WO2006046493A1 - 超解像処理の高速化方法 - Google Patents
超解像処理の高速化方法 Download PDFInfo
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- 238000003672 processing method Methods 0.000 description 67
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- 238000004364 calculation method Methods 0.000 description 29
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- 238000005457 optimization Methods 0.000 description 5
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- 238000003384 imaging method Methods 0.000 description 2
- 241000406668 Loxodonta cyclotis Species 0.000 description 1
- 238000007476 Maximum Likelihood Methods 0.000 description 1
- 238000002939 conjugate gradient method Methods 0.000 description 1
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- H—ELECTRICITY
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- G06T3/4069—Scaling of whole images or parts thereof, e.g. expanding or contracting based on super-resolution, i.e. the output image resolution being higher than the sensor resolution by subpixel displacements
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- the present invention relates to a method for speeding up super-resolution processing that speeds up super-resolution processing that estimates one high-resolution image from a plurality of low-resolution images, and in particular, in reconstruction-type super-resolution processing, estimation is performed.
- the super-resolution processing document speeds up super-resolution processing that estimates one high-resolution image from a plurality of low-resolution images, and in particular, in reconstruction-type super-resolution processing, estimation is performed.
- the present invention relates to a high-speed method for super-resolution processing that realizes high speed.
- Non-Patent Document 1 In recent years, there have been many reports on super-resolution processing that estimates one high-resolution image from multiple low-resolution images with misalignment (see Non-Patent Document 1). For example, ML (Maxinrnm-likelihood) method disclosed in Non-Patent Document 2, MAP (Maximum A Posterior) method disclosed in Non-Patent Document 3, and POCS (Projection Onto Various super-resolution processing methods such as the Convex Sets method have been proposed.
- the ML method uses a square error between the pixel value of the low-resolution image estimated from the high-resolution image and the actually observed pixel value as the evaluation function, and estimates the high-resolution image that minimizes the evaluation function. In other words, this is a super-resolution processing method based on the principle of maximum likelihood estimation.
- the MAP method is a method of estimating a high-resolution image that minimizes the evaluation function by adding the probability information of the high-resolution image to the square error, that is, using some foresight information for the high-resolution image.
- it is a super-resolution processing method that estimates a high-resolution image as an optimization problem that maximizes the posterior probability.
- the POCS method is a super-resolution process that creates high-resolution images by creating simultaneous equations for pixel values of high-resolution images and low-resolution images and solving the equations sequentially. Is the method.
- any of the above-described super-resolution processing methods first, a high-resolution image is assumed, and a point spread function (PSF function) obtained from a force mela model from the assumed high-resolution image is used for each pixel of all low-resolution images.
- PSF function point spread function
- the super-resolution processing method is called a reconfigurable super-resolution processing method.
- the unknown dimension of the number of pixels in the high-resolution image is very large, so it is not practical to obtain a high-resolution image analytically.
- the image is estimated. It is well known that the iterative calculation requires estimation for all pixels of the low-resolution image for one iteration, and the calculation cost is high. In other words, the reconfiguration-type super-resolution processing has a large calculation cost, so the reduction of the calculation cost was the main issue of the existing super-resolution processing method.
- the square error between the estimated value and the observed value is used as an estimation error evaluation function, and a high-resolution image is estimated as the result of the optimization calculation. Therefore, it is necessary to calculate the evaluation function of the square error and the derivative value of the evaluation function for the optimization calculation.
- the estimation calculation is formulated as a convolution operation with a point spread function (PSF function) corresponding to the transfer function obtained from the camera model, but the convolution operation is performed on all low-resolution images.
- PSF function point spread function
- the present invention has been made under the circumstances as described above, and an object of the present invention is to achieve super-resolution processing that achieves high-speed super-resolution processing by reducing the number of convolution operations, which is the number of estimations.
- the purpose of this is to provide a high-speed method. Disclosure of the invention
- the present invention relates to a method for speeding up super-resolution processing for speeding up super-resolution processing for estimating one high-resolution image from a plurality of low-resolution images including misalignment.
- the plurality of low resolution images are aligned in the high resolution image space, and all the pixels of the aligned low resolution images are sampled at unequal intervals in the high resolution image space.
- the second step of dividing the high-resolution image space into a plurality of small areas having a predetermined size, and the second step A third step of setting an estimated value at a predetermined representative position in the small area as an estimated value of all pixels existing in the small area, or the small area has a square shape.
- the estimated value in the third step is estimated as a convolution of the point spread function obtained from the camera model and the high resolution image. It is effectively achieved by the value obtained in this way.
- I is an evaluation function for the small area
- M is the number of all pixels belonging to the small area
- fi is the i-th position coordinate (X;, yi) within the small area.
- (X c , y J represents the representative position of the small region
- (x e , e ) represents the estimated value of the representative position, or the super solution
- the evaluation function required for image processing is expressed by the following equation:
- I is an evaluation function for the small area
- M is the number of all pixels belonging to the small area
- f has position coordinates (X i, y;) within the small area represents the observed value of the i th pixel
- (X c , y) represents the representative position of the small region
- (,) represents the estimated value of the representative region
- / represents the pixel in the small region.
- X c , y; — y J is a weight function, and represents the weight corresponding to the i-th pixel having the position coordinate (X i y i) in the small region, and its value is the position coordinate (X i, y i)
- the evaluation function necessary for the super-resolution processing is expressed by the following equation: the i-th pixel having a size becomes smaller as the distance from the representative position (X c , yc) increases.
- I is an evaluation function for the small region
- M is the number of all pixels belonging to the small region
- f is a position coordinate
- X;, yi) represents the observed value of the i th pixel
- (X c, y c .) Represents the representative position of the small region,) represents the estimated value of the representative position
- w (xi — X c , yi — y J is a weight function, which represents the weight corresponding to the i-th pixel having the position coordinate (x or y in the small region, and its value is the position coordinate (i having the position coordinate (X i, y J th pixel is the representative position (x c, y c) are UniNatsu'll be less Te ⁇ Tsu the distance from, W is corresponding to each pixel of the small region The sum of the weights, a is more effectively achieved by representing the weighted average of the subregions.
- FIG. 1 is a schematic diagram for explaining the concept of super-resolution processing by a conventional super-resolution processing method.
- FIG. 2 is a schematic diagram for explaining the concept of super-resolution processing to which the method for speeding up super-resolution processing according to the present invention is applied.
- FIG. 3 (A) shows a high-resolution image with true values.
- Fig. 3 (B) is an enlarged view of one of the low resolution images.
- Fig. 3 (C) shows the results of super-resolution processing using the conventional super-resolution processing method.
- FIG. 3 (D) is a diagram showing the result of the super-resolution processing using the method for speeding up the super-resolution processing according to the present invention.
- FIG. 4 is a diagram showing the relationship between the size of the divided small regions and the calculation time * RMS error in the super-resolution processing using the method for speeding up the super-resolution processing according to the present invention. .
- FIG. 5 is a diagram showing the super-resolution processing result using the real image (1).
- Fig. 5 (A) is an enlarged view of the low resolution image to the size of the high resolution image.
- Fig. 5 (B) shows a high-resolution image estimated by the conventional super-resolution processing method.
- FIG. 5 (C) is a diagram showing a high-resolution image estimated by the super-resolution processing method of the present invention.
- FIG. 6 is a diagram showing the super-resolution processing result using the real image (2).
- Figure 6 (A) is an enlarged view of the low resolution image to the size of the high resolution image.
- Fig. 6 (B) is a diagram showing a high-resolution image estimated by the conventional super-resolution processing method.
- Figure 6 (C) shows the results of the super-resolution processing method of the present invention. It is a figure which shows the defined high resolution image.
- Figure 6 (D) shows a high-resolution image estimated by the conventional super-resolution processing method while taking into account the deformation of the PSF.
- Super-resolution processing is processing that estimates one high-resolution image from a plurality of low-resolution images that include misalignment, which is an observed image.
- the “high-resolution image space to be restored” is referred to as a “high-resolution image space”.
- Fig. 1 (C) After aligning multiple low-resolution images including misalignment in the high-resolution image space, the data for all observed images (that is, all the observed image pixels) are shown in Fig. 1 (C). As can be seen, it can be treated as data sampled at irregular intervals in a high-resolution image space. In other words, a plurality of low-resolution images registered in the high-resolution image space can be considered as pixels sampled at unequal intervals.
- the position of the i-th data (that is, the i-th pixel after alignment) of multiple observation images (that is, multiple low-resolution images) is coordinated (X i, yi)
- the pixel value be fi.
- the pixel value observed in the high-resolution image space (hereinafter simply referred to as the observed value) of the i-th pixel after alignment (hereinafter simply referred to as the i-th pixel) is f;
- the number of data after alignment of multiple observation images is the number of data sampled at irregular intervals in the high-resolution image space, that is, the number of pixels (number of pixels) of all observation images.
- the pixel value of the i-th pixel having the position coordinates (X i, y ; ) is the point spread function (PSF function) obtained from the camera model.
- PSF function point spread function
- the reconstruction-type super-resolution processing method is the square of the observed value for each pixel and its estimated value for all pixels after alignment of the multiple observed images (the total number of pixels is N). This is a method of adjusting the high-resolution image h (x, y) so that the total error is reduced.
- N is the number of data sampled at irregular intervals in the high-resolution image space, that is, the total number of pixels in all observed images (low-resolution images).
- observation value observation data
- I the estimated value of the i-th pixel with position coordinates (X i, yi) It is.
- Equation 1 in the conventional super-resolution processing method, in order to compare the observed value (observed data) with the estimated value, for each pixel after alignment of multiple observed images, in other words, it is necessary to estimate from the high-resolution image h (X, y) only N times the number of data sampled at irregular intervals in the high-resolution image space.
- a plurality of low-resolution images are aligned in a high-resolution image space.
- the number of observation data that is, all registered low-resolution images
- the calculation cost required for the estimation is reduced, and thus the super-resolution processing can be speeded up.
- the positions of a plurality of low-resolution images including misalignments in the high-resolution image space All pixels after the alignment are assumed to be pixels distributed at irregular intervals in the high-resolution image space.
- the resolution image space is divided into a plurality of small areas having a predetermined size, and for each divided small area, an estimated value of all pixels belonging to the small area is obtained, and a predetermined position in the small area is determined.
- the maximum number of estimations required for the super-resolution processing can be reduced. It is a feature.
- the high-resolution image space can be divided into four.
- the high-resolution image space is divided into small areas of a predetermined size.
- the estimated values of the pixels are naturally different, but in the present invention, in each divided small region, Assuming that the estimated values of all pixels belonging to the small area do not change, that is, the estimated values of all pixels belonging to the small area are approximated by the representative values of the representative points in the small area.
- the divided small region for example, the shaded small region in FIG. 2 (B) is the attention region, there are three observation data in the attention region. If you apply the high-speed processing method, this estimation operation is performed once. 1
- the conventional super-resolution processing method requires three estimation operations, which is the same as the number of observation data, in order to compare these three observation data.
- the method for speeding up the super-resolution processing according to the present invention it can be expected to be three times faster than the conventional super-resolution processing method. it can.
- the sum of the square errors related to the region of interest, that is, the evaluation function for the region of interest is expressed by a mathematical formula.
- the conventional super-resolution processing method is expressed by the following equation 2
- the super-resolution processing speedup method according to the present invention is expressed by the following equation. 3
- I is the sum of the square errors between the observed values of all the pixels in the region of interest and the estimated values, that is, the evaluation function for the region of interest.
- M is the number of data sampled at unequal intervals within the region of interest, that is, the number of all pixels belonging to the region of interest.
- f represents the observed value (observed data) of the i-th pixel having the position coordinates (X i, yi) within the region of interest.
- Equation 3 Represents the estimated value of the representative position.
- the estimated value of the representative position of the attention area is a constant value. That's it.
- Equation 2 in the conventional super-resolution processing method, the number of observation data is estimated several times within the region of interest (for example, the shaded region of interest in Fig. 2 (B)). In this case, three estimation operations must be performed.
- the procedure for calculating the evaluation function I necessary for the super-resolution processing (step 1 to step 5 described later) is as follows.
- the differential value of the evaluation function necessary for the super-resolution processing is also calculated by the same procedure as the evaluation function calculation procedure.
- step 1
- the high-resolution image space is divided into a plurality of small areas having a predetermined size.
- Step 5 Repeat step 3 and step 4 for all sub-regions.
- the high-resolution image space is divided into a plurality of small regions having a predetermined shape.
- a high-resolution image space can be divided into a plurality of small square areas.
- the estimation calculation in the super-resolution processing is expressed as a convolution operation with the PSF (Point Spread Function) obtained from the camera model.
- PSF Point Spread Function
- the small area having the square shape is set to 1 / integer of the pixel size of the high resolution image.
- the small area having a square shape has been described above.
- the small area is not limited to the shape of a square.
- the high-resolution image space has another geometric shape such as a rectangle. It is also possible to divide it into small areas with various shapes.
- I is an evaluation function for the region of interest.
- M is the number of data sampled at unequal intervals in the attention area, that is, the number of all pixels belonging to the attention area.
- f i represents the observed value (observed data) of the i-th pixel having the position coordinates (X i, y i) within the region of interest.
- X y J represents the representative position of the region of interest. Represents the estimated value of the representative region.
- _ Represents the average of the observed values of the pixels in the region of interest.
- the estimated value of all pixels belonging to the attention area is constant within the attention area (that is, within a predetermined small area).
- the reliability of the representative estimate decreases.
- I is an evaluation function for the region of interest.
- M is the number of data sampled at unequal intervals in the attention area, that is, the number of all pixels belonging to the attention area.
- observation value observation of the i-th pixel having the position coordinates (X ;, yi) in the region of interest. Data).
- (X ⁇ yj represents the representative position of the region of interest.
- (X c , y c ) represents the estimated value of the representative region.
- Wi — x c 'yi — yj is the weight function, and the region of interest Represents the weight corresponding to the i th pixel having the position coordinate (X i, y i) in the, and its value is as the i th pixel having the position coordinate (X iiy J is further away from the representative position (X c , y J) Get smaller.
- Equation 7 when the square error of each pixel in the region of interest is deformed, that is, the following Equation 7 can be obtained except for the constant component of the above Equation 6.
- the evaluation function I represented by the following formula 7 can also be used.
- I is an evaluation function for the region of interest.
- ⁇ is the number of data sampled at unequal intervals in the region of interest, that is, the number of all pixels belonging to the region of interest.
- fi represents the observed value (observed data) of the i-th pixel having the position coordinates ( X i , yi) within the region of interest.
- (X c, y J represents the representative position of the region of interest.
- C ) represents the estimated value of the representative position.
- wixi — x ⁇ yi one y c ) is a weight function i with position coordinates (x ⁇ yi) in the region of interest Represents the weight corresponding to the first pixel, and its value decreases as the i-th pixel with position coordinates (X or y) moves away from the representative position (X y c ).
- the sum of the corresponding weights / represents the weighted average of the region of interest.
- Equation 7 when an observation image is given and a small region to be divided is set, W and / are uniquely determined, and thus do not change during super-resolution processing.
- the method for speeding up the super-resolution processing according to the present invention is characterized in that it aims to increase the efficiency of calculation required for each iteration.
- a plurality of low-resolution images including positional shifts are registered in a high-resolution image space, and a plurality of low-resolution images observed after the registration are aligned.
- Treat the resolution image as non-uniformly sampled pixels in the high-resolution image space then divide the high-resolution image space into multiple small areas, By approximating that the value estimated from the resolution image is constant, the super-resolution processing is speeded up.
- Non-Patent Document 5 many methods disclosed in Non-Patent Document 5 are used for matching for alignment of a plurality of low-resolution images including misalignment. Because there are, these existing matching methods can be used.
- Fig. 3 (A) shows a high-resolution image with a true value
- Fig. 3 (B) shows an enlarged view of one of the low-resolution images.
- the magnification of the high-resolution image was 3.2, and a high-resolution image with a size of 2 5 6 X 19 2 was reconstructed using the MAP method.
- MR F in the vicinity of 4 is assumed (see Non-Patent Document 6), and the constraint parameter ⁇ is set to 0.05.
- the optimization calculation uses the Fletcher-Reevess conjugate gradient method (see Non-Patent Document 7), and the initial image is obtained by bicubic interpolation. An enlarged image is used.
- the main calculation conditions are summarized in Table 1.
- Fig. 3 (C) shows the result of the super-resolution processing by the conventional super-resolution processing method
- Fig. 3 (D) shows the super-resolution processing applying the super-resolution processing speedup method according to the present invention. The results are shown respectively. 8
- FIG. 3 (C) and FIG. 3 (D) have improved resolution compared to FIG. 3 (B). Also, there is no difference between Fig. 3 (C) and Fig. 3 (D).
- the conventional super-resolution processing method (hereinafter also simply referred to as the conventional super-resolution processing method (a)) where sufficient memory can be used, and conventional memory where sufficient memory cannot be used.
- Super-resolution processing using the super-resolution processing method (hereinafter also referred to simply as the conventional super-resolution processing method (b)) and the super-resolution processing speed-up method according to the present invention
- the PSF Table 2 shows the pre-processing time required for kernel generation, the time required for iterative optimization, and the RMS error with the true value for quantitative evaluation of the image quality of high-resolution images.
- Table 2 shows the ratio when the calculation time of super-resolution processing using the high-speed method of super-resolution processing according to the present invention is set to 1 in order to compare the calculation speed. Is also shown. Note that the CPU of the computer used for super-resolution processing was 2.8 [GH z] (Pentium4) (registered trademark).
- the size of the small area to be approximated by the method for speeding up the super-resolution processing according to the present invention that is, 1 ZL, where L is an integer
- the reconstructed high-resolution image In order to make a comparison with the calculation time required to calculate a high-resolution image, the same super-resolution processing was performed using the size of the small area (1 / L) as a parameter.
- Fig. 4 shows the relationship between the RMS value of the true value of the output image (the reconstructed high-resolution image) and the calculation time required to calculate the high-resolution image and the size of the divided small regions. Shown in
- Non-Patent Document 8 Two-dimensional simultaneous matching disclosed in Non-Patent Document 8 was used.
- Fig. 5 (A) shows a low resolution image enlarged to the size of a high resolution image
- Fig. 5 (B) shows a high resolution image estimated by a conventional super-resolution processing method
- (C) shows high-resolution images estimated by the super-resolution processing method of the present invention.
- FIGS. 5 (A), 5 (B) and 5 (C) an overall view is shown on the left side, and a partially enlarged view is shown on the right side.
- Figure 5 (A), Figure 5 (B) and Figure 5 (C) are compared, and both Figure 5 (B) and Figure 5 (C) show the low-resolution image of Figure 5 (A).
- the resolution is higher than
- Fig. 5 (B) 'and Fig. 5 (C) are comparable even if they are compared in an enlarged view.
- the RMS error of the entire image representing the difference between the output image by the conventional super-resolution processing method and the output image by the super-resolution processing method of the present invention was 2.5.
- the super-resolution processing method of the present invention is 34.1 times as compared with the conventional super-resolution processing method (a). Compared with the super-resolution processing method (b), it is 3.2 times faster.
- Non-Patent Document 9 For the estimation of alignment, the simultaneous estimation method disclosed in Non-Patent Document 9 was used.
- PSF which is a transfer function from the high-resolution image to the observed image, must also be deformed strictly in accordance with the projective deformation (see Non-Patent Document 6).
- the super-resolution processing was performed by the super-resolution processing method of the present invention on the assumption that the projective deformation is so small that the deformation of PS F can be ignored.
- Fig. 6 (A) shows an enlarged view of the low resolution image to the size of the high resolution image.
- Fig. 6 (B) shows the high resolution image estimated by the conventional super-resolution processing method.
- (C) shows high-resolution images estimated by the super-resolution processing method of the present invention.
- Fig. 6 (D) considers PSF deformation. However, the high-resolution image estimated by the conventional super-resolution processing method is shown. 6 (A), 6 (B), 6 (C) and 6 (D), the left side is an overall view and the right side is a partially enlarged view. is there.
- FIG. 6 (B), FIG. 6 (C) and FIG. 6 (D) is higher than that of FIG. 6 (A).
- Table 4 shows a comparison of the calculation time required for the super-resolution processing using the conventional super-resolution processing method and the super-resolution processing method of the present invention using the real image (2) when the PSF deformation is ignored.
- the super-resolution processing method of the present invention is compared with the conventional super-resolution processing method (a) as in the case of using the real image (1). It is confirmed that the calculation time is shortened by 5 times and 3.1 times compared with the conventional super-resolution processing method (b).
- the high-resolution image space is divided into a plurality of small regions, and an approximation that the estimated value is constant in each divided small region is performed.
- the estimated number of representative points of the small area is approximately regarded as the estimated value for all the pixels existing in the small area, thereby reducing the number of estimations. Therefore, the biggest feature is to reduce the calculation cost.
- the present invention it is possible to compare the estimated value with the pixel value of a pixel in the small area as long as the estimation is performed once for one small area (estimation of the representative point of the small area). . Therefore, the decrease in the number of estimations directly leads to faster super-resolution processing.
- the high-speed super-resolution processing is realized by applying the super-resolution processing speed-up method according to the present invention to the composite image and the two types of real images. It was confirmed.
- the method for speeding up the super-resolution processing is not limited to the MAP method, but can also be applied to other super-resolution processing methods such as ML method and POCS method.
- Industrial applicability is not limited to the MAP method, but can also be applied to other super-resolution processing methods such as ML method and POCS method.
- the method for speeding up super-resolution processing according to the present invention first, a plurality of low-resolution images including misalignments in a high-resolution image space are aligned, and observation after alignment is performed.
- the plurality of low-resolution images are treated as non-uniformly sampled pixels in the high-resolution image space, and the high-resolution image space is divided into a plurality of small regions. It is assumed that the value estimated from the high-resolution image is constant. As a result, the super-resolution processing can be speeded up.
- the high-speed super-resolution processing was realized by applying the high-speed super-resolution processing method according to the present invention to the composite image and the two types of real images.
- Non-patent document 1
- Non-patent document 2
- Non-Patent Document 3 "Resolution off-off high-resolution image by simul- taneous resist-restraint-re-transition un-interpolation-off-low-resolution i main 1 ⁇ Nsu (Reconstruct 1 on of a high- resolution image by simultaneous registration, restoration, and interpolation of low-resolution images) J, profile click. IEEE Lee down the door. co-down-off. Lee menu over di profile Sensing (Proc. IEEE Int. Conf. Image Processing), Volume 2, p.539-542, 1995 Non-Patent Document 3:
- Patent Document 5 Co-authored by H. Stark and F. Oskoui, “No, Re-Resonance Image, Re-imaged, Image Plane, Arrays, Using, Convex Project, High Resolution Image Recovery from image-plane arrays, using convex projections), J. Opt. Soc. Am. A, Vol. 6, p. 1715-1726, 1989 Patent Document 5:
- Non-Patent Document 7 “Image Mosaic King And” by D. Capel SUNOI RESOLUTION (Image Mosaicing and Super-resolution) J, Springer, 2003 Non-Patent Document 7:
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CN103049885A (zh) * | 2012-12-08 | 2013-04-17 | 新疆公众信息产业股份有限公司 | 一种利用分析性稀疏表示的超分辨率图像重建方法 |
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US8009933B2 (en) | 2011-08-30 |
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