JPS60171569A - Interpolation system for picture - Google Patents

Abstract

PURPOSE:To realize highly accurate picture sharpness, enlargement, reduction, rotation, or strain correction by performing an optimum interpolation considering sensor opening characteristics of an observation picture and output picture opening characteristics. CONSTITUTION:A picture interpolation device 23 inputs an observation picture from a picture input device 15, performs interpolation processing and displays an output picture on a picture output device 20. The device 23 consists of an interpolation coordinate calculation circuit 16, interpolation processing circuit 17, weight coefficient memory 18, and interpolation function calculating circuit 19. The circuit 19 calculates the interpolation function as preprocessing from a sensor opening characteristics 21 given from outside and output opening characteristics 22, and makes it into tables to store it in the memory 18. The circuit 16 calculates the picture element coordinate of the observation picture according to respective pictures of the output pictures based on a desired output picture sampling interval and a rotating angle. The circuit 17 determines an output picture strength in said coordinate from inputted observation picture strength and displays this data on the output device.

Description

[Detailed Description of the Invention] [Field of Application of the Invention] The present invention relates to digital processing of images, and in particular to a method suitable for interpolation processing necessary for image sharpening, enlargement, reduction nine rotations, distortion correction, etc. .

[Background of the invention]

First, a general method of digital image generation and interpolation, which is the object of the present invention, will be explained.

Although the image data has nine two-dimensional waves, a one-dimensional cross section is taken here for the sake of simplicity. FIG. 1 is a diagram showing a one-dimensional change in the radiation density intensity from an object to be imaged. Continuous curve 1 includes high frequency components with varying intensity.

In the imaging system shown in FIG. 2, a sensor 2 inputs light from an object, and a sampler 3 samples this at a certain sampling frequency to obtain discrete observation data 4. 1st
Figure 3 shows observation data corresponding to the input light shown in the figure.

A gradation intensity of 7 (black circles in the figure) is obtained at constant position intervals.

This two-dimensional array of digital data is observation image data.

The X-ray images and other digital images obtained in this way are sharpened, enlarged, and reduced nine times.

There is a demand for processing such as distortion correction. In this case, an image take with a sample position different from the observed image is required. For this purpose, image interpolation is performed.

Image interpolation is performed by a processing system such as a computer as shown in FIG. It is. Taking the observation image data in Figure 3 as an example, the black circle a given as the observation data
Interpolation is to obtain the gray intensity 8 at an arbitrary position (white circle) from the light intensity 7. The position corresponding to this desired white circle is determined depending on the purpose of image distortion correction, enlargement, reduction, etc. Interpolated image data 6 can be obtained by creating a two-dimensional array using the interpolated gradation intensity 8 as digital data.

This image is a distortion-corrected observation image.

It becomes enlarged or reduced.

The general method of interpolation is as follows. From the point sequence of observation data 7 in FIG. 3, an interpolation song &19 is created to interpolate them. Next, interpolated image data 8 is obtained as the value of the desired white point position on this curve. This interpolation song I! The following type of M9 is usually used.

y(u)=Σh(u−i)X(i)−=<1
) Formula ζ where U is the coordinate of the point you want to interpolate, y(u) is the coordinate U
where i is the given integer coordinate of the observed data, x(i) is the intensity of the observed data at coordinate i, and h() is the weighting function. il, il+1. ...+
12 is an integer coordinate in the neighborhood of U, and usually takes two, four, or more pieces.

In the case of two-dimensional image data, the following form is used as the interpolation surface.

・・・・・・・・・・・・Equation (2) where (u, v) are the coordinates of the interpolation point, y (u, v) is the intensity of the interpolation surface at the coordinates, (Il j) is the given integer coordinate of the observed data, X(+, J) is the intensity of the measured data at the coordinate, h() is the weighting function, 41, il
-G1. ...+42 is an integer coordinate near U, Jll
Jl +1. ..., j2 are integer coordinates in the vicinity of V.

Here, there is an alternative method to the strange interpolation method in selecting the weighting function. There are three types of weighting functions that have been widely used in the past: For details, see, for example, the literature, K, W, 5irno
n, ”Digital image l(,e
construction and l(esampl
ing for Qeometric Manipu
ration”.

Symposium on MacJne prOce
s8ine ofRemoteJy 5ensed 1
) ata, June, 1975. checking ...

The weighting function for one-dimensional data is given by the following equation.

(1) Nearest neighbor method...Figure 4 (2)
Pilinear method・・・・・・Figure 5・・・・・・・・・(
4) Equation (3) Cubic convolution method...
Figure 6: Equation (5) By the way, these weighting functions have been determined empirically, and the interpolated image obtained by applying them does not necessarily fully capture the information contained in the original observed image. cannot be reproduced.

This is because the observation data is degraded due to the aperture characteristics of the sensor. FIG. 7 schematically shows two-dimensional sensor aperture characteristics. However, this is a one-dimensional cross section. It shows the radiation intensity from an object that the sensor captures at a certain moment.It is strong at the center and attenuates toward the periphery. The radiation intensity distribution from the object is now z(u, 'v), where u, v
) is the position coordinate, and if the sensor aperture characteristic is a (u, v), then the sensor output strength x (u, v) is X (u, v) = a (u, v) z (u, v
) --Equation (6) However, ■ is a convolution integral. Therefore, the observed image data that is the sensor output is subject to deterioration such as distortion and blurring of high frequency components due to the aperture characteristics.

The above-mentioned interpolation methods, such as the nearest neighbor method, the pi-linear method, and the cubic convolution method, do not take into account the influence of this deterioration, and therefore have the disadvantage that sufficient clarity cannot be obtained in the interpolated image.

In response to this problem, an interpolation method has been attempted in the past that uses sensor aperture characteristics to correct the deterioration. For example, literature, 几, 1) y
e,”l(,estration of Lands
atJmages b)' Direct 2 Dim
1) econ -volutiOn
”, :proc, of 10 th internal
tional Symposium on Bemote
Sensitivity of Enviro-nment
#', pp. 725-730.1976. The principle is as follows. It is now assumed that the aperture characteristic a(u,v) of the sensor is known. At this time, when the observed data x (u, v) on the left side of equation (6) is given, the estimated value z (u.

■) can be calculated using the following formula.

z (u, v) = h (u, v) x (u, v
) --Equation (7) Kokote interpolation function h(u, v) is a(u
, v) in the frequency domain by the Wiener filter method or in the real space domain by the least squares method.

For details, please refer to the above-mentioned document. In real interpolation (7)
x (u, v) on the right side of the equation takes the form of discrete data X (i, j), and the estimated value z (u, v) is the interpolated value y (u.

(2), so equation (7) takes the form of equation (2).

However, this method has the following drawbacks. In other words, the interpolation 11y(u,v) given by this method is the sampled output image, which is the estimated value Z(U,V) of the true radiation intensity distribution z(u,v) from the object as a δ function. This is an image arranged by sampling. Therefore, observation data x (i, j) and desired output image data y (i, j)
If the sampling interval or direction of
In an image using samples sampled by a function, z (u
.

■) The error becomes larger. This is because the aperture characteristics of the output image depending on the sampling interval and direction of the output image are not considered.

As mentioned above, images obtained by conventional interpolation methods have the disadvantage that they do not adequately reproduce the radiation intensity distribution from the object.

[Purpose of the invention]

An object of the present invention is to take into consideration the aperture characteristics of the sensor at the time of capturing an observation image and the aperture characteristics of the desired output image, and to provide a method suitable for sharpening, enlarging, reducing, or distorting an image with high precision. , an object of the present invention is to provide an interpolation method for digital images.

[Summary of the invention]

Here, the principle of the interpolation method used in the present invention will be explained. Now the desired sampling interval for the output image.

Assume that an aperture characteristic c(u,v) of an output image depending on the direction is given. This is as shown in the one-dimensional cross section in Figure 8.
Generally, the sensor aperture characteristic a(u,v) does not have to match the observed image. At this time, considering the aperture characteristics of the output image, the interpolated output image that most faithfully reproduces the radiation intensity distribution of the object in the sense of least squares is given by the following equation.

z (u, v)=c (u, v)■h(u,v)■
x (u, v)・・・・・・・・・・・・(8) Formula h” (u, v)=c (u, v)■h (u,
v) ・-・If we write equation (9), equation (8) becomes z(u, v)=b” (u, v)■x(u, vl
``...'' is formula 00. Here, since the observed image X is discrete data X (i, j) and the interpolated image y is given by 2, from formula 00... ...The αυ formula is obtained. Comparing this with formula (2), we can see that h''(u, v) is used as a substitute for h(u, v) as the interpolation function. Recognize. In other words, h''(u,v) is an interpolation function that takes into account the sensor aperture characteristic a(u,v) of the observed image and the aperture characteristic C(U,V) of the output image.Given a
Determine h(u,v) from (u,v) using the Wiener filter method in frequency space or the least squares method in real space, and then calculate h''(u,v) by convolving this with c(u,v).
is obtained.

By interpolating using the αυ formula, an optimal interpolated image can be obtained that takes into account the aperture characteristics of the sensor and output image.

[Embodiments of the invention]

An embodiment of the present invention will be described below with reference to the drawings.

FIG. 9 is an overall configuration diagram of an image interpolation device according to the present invention. The image interpolation device 23 inputs the observed image from the image input device 15, performs interpolation processing, and outputs the output image to the image output device 20.
Output to. The interpolation device 23 includes an interpolation coordinate calculation circuit 16, an interpolation processing circuit 17, a weighting coefficient memory 18, and an interpolation function calculation circuit 19.

The interpolation function calculation circuit 19 uses the sensor aperture characteristic a(u,v)''1 and the output aperture characteristic 22 given from the outside as preprocessing.
An interpolation function h''(u, v) is calculated from , vl to h(u) in equation (7).

■), then according to equation (9), ! 7b" (u, v)]. The interpolation coordinate calculation circuit 16 calculates the pixel of the observed image corresponding to each pixel of the output image according to the sampling interval of one rotation angle of the desired output image. The interpolation processing circuit 17 calculates the coordinates (u, v).The interpolation processing circuit 17 calculates the weighting coefficient h'' (u, v) read out from the memory 18 for the pixel coordinates (u, v).
and the intensity X(i
, j), the output image intensity y(u) at the coordinates (u, v) according to Equation 09.

V). This is output to the output device 20.

A desired output image is obtained by repeating this interpolation process for all pixels of the output image.

According to this embodiment, the sensor aperture characteristic 21 and the output aperture characteristic 22 of a given observation image are given from the outside, and the optimal interpolation function can be calculated each time accordingly.
This has the advantage that it can be applied to any output method.

[Effects of the Invention] Optimal interpolation can be performed in consideration of the aperture characteristics of the output image, and there is an effect that image sharpening, enlargement, one rotation of reduction, or distortion correction can be realized with high precision.

[Brief explanation of drawings]

Figure 1 is an example of the radiation intensity distribution from an object, Figure 2 is a configuration diagram of the imaging system, Figure 3 is observation data, Figure 4 is the weight function of the nearest T-4 Ibar method, and Figure 5 is the pi-linear method. Weighting function, Figure 6 shows the weighting function of the cubic convolution method, Figure 7 shows the sensor aperture characteristics, Figure 8 shows the aperture characteristics of the output image, and Figure 9 shows the overall configuration of the image interpolation device. It is a diagram. 1...Radiation intensity, 2...Sensor, 3...Sampler, 4...Observation image data, 5...Interpolation processing, 6...
- Interpolated image data, 7... Observation data, 8... Interpolated data, 9... Interpolated curve, 13... Sensor aperture characteristics, 14... Output aperture characteristics, 15... Image input device,
1G... Interpolation coordinate calculation circuit, 17... Interpolation processing circuit, 18... Weighting coefficient memory, 19... Interpolation function calculation circuit, 20... Image output device, 23... Image Interpolator. Agent Patent Attorney Akira Takahashi!・"1:1"1"!i'゛<
-” 1st eye bud 5 Drawing Hand Top 5 Fig. 1 Fig. 7 Fig. 8 Fig. 9 Mouth

Claims (1)

[Claims] An image interpolation method characterized in that a weighting coefficient for image interpolation processing is calculated based on an aperture characteristic of a sensor and an aperture characteristic of an output image from the sensor.