Sub-pixel edge positioning method based on conversion intensity and stable edge domain

Abstract

The application provides a sub-pixel edge positioning method based on conversion intensity and stable edge domain, comprising: S101, performing edge detection on an original image to obtain an edge detection result; S102, traversing each edge pixel based on the edge detection result to determine whether each edge pixel is in a current stable edge domain; S103, if the edge pixel is not in the current stable edge domain, obtaining a stable discrete direction sequence of the edge pixel, expanding the discrete direction sequence along a tangent direction to obtain an expansion result; S104, updating the current stable edge domain based on the expansion result to obtain an updated stable edge domain, repeating steps S102-S104 to obtain a standard stable edge domain; S105, solving effective statistical parameters in the standard stable edge domain; and S106, performing calculation based on a conversion relationship between the statistical parameters and an integral of an edge intensity curve and a step function under a continuous space to obtain a sub-pixel coordinate. The method improves positioning precision on the basis of improving operation efficiency.

Description

Technical Field

[0001] This invention relates to the field of electronic information technology, and in particular to a sub-pixel edge localization method based on conversion intensity and stable edge domain. Background Technology

[0002] Edge detection is a fundamental research area in image processing, serving as an essential processing task for advanced tasks such as object detection and image segmentation. While edge detection methods can efficiently capture edge locations in images, pixel-level detection accuracy is insufficient for high-precision applications such as industrial inspection, remote sensing, and medical imaging. Therefore, researchers have extended edge detection to the sub-pixel level to achieve higher-precision edge localization.

[0003] Traditional subpixel edge detection methods can be categorized into three types: moment-based, interpolation-based, and fitting-based methods. Moment-based methods primarily construct a series of high-order moment features to obtain subpixel coordinates. Interpolation-based methods interpolate the intensity function or derivative function satisfied by edge pixels along the gradient direction to increase edge information and achieve accurate localization. Fitting-based methods assume that the edge intensity or gradient change curve satisfies a certain functional model, and then use the least squares method to obtain the subpixel coordinates from the fitted curve.

[0004] The highest-precision methods currently available require long runtimes, making it difficult to simultaneously improve accuracy and efficiency. Furthermore, existing technologies are often limited to accurately locating individual edge points without considering the correlation between points, resulting in low robustness of edge localization. Summary of the Invention

[0005] In view of this, the present invention provides a sub-pixel edge localization method based on conversion intensity and stable edge domain to solve the above problems.

[0006] This invention provides a sub-pixel edge localization method based on conversion intensity and stable edge domain, comprising: S101, performing edge detection on the original image to obtain edge detection results; S102, traversing each edge pixel based on the edge detection results, and determining whether each edge pixel is within the current stable edge domain; S103, if the edge pixel is not within the current stable edge domain, obtaining the stable discrete direction sequence of the edge pixel, and extending the discrete direction sequence along the tangent direction to obtain an extension result; S104, updating the current stable edge domain based on the extension result to obtain an updated stable edge domain, repeating steps S102-S104, determining whether the next edge pixel is within the updated stable edge domain, and continuously updating the stable edge domain according to the determination result until all edge pixels are within the updated stable edge domain, and taking the currently updated stable edge domain as the standard stable edge domain; S105, solving for effective statistical parameters within the standard stable edge domain; S106, calculating the sub-pixel coordinates based on the statistical parameters and the conversion relationship between the edge intensity curve and the step function integral in continuous space.

[0007] In another implementation of the present invention, the sub-pixel edge localization method based on conversion intensity and stable edge domain further includes: using the mean intensity, relative gradient ratio and tail change as constraints in the process of expanding the discrete direction sequence along the tangential direction.

[0008] In another implementation of the present invention, the mean intensity is expressed as:

[0009]

[0010] Among them, g i Let be the intensity value of pixel i, and k be the extension length from the center point to one side.

[0011] In another implementation of the present invention, the relative gradient ratio is expressed as:

[0012]

[0013] Among them, G yi and G xi Let be the horizontal and vertical gradients of pixel i, and k be the extension length from the center point to one side.

[0014] In another implementation of the present invention, the tail-end change formula is expressed as:

[0015] Δ -k =|g -k -g -k+1 |

[0016] Δ k =|g k-g k-1 |

[0017] Where k is the extension length from the center point to one side, when Δ -k and Δ k When all values ​​are higher than a preset threshold, it indicates that the sequence is in a non-linear region. -k or Δ k When the value is below a preset threshold, it indicates that one side has entered the smooth region, so the expansion on that side is stopped until both sides of the sequence enter the smooth regions on both sides, at which point the expansion ends.

[0018] In another implementation of the present invention, the calculation of sub-pixel coordinates based on the statistical parameters and the transformation relationship between the edge intensity curve and the step function integral in continuous space includes: integrating the edge intensity within the range of (0.5, n+0.5) to obtain the sequence intensity I, with the corresponding formula as follows:

[0019]

[0020] The transformation relationship between the edge intensity curve and the step function integral is expressed as follows:

[0021]

[0022] The integral formula for the edge strength is solved based on the above equation:

[0023] I = (c - 0.5) * g a +(n+0.5-c)*g b

[0024] Subpixel edge coordinates are represented as:

[0025]

[0026] Where n is the number of sequences, f(x) is the nonlinear curve within the edge intensity curve, and the smooth region is located to the left of point a and to the right of point b, with intensities g and g respectively. a and g b c represents the subpixel edge coordinates, and the sequence intensity I and the sequence number n are obtained from the statistical parameters.

[0027] This invention presents a subpixel edge localization method based on conversion intensity and stable edge domain. Based on the principle of conversion intensity, it utilizes the mapping relationship between pixel intensity and subpixel intensity curves, and achieves efficient subpixel edge localization through the integral equivalence between nonlinear symmetric curves and step functions. Simultaneously, it leverages the statistical consistency of local edge regions and parameter correction of stable edge domains to correct statistical parameters on individual edge pixels, effectively reducing the impact of potential interference on edge localization. This improves both computational efficiency and localization accuracy. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. By reading the detailed description of the embodiments below, the advantages and benefits of the solutions will become clear to those skilled in the art. The accompanying drawings are only for illustrating preferred embodiments and are not intended to limit the present invention. In the accompanying drawings:

[0029] Figure 1 This is a schematic diagram of a sub-pixel edge localization method based on conversion intensity and stable edge domain, according to an embodiment of the present invention.

[0030] Figure 2 This is a schematic diagram of edge intensity curves at the pixel and sub-pixel levels, representing an embodiment of the present invention.

[0031] Figure 3(a) is a schematic diagram of sequence L of an embodiment of the present invention.

[0032] Figure 3(b) is a schematic diagram of the curve fitted by the pixel intensity on L according to an embodiment of the present invention.

[0033] Figure 3(c) is a schematic diagram of the subpixel edge intensity curve of L in an embodiment of the present invention.

[0034] Figure 4(a) is an integral diagram of the edge strength curve in an embodiment of the present invention.

[0035] Figure 4(b) is a schematic diagram of the integral over the step function according to an embodiment of the present invention.

[0036] Figure 5(a) is a partial image with edge regions according to an embodiment of the present invention.

[0037] Figure 5(b) is a magnified image of the edge region of an embodiment of the present invention.

[0038] Figure 5(c) is a schematic diagram of the three-dimensional edge strength curve of an embodiment of the present invention.

[0039] Figure 6This is a schematic diagram illustrating the process of obtaining a discrete direction sequence according to an embodiment of the present invention.

[0040] Figure 7 This is a schematic diagram illustrating the process of extending a discrete direction sequence along the tangential direction, according to an embodiment of the present invention.

[0041] Figure 8 This is a schematic diagram of a portion of a circular dataset according to an embodiment of the present invention.

[0042] Figure 9 This is a schematic diagram of a portion of a polyline dataset according to an embodiment of the present invention.

[0043] Figure 10 This is a schematic diagram of the experimental results of anti-inter-edge interference according to an embodiment of the present invention.

[0044] Figure 11 This is a schematic diagram illustrating the application test results of one embodiment of the present invention in remote sensing images and medical imaging. Detailed Implementation

[0045] To enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art should fall within the protection scope of the present invention.

[0046] Figure 1 This invention provides a sub-pixel edge localization method based on conversion intensity and stable edge domain, as exemplified by... Figure 1 As shown, this embodiment mainly includes the following steps:

[0047] S101. Perform edge detection on the original image to obtain the edge detection results.

[0048] S102. Based on the edge detection results, traverse each edge pixel and determine whether each edge pixel is within the current stable edge domain.

[0049] For example, due to the spatial discreteness of real images, it is difficult to select an arbitrary upward gradient direction. For practical application, the horizontal or vertical direction close to the gradient direction is called the discrete gradient direction. Similarly, the intensity change of the pixel sequence in the discrete gradient direction at the edge also satisfies the edge intensity curve, and it is called the discrete direction sequence.

[0050] Preferably, as shown in Figures 5(a), 5(b), and 5(c), local edge regions and associated intensity curves are given, wherein the region within the red rectangle represents the local region along the edge gradient and tangent directions, the green region covers the pixels associated with the red rectangle, the black straight line represents the edge, and the blue and purple lines represent the intensity curves along the gradient direction and the discrete gradient direction, respectively.

[0051] Meanwhile, considering the similarity between adjacent edge pixels, we give the following definition: In the local region traversed by the edge curve, each discrete direction sequence has a similar edge intensity curve. The length of the nonlinear region and the intensity value of the smooth regions on both sides can be consistent. We call this property local statistical consistency, and the local region that satisfies this property is called a stable edge region.

[0052] S103. If the edge pixel is not within the current stable edge domain, obtain the stable discrete direction sequence of the edge pixel, and extend the discrete direction sequence along the tangent direction to obtain the extension result.

[0053] For example, the specific steps to obtain the current stable edge domain are given below:

[0054] 1) Preprocessing.

[0055] 2) Obtain the initial discrete direction sequence.

[0056] 3) Extend the discrete direction sequence along the tangent direction.

[0057] During preprocessing, the Sobel algorithm is used to calculate the vertical and horizontal gradients of each pixel. Then, edge pixels are filtered based on gradient thresholding and non-maximum suppression, and the direction with the larger gradient is selected as its discrete gradient direction. Taking the edge point as the center, 2m+1 units are taken in the discrete gradient direction and 4m-1 units are taken in the other direction as the initial region (m is 3 by default). Stable edge regions will be generated within it.

[0058] Preferably, the original discrete direction sequence is obtained by extending the edge pixels to both sides of the discrete gradient direction, and the mean intensity, relative gradient ratio, and tail change are used as constraints in the extension process.

[0059] S104. Update the current stable edge domain based on the expansion result to obtain the updated stable edge domain. Repeat steps S102-S104 to determine whether the next edge pixel is in the updated stable edge domain. Update the stable edge domain continuously according to the determination result until all edge pixels are in the updated stable edge domain. Then, take the current updated stable edge domain as the standard stable edge domain.

[0060] S105. Solve for effective statistical parameters within the standard stable boundary domain.

[0061] S106. Sub-pixel coordinates are obtained by calculating based on the statistical parameters and the conversion relationship between the edge intensity curve and the step function integral in continuous space.

[0062] This invention presents a subpixel edge localization method based on conversion intensity and stable edge domain. Based on the principle of conversion intensity, it utilizes the mapping relationship between pixel intensity and subpixel intensity curves, and achieves efficient subpixel edge localization through the integral equivalence between nonlinear symmetric curves and step functions. Simultaneously, it leverages the statistical consistency of local edge regions and parameter correction of stable edge domains to correct statistical parameters on individual edge pixels, effectively reducing the impact of potential interference on edge localization. This improves both computational efficiency and localization accuracy.

[0063] In another implementation of the present invention, the sub-pixel edge localization method based on conversion intensity and stable edge domain further includes: using the mean intensity, relative gradient ratio and tail change as constraints in the process of expanding the discrete direction sequence along the tangential direction.

[0064] In another implementation of the present invention, the mean intensity is expressed as:

[0065]

[0066] Among them, g i Let be the intensity value of pixel i, and k be the extension length from the center point to one side.

[0067] For example, since the edge intensity curve is symmetrical, the mean intensity can remain stable, and the corresponding formula is as follows:

[0068]

[0069] Among them, g i Let be the intensity value of pixel i, and k be the extension length from the center point to one side.

[0070] In another implementation of the present invention, the relative gradient ratio is expressed as:

[0071]

[0072] Among them, G yi and G xi Let be the horizontal and vertical gradients of pixel i, and k be the extension length from the center point to one side.

[0073] For example, the gradient curves of this sequence also satisfy symmetry. For each pixel in the sequence, the average gradient in both directions should also remain stable. The directional stability of the sequence is described by the relative gradient ratio, and the corresponding formula is as follows:

[0074]

[0075] Among them, G yi and G xi Let i be the horizontal and vertical gradients of pixel i.

[0076] It should be understood that, during the extension to both sides, if the calculated values ​​of the above two constraints can remain basically constant, then the current region is within a stable discrete direction sequence and can be further extended; otherwise, it is considered that there is some interference in the current region, and no further calculations will be performed on that point.

[0077] In another implementation of the present invention, the tail-end change formula is expressed as:

[0078] Δ -k =|g -k -g -k+1 |

[0079] Δ k =|g k -g k-1 |

[0080] Where k is the extension length from the center point to one side, when Δ -k and Δ k When all values ​​are higher than a preset threshold, it indicates that the sequence is in a non-linear region. -k or Δ k When the value is below a preset threshold, it indicates that one side has entered the smooth region, so the expansion on that side is stopped until both sides of the sequence enter the smooth regions on both sides, at which point the expansion ends.

[0081] For example, using tail-end changes as the criterion for terminating the expansion, the formula is as follows:

[0082] Δ -k =|g -k -g -k+1 |

[0083] Δ k =|g k -g k-1 |

[0084] It should be understood that when Δ -k and Δ k When both Δ and Δ change significantly, it indicates that the sequence is in a nonlinear region; when Δ -k or Δ k When the value is below a given threshold, it indicates that one side has entered the smooth region, and the expansion on that side stops. Once the sequence has reached the smooth regions on both sides, the expansion ends. At this point, the current candidate column has contained the entire nonlinear region and is considered a stable discrete direction sequence.

[0085] like Figure 6 As shown, the process of obtaining the discrete direction sequence from pixel p0 in Figure 5(b) is given. The next step is to extend the discrete gradient sequence along the tangent direction to obtain the stable edge region of the edge pixel. At this time, the extension direction is first from the center to the left, and then from the center to the right.

[0086] It should be understood that, due to the statistical consistency of the edge region, the discrete direction sequence lengths corresponding to other edge pixels can remain unchanged during tangent extension; however, due to the various complexities that may exist in the edge environment, it is often necessary to adjust the position of the center pixel of the column to be expanded. First, the pixel with the smallest difference in the tangent direction among the edge pixels is obtained as the initial center of the expanded sequence; then, adjustments are made by observing changes at the tail end (as shown in the formula). Specifically, when Δ... -k and Δ k When the difference is large, the center pixel moves one pixel unit to the side with the larger value.

[0087] Preferably, considering the corresponding constraints in this process, the constraints are relative range and relative gradient. Given that the intensity and overall distribution of the foreground and background in the stable edge region can remain consistent, the relative range is used to evaluate the stability of the expansion process. For each candidate sequence l in the expansion process, the formula for the relative range is as follows:

[0088]

[0089] in, and Let m represent the maximum and minimum values ​​of sequence l. l This represents the mean of sequence l.

[0090] Meanwhile, local mutations and high curvature may lead to instability in the region. To address this, a constraint based on the relative gradient ratio is imposed, as shown in the formula for the relative gradient ratio. k Indicates. When r l and θ k When the changes in these changes are below their respective thresholds, the region can expand outwards. However, if any of these changes exceeds its threshold, it indicates instability or partial shift in the region, and expansion in the current direction ceases. After expansion in both directions is complete, the current region is designated as a stable edge region.

[0091] like Figure 7 As shown, it demonstrates Figure 6 The yellow sequence with K=3 expands along the tangent direction. Expansion to the left is represented by green, and expansion to the right is represented by blue.

[0092] In another implementation of the present invention, the calculation of sub-pixel coordinates based on the statistical parameters and the transformation relationship between the edge intensity curve and the step function integral in continuous space includes: integrating the edge intensity within the range of (0.5, n+0.5) to obtain the sequence intensity I, with the corresponding formula as follows:

[0093]

[0094] The transformation relationship between the edge intensity curve and the step function integral is expressed as follows:

[0095]

[0096] The integral formula for the edge strength is solved based on the above equation:

[0097] I = (c - 0.5) * g a +(n+0.5-c)*g b

[0098] Subpixel edge coordinates are represented as:

[0099]

[0100] Where n is the number of sequences, f(x) is the nonlinear curve within the edge intensity curve, and the smooth region is located to the left of point a and to the right of point b, with intensities g and g respectively. a and g b c represents the subpixel edge coordinates, and the sequence intensity I and the sequence number n are obtained from the statistical parameters.

[0101] For example, the curve satisfied by pixel intensity along the edge gradient direction is called the edge intensity curve. This curve consists of a symmetrical gradient region and smooth regions on both sides, with the x-coordinate of the center of symmetry representing the sub-pixel edge coordinates to be solved. Existing research typically treats pixel intensity as a continuous sample on the edge intensity curve, with a sampling interval of one pixel. Therefore, existing work assumes that pixel-level and sub-pixel-level intensities lie on the same curve, obtaining curve parameters by fitting the sampled intensity at the pixel location, thereby deriving the sub-pixel coordinate values. Unlike the traditional view, a new assumption is proposed: fundamentally, sub-pixel-level intensity lies on a continuous edge intensity curve, while pixel-level intensity is a local integral of this curve within a specific range, rather than a sample. Typically, for a pixel located at P, the integration interval is defined as (P-0.5, P+0.5).

[0102] Preferably, in the process of calculating sub-pixel coordinates, pixels can no longer be considered as minute units. Based on this assumption, the intensity at a pixel will not fall on the original edge intensity curve. For example... Figure 2As shown, the edge intensity curves at the pixel and sub-pixel levels can remain unchanged at the center of symmetry and smooth edges, but their variations in the non-linear region differ.

[0103] Specifically, in the gradient direction of the edge, a pixel sequence L of length n is selected. The correspondence between the intensity values ​​of this sequence at the pixel level and the sub-pixel level is shown in Figures 3(a) and 3(b). The sum of the pixel intensities from 1 to n in the sequence is equivalent to integrating the edge intensity curve over the range (0.5, n+0.5), as shown in the following formula:

[0104]

[0105] Where f(x) is a nonlinear curve within the edge intensity curve, and the smooth region is located to the left of point a and to the right of point b, with intensities g and g respectively. a and g b .

[0106] Furthermore, a step function is constructed in continuous space, with its abrupt change point located at the x-coordinate of the center of symmetry of the original curve, and the intensity on both sides remaining consistent with the original curve, as shown in Figures 3(a) and 4(b). Then, the integral of the continuous edge intensity curve between points a and b is equivalent to the integral of the step function over the same interval.

[0107] The corresponding conversion formula is as follows:

[0108]

[0109] Combining the above equation, I can be simplified to:

[0110] I = (c - 0.5) * g a +(n+0.5-c)*g b

[0111] At this point, the sub-pixel edge coordinates can be calculated as follows:

[0112]

[0113] For the above formula, the sequence intensity I and the sequence number n can be directly obtained from the corresponding gradient direction sequence. To achieve high-precision positioning, the intensity value g of the smooth regions on both sides is calculated within the stable edge region. a and g b Perform calculations to achieve greater robustness.

[0114] Specifically, pixels whose intensity falls outside the mean plus variance are divided into high-intensity and low-intensity groups. Pixels with a spatial gradient value less than 8 in these groups are extracted, and their average intensity is calculated as the initial stable intensity on both sides. During the acquisition of the stable edge region, the extent covered by the smooth regions on both sides is not required. This leads to a shift of the stable edge region to one side, resulting in lower reliability of the statistical intensity acquired on the other side. Therefore, it is difficult to simultaneously acquire the stable intensity of the smooth regions on both sides. Considering that the intensity difference between the smooth regions on both sides has a certain stability, the difference between each point in the high-intensity and low-intensity groups is first calculated, and the value with the highest frequency is selected as the stable difference. Further, the variances of the two groups are calculated. For regions with smaller variances, they are considered relatively complete smooth regions, and their initial stable intensity is used as the intensity value on that side. Subsequently, this intensity value is added to or subtracted from the stable difference to obtain the stable intensity value on the other side.

[0115] In another implementation of the present invention, to compare the positioning accuracy of different methods, a circular simulated dataset is designed. This dataset contains samples subjected to Gaussian filtering with different kernel sizes and different levels of signal-to-noise ratio (SNR), such as... Figure 8 As shown in the figure. Positioning accuracy is measured by the positioning error between the actual radius and the measured radius, where the measured radius is calculated by fitting the distance between sub-pixel points and the actual center of the circle. Table 1 shows the positioning results of different methods on a circular dataset, demonstrating that the method of this invention has higher positioning accuracy than other methods and is more robust to interference from noise and ambiguity.

[0116] The references used for comparison are as follows:

[0117] [1]Qingli LI,Shaojun Z,Zhongfu L,et al.A Improved Subpixel EdgeDetecting Algorithm Based on Polynomial Interpolation[J].Journal ofUniversity of Science and Technology Beijing,2003,25(3):280-283.

[0118] [2]Hagara M,Kulla P.Edge Detection with Sub-pixel Accuracy Based onApproximation of Edge with Erf Function[J].Radioengineering,2011,20(2):516-524.

[0119] [3]Agustín, Trujillo-Pino,Karl,et al.Accurate subpixeledge locationbased on partial area effect[J].Image&Vision Computing,2013,31(1):72-90.

[0120]

[0121]

[0122] Table 1. Accuracy Analysis Results

[0123] In another implementation of the invention, higher positioning accuracy typically leads to higher computational costs. Table 2 shows the average computation time of different methods on a circular dataset. Combined with Table 1, it can be seen that the method based on transformation intensity achieves the fastest computation speed while improving positioning accuracy; by introducing a stable edge region, it integrates more effective factors and significantly reduces positioning errors.

[0124]

[0125] Table 2. Results of computation time analysis

[0126] In another implementation of the invention, an anti-inter-edge interference experiment is used to determine whether the method can overcome the interference caused by interference between close edges. In this experiment, edge polylines with different slopes are designed as input data; a higher slope indicates more severe interference between edges. Simultaneously, a 7*7 Gaussian filter and Gaussian noise with a signal-to-noise ratio of 85 are introduced into the dataset. The dataset samples are as follows: Figure 9 As shown. Positioning error is measured using the root mean square error (RMSE). Figure 10 Based on experimental results, the method of the present invention can achieve the best positioning accuracy under various conditions and has stronger robustness than other methods.

[0127] In another implementation of the present invention, relevant images from the fields of remote sensing and medical imaging are selected for application testing. The selected images and test results are as follows: Figure 11 As shown, observe Figure 11 It is understood that the method of the present invention can achieve relatively stable and effective high-precision positioning, which can meet the application needs of high-precision fields such as remote sensing and medical imaging.

[0128] This invention presents a sub-pixel edge localization method based on conversion intensity and stable edge regions, mainly consisting of two parts: a sub-pixel edge localization method based on conversion intensity and parameter correction based on stable edge regions. Unlike traditional methods that assume pixel intensity is obtained by discrete sampling on the sub-pixel intensity curve and then obtains the original curve parameters by fitting the pixel intensity to achieve accurate localization, this application delves into the correspondence between pixel intensity and sub-pixel intensity curves, deducing a local integral mapping relationship between them. Through the integral equivalence between nonlinear symmetric curves and step functions, a concise sub-pixel edge localization method is derived. Experiments demonstrate that this sub-pixel edge localization method significantly improves computational efficiency while achieving performance comparable to the current best algorithms. Furthermore, this paper proposes parameter correction based on stable edge regions, leveraging the statistical consistency of local edge regions, to strengthen the correlation between edge points and effectively reduce the impact of potential interference on edge localization. Experiments show that introducing parameter correction based on stable edge regions yields more robust model parameters, thereby achieving more accurate sub-pixel edge localization.

[0129] Specific embodiments of the invention have now been described. Other embodiments are within the scope of the appended claims. In some cases, the actions described in the claims can be performed in a different order and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing can be advantageous.

[0130] It should be noted that all directional indicators (such as up, down, left, right, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicator will also change accordingly.

[0131] In the description of this invention, the terms "first" and "second" are used only for convenience in describing different components or names, and should not be construed as indicating or implying a sequential relationship, relative importance, or implicitly specifying the number of technical features indicated. Thus, a feature defined with "first" and "second" may explicitly or implicitly include at least one of that feature.

[0132] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0133] It should be noted that although specific embodiments of the present invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of the present invention. Various modifications and variations that can be made by those skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of the present invention.

[0134] The examples of the embodiments of the present invention are intended to concisely illustrate the technical features of the embodiments of the present invention, so that those skilled in the art can intuitively understand the technical features of the embodiments of the present invention, and are not intended to be an improper limitation of the embodiments of the present invention.

[0135] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A sub-pixel edge localization method based on conversion intensity and stable edge domain, characterized in that, include: S101. Perform edge detection on the original image to obtain the edge detection results; S102. Based on the edge detection results, traverse each edge pixel and determine whether each edge pixel is within the current stable edge region. S103. If the edge pixel is not within the current stable edge domain, obtain the stable discrete direction sequence of the edge pixel, extend the discrete direction sequence along the tangent direction to obtain the extension result; use the mean intensity, relative gradient ratio and tail change as constraints in the process of extending the discrete direction sequence along the tangent direction. S104. Update the current stable edge domain based on the expansion result to obtain the updated stable edge domain. Repeat steps S102-S104 to determine whether the next edge pixel is in the updated stable edge domain. Update the stable edge domain continuously according to the determination result until all edge pixels are in the updated stable edge domain. Then, take the current updated stable edge domain as the standard stable edge domain. S105. Solve for effective statistical parameters within the standard stable edge domain; S106. Calculate the sub-pixel coordinates based on the statistical parameters and the conversion relationship between the edge intensity curve and the step function integral in continuous space; The sub-pixel coordinates are calculated based on the statistical parameters and the transformation relationship between the edge intensity curve and the step function integral in continuous space, including: Integrating the edge intensity over the range (0.5, n+0.5) yields the sequence intensity I, as shown in the following formula: The transformation relationship between the edge intensity curve and the step function integral is expressed as follows: The integral formula for the edge strength is solved based on the above equation: Subpixel edge coordinates are represented as: Where n is the number of sequences. The curve is a nonlinear curve within the edge intensity curve. The smooth region is located to the left of point a and to the right of point b, with intensities g and g, respectively. a and g b c represents the subpixel edge coordinates, and the sequence intensity I and the sequence number n are obtained from the statistical parameters.

2. The method according to claim 1, characterized in that, The average intensity is expressed as: Among them, g i Let be the intensity value of pixel i, and k be the extension length from the center point to one side.

3. The method according to claim 1, characterized in that, The relative gradient ratio is expressed as: Among them, G yi and G xi Let be the horizontal and vertical gradients of pixel i, and k be the extension length from the center point to one side.

4. The method according to claim 1, characterized in that, The formula for the change at the tail end is expressed as follows: Where k is the extension length from the center point to one side, when and When all values ​​are higher than a preset threshold, it indicates that the sequence is in a non-linear region. or When the value is below a preset threshold, it indicates that one side has entered the smooth region, so the expansion on that side is stopped until both sides of the sequence enter the smooth regions on both sides, at which point the expansion ends.

Images