CN117270360A - Synthetic aperture imaging method based on SIFT algorithm - Google Patents
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Abstract
The invention discloses a synthetic aperture imaging method based on a SIFT algorithm, which relates to the technical field of synthetic aperture digital holographic image reconstruction, and provides a method for utilizing the synthetic aperture imaging based on the SIFT algorithm while guaranteeing the resolution, so that the space bandwidth product of a digital holographic imaging system is effectively improved, the imaging view field is enlarged.
Description
Technical field:
the invention relates to the technical field of synthetic aperture digital holographic image reconstruction, in particular to a synthetic aperture imaging method based on a SIFT algorithm.
The background technology is as follows:
as human beings enter an information age, various image data, text data and video data are complex, and more advanced display technologies are urgently needed to perform more natural and real visual display on the data. The existing 3D display technology has a lot, and the digital holographic technology can completely record the complex wave front information of the sample, including the amplitude and phase information of the sample diffraction wave, greatly increases the recorded information quantity, and is a powerful label-free quantitative phase imaging technology. With the rapid development of electronic technology and computer technology, a digital holographic technology with a large field of view and a high bandwidth will become possible, and simultaneously with the improvement of the computing capability of a chip, the real-time recording and reproduction of the digital holographic technology will be realized, so the digital holographic technology attracts more and more research interest, and the application range of the digital holographic technology is also expanded from imaging, display to the fields of deformation measurement, medical diagnosis, particle field measurement, three-dimensional image recognition and the like.
The digital holographic imaging technology uses photoelectric sensors such as CCD or COMS to obtain complex amplitude of transparent microscopic objects such as scratches, cells, tissues and the like on the surface of an optical element, and quantitative phase reconstruction of a specimen is realized by measuring the complex amplitude. In 2015 Verma et al, a combination of digital hologram technology and filter technology measured that the surface defect width of a 6line/mm grating was 20.1 μm and the surface scratch width of an optical glass plate was 6.7 μm. Trivedi et al in 2019 detected the refractive index profile of an object using single beam lensless Fourier transform digital holography and its application in defect detection. The off-axis holographic technology realizes single detection of the complex amplitude image through the off-axis interference pattern, can separate the complex amplitude image of the measured object from the twin image of the measured object in a frequency domain, and reduces the difficulty of reconstructing the holographic image.
The amount of information contained in the image acquired by the imaging system is related to the size of the spatial bandwidth product of the imaging system. The high-resolution wide light field imaging can detect more complete sample defects, and provides a whole cell morphology image, so that the imaging volume and the image field of view observed by us are greatly improved. In a microscope, the spatial bandwidth product is defined as the product of the image field of view area and the spatial bandwidth area. Because the pixel number which can be provided in the sensor of the modern microscope is far lower than the space bandwidth product of the optical microscope, a lot of optical information of the detected object can not be detected, and the microscope still has a great progress space in the aspects of large-scale high-flux imaging, so that the sensor has great significance for the fields of cell detection, drug development, tissue biology and the like. Although the off-axis holographic interference pattern has wider bandwidth, the spatial bandwidth product of the complex amplitude image is smaller and limited by the field of view of the digital holographic microscopic imaging system and the photosensitive size of the CCD camera, and the acquired holographic image contains limited information of the sample.
The invention comprises the following steps:
in order to improve the spatial bandwidth product of digital holographic imaging, the invention provides a synthetic aperture imaging method based on a SIFT (Scale-invariant feature transform) algorithm. The method records holograms with certain overlapping areas after a plurality of objects are translated in an off-axis holographic mode, realizes reconstruction of object wavefront information by simulating a diffraction reconstruction process of the holograms through computer numerical values, adopts a SIFT algorithm to extract characteristic points of reconstructed images for matching, and realizes integral weighted fusion of reconstructed sub-images, so as to obtain a large-view-field synthetic aperture map with a high space bandwidth product.
The technical problems to be solved by the invention are realized by adopting the following technical scheme:
a synthetic aperture imaging method based on SIFT algorithm comprises the following steps:
and 1, imaging a measured object by using a transmission type off-axis holographic optical path system based on a Mach-Zehnder interferometer principle, acquiring holograms by using a CCD camera, fixing the measured object on a three-dimensional translation stage, and ensuring that the surfaces of the CCD camera and the measured object are required to be kept at a fixed distance and parallel to each other, so that only a two-dimensional translation transformation relation exists between the acquired holograms. In order to make the collected hologram set contain the whole area of the measured object, the collected path is: the CCD camera firstly acquires a row of images at equal intervals from left to right in the horizontal direction, and the images are sequentially named as I 11 、I 12 、……、I 1b Subsequently, the translation stage is adjusted to measure the objectThe body moves downwards for a certain distance, a second row of images are acquired at equal intervals in the direction from right to left, and the images are sequentially named as I 2b 、……、I 22 、I 21 Then the measured object is moved downwards for a certain distance, a row of images is acquired from left to right, and so on, a×b holograms are acquired in total (a=2 v ，v＝1，2，3，……；b＝2 u U=1, 2,3, … …), i.e. the hologram set of the measured object, where a is the number of rows and b is the number of columns.
Step 2, reconstructing the hologram set obtained in the step 1 in a piece-by-piece holographic subgraph manner to obtain a reconstructed image set of the measured object, wherein the image set contains a multiplied by b images, and the images are named as A in sequence 11 、A 12 、……、A ab 。
The reconstruction method of the holographic subgraph in the step 2 comprises the following steps:
s1, the interference intensity P (x, y) of the holographic image can be expressed as:
P(x,y)＝|O(x,y)| 2 +|R(x,y)| 2 +O * (x,y)R(x,y)+O(x,y)R * (x,y) (0)
in formula (1) |O (x, y) | 2 And |R (x, y) | 2 The intensity distribution of the corresponding object light and reference light, i.e. the zero order of diffraction, O * (x, y) and R * (x, y) is the conjugate of O (x, y) and R (x, y), respectively, the third term O * (x, y) R (x, y) is a twin image, and O (x, y) R * (x, y) is the desired reconstruction.
If the reproduction distance is z and the reproduction light wave irradiated on the hologram is C (x, y), the diffracted light field from the hologram surface to the reproduction distance z is the reproduction object light field, the distribution U of complex amplitude thereof z (x ', y') can be expressed as:
in the formula (2), F and F -1 Respectively representing a two-dimensional Fourier transform and a two-dimensional inverse Fourier transform, (f) x ,f y ) To reproduce the frequency domain coordinates of the image.
S2, in order to extractThe phase information ψ (x ', y') of the reproduced image requires a complex amplitude distribution U for the reproduced image z (x ', y') is numerically analyzed, and the imaginary part Im [ U ] of the complex amplitude is obtained z (x ', y') and real part Re [ U ] z (x',y')]The value of the ratio is the arctangent, and the expression is:
and 3, for the image A (x, y) to be spliced, firstly, carrying out image denoising and image enhancement on the image A (x, y) to be spliced so as to improve the accuracy and stability of the subsequent steps, and then carrying out feature point extraction on the image to be spliced.
The specific steps of the step 3 are as follows:
s1, establishing a scale space: performing scale transformation on the image A (x, y) to be spliced to construct a Gaussian differential scale space D (x, y, sigma):
D(x,y,σ)＝(G(x,y,kσ)-G(x,y,σ))*A(x,y) (4)
in the formula (4), G (x, y, σ) is a gaussian function, σ is a scale parameter, k is a scaling factor, and x represents a convolution operation of the two functions.
S2, detecting characteristic points, and searching matching information of the images to be spliced: and detecting local extreme points, namely, possible characteristic points, on each scale in the constructed Gaussian differential scale space by using a differential Gaussian filter. From the second-order Taylor's expansion of the scale-space function D (x, y, sigma), the shift of the feature point position is knownThe method comprises the following steps:
when (when)When the characteristic points are removed; when->In this case, the feature point also needs to be removed.
S3, describing characteristic points: the SIFT algorithm uses an image area around a feature point to calculate a descriptor, and in order to ensure invariance to rotation and scale transformation, a gradient direction histogram in the vicinity around the feature point needs to be calculated, wherein a gradient modulus value m (x, y) and a gradient direction theta (x, y) of a pixel point in the feature area are as follows:
in equations (6) and (7), L (x, y) is a spatial scale function.
And 4, splicing the two images by adopting a SIFT algorithm: and 3, extracting characteristic points of the two images to be spliced by using the method in the step 3 for matching, calculating a transformation matrix between the two images, performing perspective transformation on the two images to be spliced, projecting the two images to be spliced into an spliced image space, carrying out average weighting on gray values of the two images to be spliced, and then fusing the gray values to realize smooth splicing between the two images to be spliced, so as to obtain a new image.
Step 5, grouping all the line atlases, wherein two adjacent sub-images in each line are a group (such as A in the first line 11 And A is a 12 Is a group of A 13 And A is a 14 One group) of images in the line graph set are spliced by adopting the method of the step 4 until all the line graph sets are spliced, at the moment, one spliced image is obtained in each line, and all the spliced images are rearranged into a new line graph set W in sequence i (i＝1，2，3，……，a)。
Step 6, the line drawing set W obtained in step 5 i The images in the row image set are grouped, two adjacent sub-images are grouped, and the row image set W is subjected to the method of the step 4 i Each group of images in a cameraStitching until the atlas W i And (3) splicing all the images in the model (3) to finally obtain a spliced image, namely a synthetic aperture diagram W (x, y) with a high spatial bandwidth product after the object to be measured is reconstructed.
The beneficial effects of the invention are as follows:
1. the invention provides a better fusion method for the sub-images reconstructed by the holographic sub-images, can realize fusion and splicing among the reconstructed sub-images, and can obtain a smooth splicing result.
2. The invention provides a synthetic aperture imaging method based on a SIFT algorithm, which can effectively improve the space bandwidth product of a digital holographic imaging system and enlarge the imaging field of view, under the condition of being limited by the imaging field of view, a plurality of off-axis holographic sub-images with a certain overlapping area can be acquired by adjusting a precise translation stage according to the actual measurement requirement or the imaging field of view requirement, then the SIFT algorithm is used for extracting the characteristic points of the reconstructed sub-images for matching, and then the images are weighted and fused to obtain a large-field synthetic aperture image containing the information of a measured object.
Description of the drawings:
FIG. 1 is a flow chart of a synthetic aperture imaging method according to the present invention;
FIG. 2 is a schematic diagram of a transmissive digital off-axis holographic microscopy interferometry system according to the present invention;
wherein, a Laser-Laser, an NF-attenuation sheet, a BE-beam expander and a BS 1 、BS 2 -a beam-splitting prism, M 1 、M 2 -a mirror, a P-polarizer, a MA-object under test, MO 1 、MO 2 -a microscope objective, CCD-a camera receiving a digital holographic interference pattern;
FIG. 3 is a hologram set acquired by a transmission type digital off-axis holographic microscopy interferometry system according to the present invention; wherein, figures 3a-3d respectively show holographic subgraphs with a certain overlapping area on the surface of the measured object;
FIG. 4 is a reconstructed atlas corresponding to a hologram acquired by a transmission type digital off-axis holographic microscopic interference system; wherein, FIGS. 4a-4d are reconstructed subgraphs corresponding to the holographic subgraphs in FIG. 3, respectively;
fig. 5 is a graph of feature point detection results for reconstructed sub-graphs 4a and 4 b;
FIG. 6 is a synthetic aperture diagram of FIG. 5;
FIG. 7 is a synthetic aperture map of reconstructed atlases 4a-4d using the method of the present invention;
fig. 8 is a synthetic aperture map obtained by reconstructing the atlases 4a-4d using a phase-based operation method.
The specific embodiment is as follows:
the invention is further described below with reference to specific embodiments and illustrations in order to make the technical means, the creation features, the achievement of the purpose and the effect of the implementation of the invention easy to understand.
The method provided by the invention is adopted to collect off-axis holographic sub-images with a certain overlapping area by adjusting a three-dimensional translation stage, analyze the reconstruction method of the off-axis holographic images from the fluctuation theory of light, simulate the diffraction reconstruction process of the hologram by computer numerical values, realize the reconstruction of the object wave front information, and use SIFT algorithm to carry out weighted fusion on the reconstructed sub-images so as to obtain a synthetic aperture map with high space bandwidth product.
The invention provides a synthetic aperture imaging method based on a SIFT algorithm, which is shown in figure 1 and comprises the following specific steps:
step 1, a transmission type off-axis holographic optical path system based on Mach-Zehnder interferometer principle is built, as shown in fig. 2, a helium-neon polarized Laser with the wavelength of 632.8nm is used as a light source to emit a beam of polarized light, after passing through an attenuation sheet NF, the beam is collimated and amplified by a collimating and beam expander BE to form an expanded beam, and a beam splitting prism BS 1 Dividing the expanded beam into two parts, taking one part of light as an object beam, adjusting the polarization direction of the beam by a polarizer P, and then using a reflector M 2 The direction of the light is changed and the light is transmitted through the object MA, the polaroid can also filter stray light, the imaging quality of an optical system is improved, and then the microscopic objective MO 1 The light beam containing the surface information of the measured object is amplified and then enters a beam splitter prism BS 2 The method comprises the steps of carrying out a first treatment on the surface of the Another part of the light continues to propagate forward as a reference beam and is then reflected by the mirror M 1 Change propagationIncident to the microscope objective MO 2 Post-and object light is reflected by beam splitter prism BS 2 Holographic interference occurs in the combined beam, and a CCD image sensor collects holographic interference images of the measured object.
The measured object is fixed on the three-dimensional translation table, the CCD camera surface and the measured object surface are required to be kept at a fixed distance and are parallel to each other, and only two-dimensional translation transformation relation exists between collected holograms. In order to make the collected hologram set contain the whole area of the measured object, the collected path is: the CCD camera firstly acquires a row of images at equal intervals from left to right in the horizontal direction, and the images are sequentially named as I 11 、I 12 Then the translation stage is regulated to move the measured object downwards for a certain distance, a second row of images are acquired at equal intervals in the right-to-left direction, and the images are sequentially named as I 22 、I 21 A total of 2×2 holograms were acquired as a hologram set of the object to be measured as shown in fig. 3.
And 2, reconstructing the hologram set obtained in the step 1 in a piece-by-piece holographic subgraph manner, and obtaining a reconstructed image set of the measured object, as shown in fig. 4. The atlas contains 2 x 2 images, which are named a in turn 11 、A 12 、A 21 、A 22 。
The reconstruction method of the holographic subgraph in the step 2 comprises the following steps:
s1, the interference intensity P (x, y) of the holographic image can be expressed as:
P(x,y)＝|O(x,y)| 2 +|R(x,y)| 2 +O * (x,y)R(x,y)+O(x,y)R * (x,y) (0)
in formula (1) |O (x, y) | 2 And |R (x, y) | 2 The intensity distribution of the object light and the reference light, i.e. the zero order of diffraction, O * (x, y) and R * (x, y) is the conjugate of O (x, y) and R (x, y), respectively, the third term O * (x, y) R (x, y) is a twin image, and O (x, y) R * (x, y) is the desired reconstruction. In off-axis digital holography, since the object light and the reference light have a certain included angle theta, after the hologram is subjected to Fourier transformation, all interference terms are separated from each other in a frequency domain. If the deflection angle theta is large enough, the spectrum of the twin image can be completely separated, and then the twin image is communicatedThe filter wave technology extracts the spectrum of the reconstructed image, and the off-axis hologram can be reconstructed by utilizing an angular spectrum method, so that the reconstructed image is obtained.
If the reproduction distance is z and the reproduction light wave irradiated on the hologram is C (x, y), the diffracted light field from the hologram surface to the reproduction distance z is the reproduction object light field, the distribution U of complex amplitude thereof z (x ', y') can be expressed as:
in the formula (2), F and F -1 Respectively representing a two-dimensional Fourier transform and a two-dimensional inverse Fourier transform, (f) x ,f y ) To reproduce the frequency domain coordinates of the image.
S2, in order to extract the phase information psi (x ', y') of the reproduction image, the complex amplitude distribution U of the reproduction image is required z (x ', y') is numerically analyzed, and the imaginary part Im [ U ] of the complex amplitude is obtained z (x ', y') and real part Re [ U ] z (x',y')]The value of the ratio is the arctangent, and the expression is:
step 3, for the image A (x, y) to be spliced, firstly, carrying out image denoising and image enhancement on the image A (x, y) to be spliced to improve the accuracy and stability of the subsequent steps, and then carrying out feature point extraction on the image to be spliced, wherein the specific steps are as follows:
s1, establishing a scale space: performing scale transformation on the image A (x, y) to be spliced to construct a Gaussian differential scale space D (x, y, sigma):
D(x,y,σ)＝(G(x,y,kσ)-G(x,y,σ))*A(x,y) (4)
in the formula (4), G (x, y, σ) is a gaussian function, σ is a scale parameter, k is a scaling factor, and x represents a convolution operation of the two functions.
S2, detecting characteristic points, and searching matching information of the images to be spliced: at each scale in the constructed Gaussian differential scale space, a differential Gaussian filter is used to detect local extremaPoints, i.e. possible feature points. From the second-order Taylor's expansion of the scale-space function D (x, y, sigma), the shift of the feature point position is knownThe method comprises the following steps:
when (when)When the characteristic points are removed; when->In this case, the feature point also needs to be removed. The feature point detection results of the images 4a and 4b to be spliced are shown in fig. 5.
S3, describing characteristic points: the SIFT algorithm uses an image area around a feature point to calculate a descriptor, and in order to ensure invariance to rotation and scale transformation, a gradient direction histogram in the vicinity around the feature point needs to be calculated, wherein a gradient modulus value m (x, y) and a gradient direction theta (x, y) of a pixel point in the feature area are as follows:
in equations (6) and (7), L (x, y) is a spatial scale function.
And 4, splicing the two images by adopting a SIFT algorithm: and 3, extracting characteristic points of the two images to be spliced according to the method in the step 3, matching, calculating a transformation matrix between the two images, performing perspective transformation on the two images to be spliced, projecting the two images to be spliced into an spliced image space, carrying out average weighting on gray values of the two images to be spliced, and then fusing the gray values to realize smooth splicing between the two images to be spliced, so as to obtain a new image. The result of stitching the images 4a and 4b to be stitched is shown in fig. 6.
Step 5, grouping all the line atlases, wherein two adjacent sub-images in each line are a group, such as A in the first line 11 And A is a 12 Is a group of A 13 And A is a 14 For one group, the method of step 4 is adopted to splice each group of images in the line graph set until all the line graph sets are spliced, at this time, one spliced image is obtained in each line, and all the spliced images are rearranged into a new line graph set W in sequence i (i＝1,2)。
Step 6, the line drawing set W obtained in step 5 i The images in the row image set are grouped, two adjacent sub-images are grouped, and the row image set W is subjected to the method of the step 4 i Each group of images in the image is spliced until the atlas W i The image after the splicing is completed is finally obtained, namely, a synthetic aperture diagram W (x, y) with a high spatial bandwidth product after the object to be measured is reconstructed is obtained, as shown in fig. 7, and 4 reconstructed sub-images use a synthetic aperture diagram T (x, y) based on phase operation, as shown in fig. 8.
In order to further compare the splicing effect of the method with that of the conventional phase splicing method, gray variance values of the synthetic aperture maps W (x, y) and T (x, y) are calculated respectively: the gray variance of the image characterizes the average degree of the gray variation of the image, the larger the average degree of the gray variation is, the clearer the image is, the smaller the average degree of the gray variation is, and the more blurred the image is. Gray average value of all pixels of synthetic aperture map W (x, y)The method comprises the following steps:
n in formula (8) x And N y The number of pixels in the x and y directions of the synthetic aperture map W (x, y), respectively. From the gray average value of the pixels of the image W (x, y), the image W is calculatedThe gray variance s of (x, y) is:
using equations (8) and (9), the grayscale variance of fig. 7 can be calculated as 4983.06 and the grayscale variance of fig. 8 as 4406.17. This demonstrates that the gray scale transformation of fig. 7 is averaged to a greater extent and the detail of the image is more clear than in fig. 8.
The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (4)
1. The synthetic aperture imaging method based on the SIFT algorithm is characterized by comprising the following steps of:
step 1, imaging a measured object by using a transmission type off-axis holographic optical path system based on a Mach-Zehnder interferometer principle, acquiring holograms by using a CCD camera, fixing the measured object on a three-dimensional translation stage, keeping a fixed distance between the surface of the CCD camera and the surface of the measured object and keeping the fixed distance parallel to each other, and ensuring that only a two-dimensional translation transformation relation exists between the acquired holograms;
step 2, reconstructing the hologram set obtained in the step 1 in a piece-by-piece holographic subgraph manner to obtain a reconstructed image set of the measured object, wherein the image set contains a multiplied by b images, and the images are named as A in sequence 11 、A 12 、……、A ab ；
Step 3, for the image A (x, y) to be spliced, firstly performing image denoising and image enhancement operations on the image A (x, y), and then extracting feature points of the image to be spliced;
and 4, splicing the two images by adopting a SIFT algorithm: extracting characteristic points of two images to be spliced by using the method in the step 3 for matching, calculating a transformation matrix between the two images, performing perspective transformation on the two images to be spliced, projecting the two images to be spliced into an spliced image space, carrying out average weighting on gray values of the two images to be spliced, and then fusing the gray values to realize smooth splicing between the two images to be spliced to obtain a new image;
step 5, grouping all the line atlases, wherein two adjacent sub-images in each line are a group, splicing each group of images in the line atlases by adopting the method of step 4 until all the line atlases are spliced, obtaining a spliced image in each line, and rearranging all the spliced images into a new line atlas W in sequence i (i＝1，2，3，……，a)；
Step 6, the line drawing set W obtained in step 5 i The images in the row image set are grouped, two adjacent sub-images are grouped, and the row image set W is subjected to the method of the step 4 i Each group of images in the image is spliced until the atlas W i And (3) splicing all the images in the model (3) to finally obtain a spliced image, namely a synthetic aperture diagram W (x, y) with a high spatial bandwidth product after the object to be measured is reconstructed.
2. The synthetic aperture imaging method of claim 1 wherein in step 1, in order to make the acquired hologram set contain the entire area of the object under test, the acquisition path is: the CCD camera firstly acquires a row of images at equal intervals from left to right in the horizontal direction, and the images are sequentially named as I 11 、I 12 、……、I 1b Then the translation stage is regulated to move the measured object downwards for a certain distance, a second row of images are acquired at equal intervals in the right-to-left direction, and the images are sequentially named as I 2b 、……、I 22 、I 21 Then the measured object is moved downwards for a certain distance, a row of images is acquired from left to right, and so on, a×b holograms are acquired in total (a=2 v ，v＝1，2，3，……；b＝2 u U=1, 2,3, … …), i.e. the hologram set of the measured object,where a is the number of rows and b is the number of columns.
3. The synthetic aperture imaging method according to claim 1 or 2, wherein the reconstruction method of the hologram in step 2 is:
s1, the interference intensity P (x, y) of the holographic image can be expressed as:
P(x,y)＝|O(x,y)| 2 +|R(x,y)| 2 +O * (x,y)R(x,y)+O(x,y)R * (x,y) (0)
in formula (1) |O (x, y) | 2 And |R (x, y) | 2 The intensity distribution of the corresponding object light and reference light, i.e. the zero order of diffraction, O * (x, y) and R * (x, y) is the conjugate of O (x, y) and R (x, y), respectively, the third term O * (x, y) R (x, y) is a twin image, and O (x, y) R * (x, y) is the desired reconstruction;
if the reproduction distance is z and the reproduction light wave irradiated on the hologram is C (x, y), the diffracted light field from the hologram surface to the reproduction distance z is the reproduction object light field, the distribution U of complex amplitude thereof z (x ', y') can be expressed as:
in the formula (2), F and F -1 Respectively representing a two-dimensional Fourier transform and a two-dimensional inverse Fourier transform, (f) x ,f y ) Frequency domain coordinates for reproducing the image;
s2, in order to extract the phase information psi (x ', y') of the reproduction image, the complex amplitude distribution U of the reproduction image is required z (x ', y') is numerically analyzed, and the imaginary part Im [ U ] of the complex amplitude is obtained z (x ', y') and real part Re [ U ] z (x',y')]The value of the ratio is the arctangent, and the expression is:
4. a synthetic aperture imaging method according to any one of claims 1-3, characterized in that the specific steps of step 3 are as follows:
s1, establishing a scale space: performing scale transformation on the image A (x, y) to be spliced to construct a Gaussian differential scale space D (x, y, sigma):
D(x,y,σ)＝(G(x,y,kσ)-G(x,y,σ))*A(x,y) (4)
in the formula (4), G (x, y, σ) is a gaussian function, σ is a scale parameter, k is a scaling factor, and x represents convolution operation of the two functions;
s2, detecting characteristic points, and searching matching information of the images to be spliced: detecting local extremum points, namely possible characteristic points, on each scale in the constructed Gaussian differential scale space by using a differential Gaussian filter; from the second-order Taylor's expansion of the scale-space function D (x, y, sigma), the shift of the feature point position is knownThe method comprises the following steps:
when (when)When the characteristic points are removed; when->When the characteristic points are also needed to be removed;
s3, describing characteristic points: the SIFT algorithm uses an image area around a feature point to calculate a descriptor, and in order to ensure invariance to rotation and scale transformation, a gradient direction histogram in the vicinity around the feature point needs to be calculated, wherein a gradient modulus value m (x, y) and a gradient direction theta (x, y) of a pixel point in the feature area are as follows:
in equations (6) and (7), L (x, y) is a spatial scale function.
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