CN112288847B - Light field three-dimensional reconstruction method based on fast Fourier transform - Google Patents
Light field three-dimensional reconstruction method based on fast Fourier transform Download PDFInfo
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Abstract
The invention discloses a light field three-dimensional reconstruction method based on fast Fourier transform, which comprises the following steps: converting the collected light field diagram stack into 4D phase space information; rearranging the pixels at the corresponding positions in the light field image to convert the pixels into multi-angle phase space information; initializing three-dimensional information according to the phase space information, and converting the three-dimensional information into three-dimensional frequency domain information; arranging the five-dimensional phase space point diffusion functions according to two-dimensional angles to obtain space information of three-dimensional point diffusion functions corresponding to all the angles, and converting the point diffusion functions into frequency domains; forwarding the three-dimensional body to obtain two-dimensional frequency domain information of a forwarded image; the forward projection of the frequency domain is reversely transmitted to obtain the reversely transmitted three-dimensional frequency domain information; transforming into space domain information through inverse Fourier transform; converting the acquired phase space information to a frequency domain, and converting the phase space information into space domain information through inverse transmission and inverse Fourier transform; and updating the spatial information of the three-dimensional body until the iteration is finished. The method can rapidly process the light field data to obtain an accurate three-dimensional reconstruction result.
Description
Technical Field
The invention relates to the technical field of three-dimensional reconstruction, in particular to a light field three-dimensional reconstruction method based on fast Fourier transform.
Background
Light Field (LF) imaging is a fast volumetric imaging method. The light field system adds a micro-lens array on the original imaging surface, and uses a sensor to record 4D light field information. Since three-dimensional information of a scene can be recorded with a single exposure, it has been widely used in the field of three-dimensional imaging in recent years.
For 4D light field information acquired by a light field system, the existing three-dimensional reconstruction methods include Richard-Lucy reconstruction algorithm, phase space-based reconstruction method and the like, but the method usually relates to a two-dimensional convolution process, the reconstruction speed is positively correlated with the size of an image and the reconstruction depth, the speed is very low, and a large amount of calculation resources are occupied. In addition, the use of the Richard-Lucy reconstruction algorithm can also introduce artifacts into the focal plane.
Due to the fast volumetric imaging nature of light field systems, light field systems are often used to record dynamic processes, thereby often requiring the processing of large amounts of light field data. Therefore, fast three-dimensional reconstruction of light field data is a problem that needs to be solved by those skilled in the art.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, the invention aims to provide a light field three-dimensional reconstruction method based on fast Fourier transform, which can rapidly process light field data to obtain an accurate three-dimensional reconstruction result.
In order to achieve the above object, an embodiment of the present invention provides a light field three-dimensional reconstruction method based on fast fourier transform, including the following steps: step S1, collecting a light field map stack, and converting the light field map stack into 4D phase space information; step S2, initializing information of the three-dimensional body according to the phase space information to obtain initialized three-dimensional information, and converting the initialized three-dimensional information into frequency domain three-dimensional information; step S3, obtaining a light field phase space point diffusion function, arranging the light field phase space point diffusion function according to two-dimensional angles to obtain the space information of a three-dimensional point diffusion function corresponding to each angle, and transferring the three-dimensional point diffusion function to a frequency domain to obtain a frequency domain phase space point diffusion function; step S4, forwarding the three-dimensional frequency domain information by using the frequency domain phase space point spread function to obtain a frequency domain forward projection; step S5, inverting the frequency domain forward projection to obtain inverted three-dimensional frequency domain information, and converting the inverted three-dimensional frequency domain information into first space domain information through inverse Fourier transform; a step S6 of converting the phase space information of the step S1 to a frequency domain, and converting the phase space information into second spatial information through inversion and inverse fourier transform; and S7, dividing the second spatial information and the first spatial information, updating the spatial information of the three-dimensional body according to the division result, and iterating the steps S3-S7 until the end.
According to the light field three-dimensional reconstruction method based on the fast Fourier transform, the reconstruction process of a space domain is converted into a frequency domain, the phase space based method is accelerated by using the fast Fourier transform, and compared with the traditional three-dimensional light field reconstruction algorithm, the method is high in speed, occupies less display memory and memory, does not bring artifacts to a focal plane of a reconstruction result, and can obtain an accurate three-dimensional reconstruction result.
In addition, the method for three-dimensional reconstruction of a light field based on fast fourier transform according to the above embodiment of the present invention may further have the following additional technical features:
further, in one embodiment of the present invention, the light field phase space point spread function is a five-dimensional function, where three dimensions are space coordinates (x, y, z) and two dimensions are phase space coordinates (u, v).
Further, in an embodiment of the present invention, in the step S3, the point spread function of the phase space coordinates (u, v) is converted into a frequency domain to obtain a frequency domain phase space point spread function, where an index is (fx, fy, fz).
Further, in an embodiment of the present invention, the step S4 further includes: performing three-dimensional Fourier transform on the initialized three-dimensional information to obtain frequency domain phase space data; and multiplying the frequency domain phase space data by the frequency domain phase space point spread function point, and summing along the z axis to obtain the frequency domain forward projection.
Further, in an embodiment of the present invention, the step S5 further includes: turning the frequency domain forward projection along a z axis, and simultaneously rotating the frequency domain forward projection 180 degrees along an XY plane to obtain a backward propagation phase space point diffusion function; carrying out three-dimensional fast Fourier transform on the light field phase space point spread function to obtain a frequency domain phase space back propagation point spread function; copying Z parts of the frequency domain forward projection along a Z axis, wherein Z is the number of reconstruction layers to obtain HXstress _ Z; and performing point multiplication on the HXstress _ z and the frequency domain phase space inverse propagation point spread function, and performing three-dimensional fast inverse Fourier transform to obtain the first spatial domain information.
Further, in an embodiment of the present invention, the step S6 further includes: performing three-dimensional fast Fourier transform on the wigner obtained in the step S1 under each angle to obtain frequency domain phase space data; and performing point multiplication on the frequency domain phase space data and the inverse propagation phase space point spread function, and performing three-dimensional fast inverse Fourier transform to obtain second airspace information.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of a fast Fourier transform-based light field three-dimensional reconstruction method according to an embodiment of the present invention;
FIG. 2 is a flowchart of an algorithm of a fast Fourier transform-based light field three-dimensional reconstruction method according to an embodiment of the present invention;
fig. 3 is an explanatory diagram of spatial-frequency domain conversion in the fast fourier transform-based light field three-dimensional reconstruction method according to an embodiment of the invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The three-dimensional light field reconstruction method based on the fast fourier transform proposed by the embodiment of the invention is described below with reference to the accompanying drawings.
Fig. 1 is a flowchart of a fast fourier transform-based light field three-dimensional reconstruction method according to an embodiment of the present invention.
Fig. 2 is a flowchart of an algorithm of a fast fourier transform-based light field three-dimensional reconstruction method according to an embodiment of the present invention.
As shown in fig. 1 and 2, the fast fourier transform-based light field three-dimensional reconstruction method includes the following steps:
in step S1, a light field stack is collected, which is translated into 4D phase space information.
Specifically, pixels at corresponding positions in the light field pattern are rearranged and converted into phase space information corresponding to multiple angles, that is, the collected light field pattern stack is converted into 4D phase space information. For example, in the optical field system, each microlens corresponds to N × N sensor pixels, pixels at corresponding positions in the optical field pattern are extracted and then rearranged, so that N × N phase spatial data can be obtained and identified by wigner (u, v), where u and v are corresponding phase spatial coordinates.
In step S2, the information of the three-dimensional volume is initialized according to the phase space information, so as to obtain initialized three-dimensional information, and the initialized three-dimensional information is converted into frequency domain three-dimensional information.
Specifically, according to wigner (u, v) obtained in step S1, the total energy value of all phase space images is calculated, and then the value is evenly distributed to each unit of the initialized three-dimensional information Xguess, so as to obtain frequency domain three-dimensional information fft (Xguess).
In step S3, a light field phase space point spread function is obtained, the light field phase space point spread functions are arranged according to two-dimensional angles, spatial information of a three-dimensional point spread function corresponding to each angle is obtained, and the three-dimensional point spread function is converted to a frequency domain, so that a frequency domain phase space point spread function is obtained.
Further, in one embodiment of the present invention, the light field phase space point spread function is a five-dimensional function, where three dimensions are the spatial coordinates (x, y, z) and two dimensions are the phase space coordinates (u, v).
Specifically, the point spread function for each angle (u, v) (i.e., phase space coordinate (u, v)) is transferred to the frequency domain, resulting in a frequency domain phase space point spread function FFTPSF, with subscripts (fx, fy, fz).
In step S4, the three-dimensional frequency domain information is forwarded by using a frequency domain phase space point spread function, so as to obtain a frequency domain forward projection.
Specifically, as shown in fig. 3, the initialized three-dimensional information Xguess is subjected to three-dimensional fourier transform to obtain frequency domain phase space data FFTWIG; and (3) performing point multiplication on the frequency domain phase space data FFTWIG and the frequency domain phase space point spread function FFTPSF, and then summing along the z axis to obtain the two-dimensional Fourier change Hxguess (frequency domain forward projection) of the forward projection.
In step S5, the frequency domain forward projection is inverted to obtain inverted three-dimensional frequency domain information, and the inverted three-dimensional frequency domain information is converted into first spatial domain information by inverse fourier transform.
Specifically, as shown in fig. 3, the phase space point spread function in the airspace is turned over along the z-axis, and is rotated 180 degrees along the XY plane to obtain a back propagation phase point spread function FFTPSF; performing three-dimensional fast Fourier transform on the back propagation phase space point spread function to obtain a frequency domain phase space back propagation point spread function FFTPSF 2; and copying Z parts of the frequency domain forward projection HXstress along the Z axis, wherein Z is the number of reconstruction layers to obtain HXstress _ Z. And performing point multiplication on HXgauge _ z and a frequency domain phase space inverse propagation point spread function FFTPSF2, and performing three-dimensional fast Fourier transform to obtain first spatial information HB.
In step S6, the phase space information in step S1 is converted to the frequency domain, and becomes second spatial information by inversion and inverse fourier transform.
Specifically, as shown in fig. 3, the wigner obtained in step S1 at each angle is subjected to three-dimensional fast fourier transform to obtain frequency domain phase space data FFTWIG; and multiplying the frequency domain phase space data FFTWIG by a reverse propagation phase space point spread function FFTPSF2, and then performing three-dimensional fast inverse Fourier transform to obtain second spatial domain information WB.
In step S7, the second spatial information is divided by the first spatial information, and the spatial information of the three-dimensional body is updated according to the division result, and the iteration steps S3-S7 are performed until the end.
Specifically, the real part of WB/HB is obtained through calculation, the three-dimensional information Xgusess is initialized through certain proportion updating, and the steps S3-S7 are repeated until the iteration is finished.
According to the light field three-dimensional reconstruction method based on the fast Fourier transform, which is provided by the embodiment of the invention, the reconstruction process of a space domain is converted into a frequency domain, and the phase space-based method is accelerated by using the fast Fourier transform.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or to implicitly indicate the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of the feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are exemplary and not to be construed as limiting the present invention, and that changes, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
Claims (6)
1. A light field three-dimensional reconstruction method based on fast Fourier transform is characterized by comprising the following steps:
step S1, collecting a light field map stack, and converting the light field map stack into 4D phase space information;
step S2, initializing information of the three-dimensional body according to the phase space information to obtain initialized three-dimensional information, and converting the initialized three-dimensional information into frequency domain three-dimensional information;
step S3, obtaining a light field phase space point diffusion function, arranging the light field phase space point diffusion function according to two-dimensional angles to obtain the space information of a three-dimensional point diffusion function corresponding to each angle, and transferring the three-dimensional point diffusion function to a frequency domain to obtain a frequency domain phase space point diffusion function;
step S4, forwarding the three-dimensional frequency domain information by using the frequency domain phase space point spread function to obtain a frequency domain forward projection;
step S5, the forward projection of the frequency domain is reversed to obtain reversed three-dimensional frequency domain information, and the reversed three-dimensional frequency domain information is converted into first spatial domain information through inverse Fourier transform;
a step S6 of converting the phase space information of the step S1 to a frequency domain, and converting the phase space information into second spatial information through inversion and inverse fourier transform;
and S7, dividing the second spatial information and the first spatial information, updating the spatial information of the three-dimensional body according to the division result, and iterating the steps S3-S7 until the end.
2. The fast fourier transform-based light field three-dimensional reconstruction method according to claim 1, wherein the light field phase space point spread function is a five-dimensional function, where three dimensions are space coordinates (x, y, z) and two dimensions are phase space coordinates (u, v).
3. The method for three-dimensional reconstruction of a light field based on fast fourier transform as claimed in claim 2, wherein the step S3 is to convert the point spread function of the phase space coordinates (u, v) into the frequency domain to obtain a frequency domain point spread function of phase space, which is denoted by (fx, fy, fz).
4. The fast fourier transform-based light field three-dimensional reconstruction method according to claim 1, wherein the step S4 further comprises:
performing three-dimensional Fourier transform on the initialized three-dimensional information to obtain frequency domain phase space data;
and multiplying the frequency domain phase space data by the frequency domain phase space point spread function point, and summing along the z axis to obtain the frequency domain forward projection.
5. The fast fourier transform-based light field three-dimensional reconstruction method according to claim 1, wherein the step S5 further comprises:
turning the frequency domain forward projection along a z axis, and simultaneously rotating the frequency domain forward projection 180 degrees along an XY plane to obtain a backward propagation phase space point diffusion function;
carrying out three-dimensional fast Fourier transform on the light field phase space point spread function to obtain a frequency domain phase space back propagation point spread function;
copying Z parts of the frequency domain forward projection along a Z axis, wherein Z is the number of reconstruction layers to obtain HXguss _ Z;
and performing point multiplication on the HXgain _ z and the frequency domain phase space back-propagation point spread function, and then performing three-dimensional fast Fourier transform to obtain the first spatial domain information.
6. The fast fourier transform-based light field three-dimensional reconstruction method according to claim 1, wherein the step S6 further comprises:
performing three-dimensional fast Fourier transform on the wigner obtained in the step S1 under each angle to obtain frequency domain phase space data;
and performing point multiplication on the frequency domain phase space data and the inverse propagation phase space point spread function, and performing three-dimensional fast inverse Fourier transform to obtain second airspace information.
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| CN109360212A (en) * | 2018-11-02 | 2019-02-19 | 太原科技大学 | A kind of frequency domain light field number refocusing algorithm can inhibit resampling error |
| CN109615651A (en) * | 2019-01-29 | 2019-04-12 | 清华大学 | Three-dimensional microscopy method and system based on light field microscopic system |
| CN110320654A (en) * | 2019-06-11 | 2019-10-11 | 清华大学 | Based on the microscopical quick three-dimensional body imaging system of multi-angle 4Pi and method |
| EP3657786A1 (en) * | 2018-11-22 | 2020-05-27 | InterDigital CE Patent Holdings | Light field reconstruction |
| CN111429500A (en) * | 2020-02-18 | 2020-07-17 | 清华大学 | Reconstruction and splicing method and device for axial scanning light field data |
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| CN109360212A (en) * | 2018-11-02 | 2019-02-19 | 太原科技大学 | A kind of frequency domain light field number refocusing algorithm can inhibit resampling error |
| EP3657786A1 (en) * | 2018-11-22 | 2020-05-27 | InterDigital CE Patent Holdings | Light field reconstruction |
| CN109615651A (en) * | 2019-01-29 | 2019-04-12 | 清华大学 | Three-dimensional microscopy method and system based on light field microscopic system |
| CN110320654A (en) * | 2019-06-11 | 2019-10-11 | 清华大学 | Based on the microscopical quick three-dimensional body imaging system of multi-angle 4Pi and method |
| CN111429500A (en) * | 2020-02-18 | 2020-07-17 | 清华大学 | Reconstruction and splicing method and device for axial scanning light field data |
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