High-dimensional fault-tolerant microcrystal array encoding and adaptive image decoding method

Abstract

The application discloses a high-dimensional fault-tolerant microcrystal array encoding and adaptive image decoding method, which comprises two stages of forward encoding and reverse decoding, wherein the forward encoding receives dynamic payload data, generates a code word containing error correction redundancy according to a target array dimension, and maps the code word into a discrete microcrystal array without a fixed locator; the reverse decoding pre-processes a collected microcrystal array image and extracts effective feature points, reconstructs a reading grid based on the spatial distribution of the feature points, restores data according to the reconstructed grid, and performs error correction verification. The application discards the traditional locator, has high concealment, can resist point position loss, effectively avoids grid dimension collapse, and greatly improves the industrial application feasibility of the anti-fake identification.

Description

Technical Field

[0001] This invention relates to the fields of computer vision, data encoding technology, and information security and anti-counterfeiting technology, and in particular to a high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method. Background Technology

[0002] With the rapid development of product traceability, brand anti-counterfeiting, and digital marketing, higher requirements are being placed on information coding and marking on product packaging. Traditional two-dimensional barcodes such as QR codes and DataMatrix are widely used due to their advantages of large capacity and ease of reading. However, these codes rely on fixed rectangular or L-shaped positioning anchors, which not only damage the overall aesthetics and design integrity of the product packaging, but also render the entire code unreadable if the anchors are worn, soiled, or obstructed. This severely limits their application in high-end consumer goods and luxury goods, where packaging aesthetics are paramount. To address these issues, discrete dot matrix coding technology without fixed positioning symbols has emerged. By carrying information through a discretely distributed dot matrix, it offers higher concealment and artistic integration, allowing for seamless integration with product packaging design and becoming an important development direction in the current information anti-counterfeiting field.

[0003] Currently, mainstream discrete dot matrix encoding technologies without fixed locators generally employ row and column projection for grid reconstruction. The core principle is to project the acquired dot matrix image onto the X and Y axes respectively, and determine the row and column coordinates by statistically analyzing the positions of the projection peaks, thereby constructing the read grid. However, this type of technology suffers from insurmountable technical defects in practical industrial applications: when the dot matrix image is damaged by printing wear or scratches resulting in missing points, or when rotation or scaling distortion occurs due to the shooting angle, the projection peaks may be missing or shifted, easily leading to "empty rows" or "empty columns," which in turn causes grid dimensional collapse, making accurate reconstruction of the read grid impossible. Furthermore, existing technologies lack dynamic adaptability in the mapping between the bitstream and the error correction space, failing to adaptively adjust error correction redundancy according to the array dimension. This results in wasted capacity in low-impact scenarios and ineffective error correction in high-impact scenarios, ultimately leading to a significant decrease in decoding success rate and failing to meet the high-fault-tolerant decoding requirements of complex environments in industrial production.

[0004] In summary, existing discrete dot matrix coding techniques without fixed locators rely on continuous projection peaks for grid reconstruction, lack effective dimension loss compensation mechanisms and adaptive error correction architectures, and suffer from technical defects such as easy grid collapse, low fault tolerance, and poor rotation adaptability. They cannot meet the requirements of high concealment and high robustness in industrial applications. Summary of the Invention

[0005] The main objective of this invention is to propose a high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method. It aims to solve the problems of grid reconstruction and data restoration in the case of rotational distortion and missing points in anchor-free array encoding by introducing non-zero feature avoidance constraints, virtual anchor point compensation mechanism and orthogonal multidimensional phase space parallel analytical architecture, so as to achieve adaptive decoding with high concealment, high fault tolerance and low computing power.

[0006] To achieve the above objectives, this invention proposes a high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method, comprising the following steps:

[0007] Forward encoding: Receive dynamic payload data, generate codewords containing error correction redundancy according to the target array dimension, and map the codewords to a discrete microcrystal array without fixed location symbols;

[0008] Reverse decoding: The acquired microcrystalline array image is preprocessed and effective feature points are extracted. The reading grid is reconstructed based on the spatial distribution of the feature points. The data is restored based on the reconstructed grid and error correction verification is performed.

[0009] Furthermore, the forward encoding stage specifically includes:

[0010] S1: Adaptively calculate the total capacity, effective capacity, and error correction redundancy based on the target microcrystal array order Ψ;

[0011] S2: The payload data is encoded using error correction to generate codewords and then serialized into a binary bit stream;

[0012] S3: Convert the bitstream into a Boolean matrix, apply non-zero features to avoid constraints, and then generate a microcrystalline array.

[0013] Furthermore, the adaptive calculation described in step S1 specifically includes:

[0014] Total bit capacity: ;;

[0015] Byte-aligned effective capacity: ;

[0016] Code length: ;

[0017] Adaptive error correction redundancy: ;

[0018] Effective payload bytes: .

[0019] Furthermore, the non-zero feature avoidance constraint mentioned in step S3 is as follows: for each row of the Boolean matrix, if all elements in a row are 0, then a logic 1 is set at a preset position in that row.

[0020] Furthermore, the preset position is the last column of that row.

[0021] Furthermore, the reverse decoding stage specifically includes:

[0022] S1': Normalize and perform multi-level nonlinear filtering on the acquired image to obtain a binarized feature image;

[0023] S2': The set of coordinates of effective microcrystal points extracted from the binarized feature image;

[0024] S3': Reconstructing the reading grid of Ψ×Ψ based on the coordinate distribution of effective microcrystal points;

[0025] S4': Reconstruct the Boolean matrix from the read grid and decode to obtain the original data.

[0026] Furthermore, the reconstruction of the reading grid in step S3' specifically involves: performing one-dimensional projection clustering of effective microcrystal points onto orthogonal bi-axis to obtain initial row and column coordinate vectors; if dimension loss is detected, a virtual anchor point compensation mechanism is triggered to fill in the missing coordinates, so that the final grid dimension is strictly equal to Ψ×Ψ.

[0027] Furthermore, the virtual anchor point compensation mechanism specifically involves: calculating the average spacing gradient of the current coordinate vector, and using this gradient as a step size to linearly extrapolate from the last valid coordinate to fill in all missing coordinates.

[0028] Furthermore, step S4' also includes: constructing a phase space containing multiple orthogonal rotation phases, starting multi-threaded decoding of images with different phases in parallel, and outputting the result once the decoding of any phase passes verification.

[0029] Furthermore, the target microcrystal array has an order Ψ > 6, and the error correction coding adopts Galois domain polynomial error correction coding.

[0030] The technical solution of this invention includes two stages: forward encoding and reverse decoding. Forward encoding receives dynamic payload data, generates codewords with error-correcting redundancy based on the target array dimension, and maps these codewords to a discrete microcrystalline array without fixed locators. Reverse decoding preprocesses the acquired microcrystalline array image and extracts effective feature points. Based on the spatial distribution of these feature points, it reconstructs the reading grid, restores the data using the reconstructed grid, and performs error correction verification. This invention abandons traditional locators, possesses high concealment, resists missing points, effectively avoids grid dimensional collapse, and significantly improves the industrial application feasibility of anti-counterfeiting labels. Attached Figure Description

[0031] Figure 1 This is an example diagram of the overall process structure of the present invention;

[0032] Figure 2Example diagram of the process structure for forward coding;

[0033] Figure 3 This is an example diagram of the reverse decoding process structure. Detailed Implementation

[0034] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0035] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, top, bottom, inside, outside, vertical, horizontal, longitudinal, counterclockwise, clockwise, circumferential, radial, axial, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0036] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, features defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0037] Existing discrete dot matrix encoding techniques without fixed locators mainly rely on row and column projection peaks for grid reconstruction. When more than 20% of the dots are missing, the projection peaks become continuously missing, causing grid dimensional collapse and making accurate grid reconstruction impossible. Furthermore, existing techniques typically use a fixed error correction redundancy ratio, which cannot be adaptively adjusted according to the array dimension. Rotation decoding also requires trying each angle, resulting in high computational overhead and slow decoding speed. To address these technical problems, this embodiment provides a high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method. By using non-zero features at the encoding end to avoid constraints and prevent rows of all zeros from the source, and employing a virtual anchor point compensation mechanism at the decoding end to fill in missing dimensions, combined with orthogonal multi-phase parallel decoding, it achieves full-angle adaptive parsing, significantly improving the error tolerance of the encoding and the decoding efficiency.

[0038] The process of this invention is divided into two independent stages: forward encoding and reverse decoding. The forward encoding stage converts the business data into a printable anchorless microcrystalline array image, and the reverse decoding stage restores the acquired microcrystalline array image back to the original business data.

[0039] This invention proposes a high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method.

[0040] In embodiments of the present invention, such as Figures 1 to 3 As shown, the method described in this invention is typically integrated as a software module into product traceability, anti-counterfeiting labeling, or digital marketing systems. This module receives dynamic payload data to be encoded, generates a microcrystalline array image through forward encoding, and then captures the image through an optical device (such as a mobile phone camera) during the reverse decoding stage, processes it, and outputs the original data. Figure 1 A flowchart of forward coding is shown. Figure 2 A flowchart of the reverse decoding process is shown.

[0041] Part 1: Forward Encoding Phase

[0042] The detailed process of the forward coding phase is as follows: Figure 2 As shown, its core objective is to convert arbitrary dynamic payload data into a discrete microcrystalline array without fixed locators that meets the requirements, while ensuring the robustness of subsequent decoding from the encoding source. This stage includes three sub-steps: capacity adaptive calculation, data mapping and error correction coding, and non-zero feature constraint avoidance and lattice generation.

[0043] S1: Capacity Adaptive Calculation

[0044] This step dynamically calculates the total capacity, effective capacity, and error correction redundancy based on the order Ψ (Ψ>6) of the target microarray, maximizing the effective data capacity while ensuring error correction capability. The calculation formulas and meanings of each parameter are as follows:

[0045] Total bit capacity Ω _total =Ψ×Ψ: Represents the total number of bits that a Ψ×Ψ Boolean matrix can hold, with each matrix element corresponding to one bit.

[0046] Byte-aligned effective capacity Ω _eff =Ω _total— (Ω _totalmod8 Since computer systems typically process data in bytes, the total capacity is rounded down to the nearest multiple of 8 to achieve byte alignment.

[0047] Code word length Λ=Ω _eff / / 8 : Indicates the total number of bytes that the entire array can carry after byte alignment, including valid data and error correction redundancy.

[0048] Adaptive error correction redundancy Γ_ec =max(floor(Λ / 2), 2): The number of error correction redundancy bytes is dynamically adjusted according to the total codeword length, with a maximum of half the total number of bytes, while ensuring at least 2 bytes of error correction redundancy. This design ensures that small arrays have sufficient error correction capability, while large arrays do not waste capacity due to excessive redundancy.

[0049] Effective payload bytes K = Λ - Γ _ec : Indicates the number of bytes that can be used to carry actual business data.

[0050] For example, when Ψ=16, the total bit capacity is 256 bits, which remains 256 bits after byte alignment. The total codeword length is 32 bytes, the error correction redundancy is 16 bytes, and the effective payload is 16 bytes. When Ψ=8, the total bit capacity is 64 bits, the total codeword length is 8 bytes, the error correction redundancy is 4 bytes, and the effective payload is 4 bytes.

[0051] S2: Data Mapping and Error Correction Coding

[0052] The business data to be encoded (such as product ID, traceability information, production batch, etc.) is converted into binary data. To facilitate data transmission and processing, the business data is usually first converted into Base36 or Base64 strings, and then converted into K-byte binary data.

[0053] Galois multinomial error correction coding is used to encode K bytes of valid data to generate Λ bytes of codewords. This invention preferably uses Reed-Solomon (RS) coding, a forward error correction coding widely used in data storage and communication, which can effectively correct burst errors and random errors. The error correction capability of RS coding is: it can correct up to Γ bytes of errors. _ec / 2 bytes of error data. For example, when Γ _ec When the value is 16, it can correct errors of up to 8 bytes, corresponding to 64-bit errors in a 256-bit bitstream. Combined with the grid reconstruction capability of this invention, it can achieve a bit loss tolerance of up to 20%.

[0054] Finally, the codeword of Λ bytes is serialized bitwise into Ω. _eff A binary bit stream of 12 bits, with any missing bits appended with logical 0.

[0055] S3: Non-zero feature avoidance constraints and lattice generation

[0056] Ω _eff The binary bit stream is folded into an Ψ×Ψ Boolean matrix M in row-major order. The positions of logic "1" in the matrix correspond to the positions of micro-crystal points, and the positions of logic "0" correspond to blank positions.

[0057] To avoid rows of all zeros at the source of encoding, this invention introduces a non-zero feature avoidance constraint. Rows of all zeros cause missing projection peaks during decoding, leading to grid dimension collapse, which is one of the main drawbacks of existing technologies. The specific rule of the non-zero feature avoidance constraint is as follows: For each row of the Boolean matrix, if all elements in a row are 0, a logic 1 is set at a preset position in that row. As a preferred implementation, the preset position is the last column of that row. The reason for choosing the last column is that the bits in the last column are usually trailing logic 0s, and modifying this position will not affect the correctness of the valid data. At the same time, placing all forcibly added logic 1s uniformly in the last column facilitates identification and processing at the decoding end; during decoding, only the forced bits in the last column need to be ignored to restore the original bitstream.

[0058] Finally, based on the positions of logic "1"s in the Boolean matrix, solid microcrystal dots are drawn to generate the final anchor-free microcrystal array image. The shape of the microcrystal dots is preferably an anti-aliased circular shape to improve the robustness of printing and recognition. The size of the microcrystal dots is determined according to the printing resolution and array size, typically with a diameter of 2-5 pixels.

[0059] Part Two: Reverse Decoding Stage

[0060] The detailed process of the reverse decoding stage is as follows: Figure 3 As shown, its core objective is to accurately reconstruct the original operational data from the acquired microcrystalline array images, which contain distortion, noise, and wear, without relying on any fixed locators. This stage includes four sub-steps: image preprocessing and polarity mapping, effective microcrystalline point extraction and scale estimation, read grid reconstruction and virtual anchor point compensation, and Boolean matrix restoration and parallel decoding.

[0061] S1': Image preprocessing and polarity mapping

[0062] The microcrystalline array image captured by the mobile phone camera or other optical devices is scaled proportionally to the reference width W. _norm The selection of the reference width needs to balance decoding accuracy and speed; in this invention, 300 pixels is preferred.

[0063] To eliminate the effects of ambient light noise, printing particle noise, and image blurring, this invention employs multi-level nonlinear spatial filtering to process the image. Specifically, Gaussian filtering, median filtering, and bilateral filtering are performed sequentially: Gaussian filtering smooths the image and eliminates Gaussian noise; median filtering eliminates salt-and-pepper noise and isolated point noise; and bilateral filtering smooths the image while preserving edge information, avoiding blurring of microcrystalline point edges.

[0064] After filtering, Otsu's dynamic thresholding method is used for binarization. The Otsu algorithm can automatically determine the optimal threshold based on the image's grayscale histogram, adapting to images under different lighting conditions. Subsequently, polarity inversion is performed to obtain a binarized feature image I_polar with microcrystalline dots in the foreground and a black background.

[0065] S2': Effective microcrystal point extraction and size estimation

[0066] For binarized feature image I _polar Perform connected component analysis to extract all closed contours. For each contour e, calculate its area S(e) and minimum circumcircle radius R(e).

[0067] To distinguish genuine microcrystalline points from background noise and pseudo-feature points, this invention introduces the equivalent curvature ratio (also known as the roundness coefficient) as a screening criterion. The formula for calculating the equivalent curvature ratio is: κ_e = S(e) / (π·R(e)²). The equivalent curvature ratio reflects the degree to which the profile approximates a standard circle. For a perfect circle, κ_e... _e =1; for irregular shapes, κ =1; for irregular shapes, κ _e <1. When κ _e >τ _κ Furthermore, if the area and radius lower limits are met, it is determined to be a valid microcrystalline point. Wherein, τ _κ The equivalent curvature ratio threshold is preferably 0.6 in this invention. The lower limits for area and radius are determined based on the reference width and the size of the microcrystal point. For example, when the reference width is 300 pixels, the lower limit for area is 5 pixels and the lower limit for radius is 1 pixel.

[0068] Extract the center coordinates of all effective microcrystal points and calculate the average characteristic radius μ. _R The average feature radius is an important parameter for determining the clustering window size and receptive field size in subsequent steps.

[0069] S3': Reading Mesh Reconstruction and Virtual Anchor Point Compensation

[0070] This step is the core of the reverse decoding stage, and its goal is to reconstruct an Ψ×Ψ regular read grid from discrete feature point coordinates. This invention uses a one-dimensional projection clustering method for initial grid reconstruction and solves the dimension loss problem through a virtual anchor point compensation mechanism.

[0071] First, project the center coordinates of all effective microcrystal points one-dimensionally onto the X and Y axes, and count the number of projected points at each pixel location. The position of the projection peak corresponds to the row and column coordinates of the grid.

[0072] Then, at 1.5μ _RThe clustering window is used to cluster the projected peaks. The clustering window size is chosen to be 1.5 times the average feature radius to group projected peaks belonging to the same row and column together, while avoiding confusion between peaks in adjacent rows and columns. After clustering, the initial row coordinate vector V is obtained. _row and column coordinate vector V _col .

[0073] Due to printing wear and scratches, some feature points in rows and columns may be completely lost, causing the dimension of the initial row and column coordinate vector to be less than Ψ. To address this issue, this invention proposes a virtual anchor point compensation mechanism. The specific implementation steps are: calculating the average spacing gradient ▽ of the current coordinate vector. _avg =(1 / (ψ _curr ))·Σ(V[k]-V[k-1]), where ψ _curr V represents the current dimension, and V is the coordinate vector. The average spacing gradient reflects the average distance between grid rows and columns.

[0074] Using the average spacing gradient as the step size, linear extrapolate from the last valid coordinate to fill in all missing coordinates, so that the final dimension is strictly equal to Ψ.

[0075] If the current dimension is less than 2 (i.e., there is only one or zero valid coordinates), then use 2μ _R Extrapolate to ensure a minimum step size.

[0076] The virtual anchor point compensation mechanism utilizes the prior knowledge of the uniform distribution of the microcrystalline array mesh and infers the missing coordinates from the existing valid coordinates. It can accurately reconstruct the complete reading mesh even when up to 20% of the points are missing.

[0077] S4': Boolean Matrix Restoration and Parallel Decoding

[0078] At each intersection (V) of the reconstructed Ψ×Ψ grid _row[i] V _col[j] At point ), establish a side with a length of 2μ _R A square sampling window is used. The activation rate Φ is calculated as the ratio of the number of foreground pixels within the window to the total number of pixels in the window. _act When Φ _act >τ _act When τ is selected, the grid bit is determined to be 1; otherwise, it is 0. _act The activation rate threshold is preferably 0.1 in this invention. This local receptive field confidence sampling method effectively resists the effects of local noise and point ambiguity, reconstructing an accurate Boolean matrix M'.

[0079] To achieve rotation-invariant decoding across all angles, this invention employs an orthogonal multidimensional phase space parallel parsing architecture. Since the microcrystalline array is square, its rotational symmetry determines that only four directions—0°, 90°, 180°, and 270°—are rotationally invariant. Therefore, an orthogonal phase set Θ = {0°, 90°, 180°, 270°} is constructed, and multiple threads are initiated to execute steps S1' to S4' in parallel. Once any phase successfully passes error correction verification (e.g., RS verification is successful), other threads are terminated and the result is output. This parallel parsing method avoids the computational overhead of attempting rotations angle by angle, significantly improving decoding efficiency.

[0080] This method, as a highly concealed and robust information encoding and decoding technology, can be widely applied in fields such as product anti-counterfeiting, brand traceability, and electronic ticketing. A typical application is the "Invisible Anti-counterfeiting Labeling System for Product Packaging." In this system, this method encodes the product's unique identifier (such as serial number or production batch) into an anchorless microcrystalline array and prints it on the product packaging. Consumers use a mobile app to photograph the array, and the reverse decoding module of this method can quickly restore the identifier, thus verifying authenticity. Since it eliminates the need for traditional locators, this label can be perfectly integrated into the packaging design, while also possessing excellent wear and rotation resistance.

[0081] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method, characterized in that, Includes the following steps: Forward encoding: Receive dynamic payload data, generate codewords containing error correction redundancy according to the target array dimension, and map the codewords to a discrete microcrystal array without fixed location symbols; Reverse decoding: The acquired microcrystalline array image is preprocessed and effective feature points are extracted. The reading grid is reconstructed based on the spatial distribution of the feature points. The data is restored based on the reconstructed grid and error correction verification is performed.

2. The high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method as described in claim 1, characterized in that, The forward encoding stage specifically includes: S1: Adaptively calculate the total capacity, effective capacity, and error correction redundancy based on the target microcrystal array order Ψ; S2: The payload data is encoded using error correction to generate codewords and then serialized into a binary bit stream; S3: Convert the bitstream into a Boolean matrix, apply non-zero features to avoid constraints, and then generate a microcrystalline array.

3. The high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method as described in claim 2, characterized in that, The adaptive calculation in step S1 specifically refers to: Total bit capacity: ; Byte-aligned effective capacity: ; Code length: ; Adaptive error correction redundancy: ; Effective payload bytes: .

4. The high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method as described in claim 2, characterized in that, The non-zero feature avoidance constraint mentioned in step S3 is as follows: for each row of the Boolean matrix, if all elements in a row are 0, then a logic 1 is set at a preset position in that row.

5. The high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method as described in claim 4, characterized in that, The preset position is the last column of the row.

6. The high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method as described in claim 1, characterized in that, The reverse decoding stage specifically includes: S1': Normalize and perform multi-level nonlinear filtering on the acquired image to obtain a binarized feature image; S2': The set of coordinates of effective microcrystal points extracted from the binarized feature image; S3': Reconstructing the reading grid of Ψ×Ψ based on the coordinate distribution of effective microcrystal points; S4': Reconstruct the Boolean matrix from the read grid and decode to obtain the original data.

7. The high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method as described in claim 6, characterized in that, The reconstruction of the reading mesh described in step S3' is specifically as follows: the effective microcrystal points are subjected to one-dimensional projection clustering on the orthogonal bi-axis to obtain the initial row and column coordinate vectors; if a dimension is missing, the virtual anchor point compensation mechanism is triggered to fill in the missing coordinates so that the final mesh dimension is strictly equal to Ψ×Ψ.

8. The high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method as described in claim 7, characterized in that, The virtual anchor point compensation mechanism is as follows: calculate the average spacing gradient of the current coordinate vector, and use this gradient as the step size to linearly extrapolate from the last valid coordinate to fill in all missing coordinates.

9. The high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method as described in claim 6, characterized in that, Step S4' also includes: constructing a phase space containing multiple orthogonal rotation phases, starting multi-threaded decoding of images with different phases in parallel, and outputting the result once the decoding of any phase passes verification.

10. The high-dimensional fault-tolerant microcrystalline array encoding and adaptive image decoding method according to any one of claims 1 to 9, characterized in that, The target microcrystal array has an order Ψ>6, and the error correction coding adopts Galois domain polynomial error correction coding.

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