32 in a two dimensional scanning mode so that a radiation image is recorded on the copy film 34 in the gradation processed form.

As for the copy film 35 can be used a photosensitive material like a silver halide photographic film, diazo film, electrophotographic material and so forth. Further, it is possible to display the image on a monitor like a CRT instead of recording the image on a photosensitive material.

Claims

1. A method of gradation processing a chest radiation image in a radiation image recording system in which a stimulable phosphor is scanned with a stimulating ray and the chest radiation image information recorded therein is read out and converted into an electric signal upon stimulation thereof and then a visible image is recorded on a recording medium by use of a scanning recording beam modulated by the electric signal, said method comprising processing the gradation of the image by lowering the level of the electric signal generally in the range of the level corresponding to the density range between the substantial maximum and minimum densities of the image with the level of the electric signal corresponding to the density at the boundary between the lungs and the heart lowered to the most extent in said range.

2. A method of gradation processing a chest radiation image in a radiation image recording system as defined in claim 1 wherein said level of the electric signal corresponding to the density of the boundary is lowered by the level of 0.1 to 0.5 in terms of optical density of the finally recording medium.

3. A method of gradation processing a chest radiation image in a radiation image recording system as defined in claim 1 wherein the level of the electric signal is continuously lowered in said density range with said level of the boundary lowered to the most extent.

4. An apparatus for performing gradation processing of a chest radiation image in a radiation image recording system in which a stimulable phosphor is scanned with a stimulating ray and the chest radiation image information recorded therein is read out and converted into an electric signal upon stimulation thereof and then a visible image is recorded on a recording medium by use of a scanning recording beam modulated by the electric signal, said gradation processing apparatus comprising means for determining a signal level corresponding to the boundary between the heart and the lungs of the chest radiation image, means for detecting the substantial maximum and minimum values of said electric signal, and gradation processing means for processing the gradation of the image by lowering the level of the electric signal generally in the range of the level corresponding to the density range between the substantial maximum and minimum densities of the image with the level of the electric signal corresponding to the density at the boundary between the lungs and the heart lowered to the most extent in said range.

5. An apparatus as defined in claim 4 further comprising means for continuously lowering the level of said signal in said density range with said level of the boundary lowered to the most extent.