Interference fringe image contrast improving method based on polynomial rooting principle
By improving the contrast of interference fringe images using the principle of polynomial root finding, the problem of low contrast caused by large optical path difference is solved, high-precision interference fringe image processing is achieved, details are enhanced and noise is suppressed, and color consistency is maintained.
Patent Information
- Application Number
- CN202511525445.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-24
- Publication Date
- 2026-02-10
AI Technical Summary
Existing coherent dispersive spectroscopy imaging devices suffer from low contrast in interference fringe images under large optical path difference conditions, which affects detection accuracy.
By employing the principle of polynomial root finding, a local polynomial model is constructed by transforming the image to a perceptually uniform brightness space, applying a nonlinear transformation function, mapping the brightness distribution to a high contrast range, and transferring color information while maintaining color consistency.
It achieves contrast enhancement with strong local adaptability, good noise suppression capability, enhanced detail and high color fidelity, thereby improving the detection accuracy of interference fringe images.
Smart Images
Figure CN121504784A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of non-contact measurement technology of unit vibration, and in particular relates to a method for improving the contrast of interference fringe images based on the principle of polynomial root finding. Background Technology
[0002] High-precision radial velocity measurement using coherent dispersive spectroscopy imaging is an excellent multi-target Doppler detection technique with great application prospects in various fields such as exoplanet exploration, equipment vibration mode monitoring, atmospheric wind field monitoring, and medical ultrasound detection. A coherent dispersive spectroscopy imaging device consists of a Michelson interferometer and a low- or medium-resolution post-dispersion module. Its effective resolution is mainly determined by the interferometer. The resolution of the dispersive coherent dispersive spectrometer is much lower than that of a traditional high-resolution echelle grating cross-dispersion spectrometer, thus providing higher light throughput. The post-dispersion module effectively creates a series of very narrow continuous bandpasses for the interferometer, thereby improving the contrast of the interference fringes. All the information needed to detect the target is contained in the phase information and contrast of the interference fringes.
[0003] The fringe phase of the interference spectrum image acquired by the detector has a direct correspondence with the center wavelength of the absorption / emission lines. When the spectral resolution is the same, a larger optical path difference results in a larger shift in the interference fringes when the target frequency changes. Therefore, increasing the optical path difference in a coherent dispersive spectroscopy imaging device is beneficial for improving the system's detection accuracy. However, to facilitate spectral extraction and meet basic noise immunity requirements, the contrast of the interference fringes output by the coherent dispersive spectroscopy imaging device should be greater than 0.15. To ensure high detection accuracy of the coherent dispersive spectroscopy imaging device, it is necessary to improve the contrast of the interference fringes while preserving the phase information through data processing. Summary of the Invention
[0004] The purpose of this application is to provide a method for improving the contrast of interference fringe images based on the principle of polynomial root finding, which solves the problem that the large optical path difference leads to excessively low contrast of interference fringe images, interfering with the detection accuracy of coherent dispersive spectroscopy imaging devices.
[0005] To achieve the above objectives, this application provides the following technical solution:
[0006] This application provides a method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding, including:
[0007] Step 1: Acquire the interference fringe image, convert the image to a perceptually uniform brightness space, and provide a basic brightness channel L;
[0008] Step 2: Transform the local brightness distribution of the image into a polynomial coefficient expression, providing a mathematical object P for the subsequent root transformation.p (z);
[0009] Step 3: Transform the static polynomial coefficient representation into a dynamic, iterable root state space;
[0010] Step 4: By applying a nonlinear transformation function, the brightness distribution of the low-contrast interference fringe image is mapped to the target range of the high-contrast interference fringe image;
[0011] Step 5: Re-decode the result after root space transformation into a new perceptual brightness map with high dynamic range;
[0012] Step 6: Perform color space transfer, and while maintaining color consistency, transfer color information from the low-contrast interference fringe image domain to the high-contrast interference fringe image domain.
[0013] As a feasible approach, interference fringe images acquired by a coherent dispersive spectroscopy imaging device are obtained. A standard brightness extraction formula is used, and gamma correction is introduced to linearize the brightness values, transforming the image into a perceptibly uniform brightness space. The formula is as follows:
[0014] Y linear = 0.2126*R + 0.7152*G + 0.0722*B
[0015]
[0016] In the formula, γ is the gamma value of approximately sRGB, and RGB represents the three dimensions of the luminance space.
[0017] As an feasible approach, the brightness value L(x,y) of each pixel in the image is considered as the root of an Nth-degree complex coefficient polynomial P(z); assuming the image has M pixels, then the degree of the polynomial N≥M;
[0018] Calculate the perceived brightness gradient map based on the Sobel operator:
[0019]
[0020] This formula is an expression based on the Sobel operator for calculating the perceived brightness gradient map;
[0021] For the center pixel p, define a 5*5 local window W(p);
[0022] Then the degree N of the adaptive polynomial p for:
[0023] N p =base N +floor(λ*avg Gradient(W(p)))
[0024] In the formula, base N Based on the number of times; avg Gradient (...) represents the average gradient value within the calculation window; λ is a hyperparameter that controls the strength of the gradient's influence on the order; floor is the floor function;
[0025] For N within window W(p) p Each pixel, brightness value The polynomial P constructed for pixel p p The roots of (z) are given by the polynomial written as:
[0026]
[0027] In the formula, This is the brightness value. The coefficient of the first term, N represents the coefficients of the polynomial. p Let Z be the number of pixels, and Z be the independent variable of the polynomial.
[0028] As an feasible approach, the first term coefficient coefficients of the polynomial Using Vieta's formulas from the root L i Calculated.
[0029] As an implementable approach, base N The value is 3, and λ is 2.2.
[0030] As a feasible approach, an iteration based on the Durand-Kerner algorithm is performed to transform the static polynomial coefficient representation into a dynamic, iterable root state space, as shown in the following iterative formula:
[0031]
[0032] In the formula, r i (k) Let P(r) be the approximate value of the k-th root after the i-th iteration. i (k) () is a polynomial, and the denominator is the product of the differences between all other roots and the currently considered root;
[0033] Using the original luminance root set As the initial value for iteration
[0034] As an feasible approach, after obtaining the perturbation root set Applying a monotonically increasing, adjustable nonlinear transformation function T(·) to the root yields a new set of roots r with expanded dynamic range.i '.
[0035] As a feasible approach, the nonlinear transformation T maps the brightness distribution [0,1] of the low-contrast interference fringe image to the target range [L] of the high-contrast interference fringe image. min HDR,L max HDR achieves expanded dynamic range and reconstructed contrast. The adaptive S-curve function formula used is as follows:
[0036]
[0037] In the formula, α represents the steepness of the control curve, β represents the center point of the control curve, and κ is an exponential factor.
[0038] As an implementable approach, through the new polynomial Q p (z) The value near the original center pixel brightness determines the brightness value of the high-contrast interference fringe image after the transformation of the center pixel p, and the new polynomial Q p The expression for (z) is:
[0039]
[0040] In the formula, Z is the unknown, and ri' (i = 1, 2, ..., N) p The result is obtained from the previous formula;
[0041] By calculating the brightness value L of the original center pixel using the new polynomial p The function value at point p is taken and scaled to obtain the new brightness value L' of the center pixel p. p :
[0042] L' p =η*|Q p (L p )|
[0043] In the formula, η is a normalization factor, and Q p (L p ) is the L obtained from the above formula. p The function value Q at that point p (z).
[0044] As an feasible approach, the color scaling method used in step 6 produces a high-contrast interference fringe image C after algorithm processing. out for:
[0045] C out =C in *(L' p / L linear )σ,C∈R,G,B
[0046] In the formula, C in L represents the original color channel values in the linear RGB color space. linear This is the linear luminance calculated using gamma values approximating sRGB; L' p σ represents the linear brightness of the reconstructed high-contrast interference fringe image; σ is a color saturation control parameter.
[0047] Compared with existing technologies, the interference fringe image contrast enhancement method based on the polynomial root-finding principle provided in this application has the following advantages:
[0048] This application exhibits excellent local adaptability and precise control. By constructing an independent polynomial model for each local window, it achieves a higher level of adaptation that is tightly coupled with the semantics of local image content (expressed through gradients). By dynamically associating local gradients with polynomial degrees, low-order polynomials are used for flat regions to smooth the image and effectively suppress noise; while high-order polynomials are used for edge and textured regions to give the model stronger expressiveness. This allows it to capture and enhance extremely subtle contrast changes and detailed structures. This mechanism enables it to excel in both maintaining the clean smoothness of flat regions and enhancing the details of textured regions.
[0049] This application features highly flexible and nonlinear dynamic range mapping. By applying a monotonically increasing nonlinear transformation function to the root space, this application achieves extremely fine and independent manipulation of different brightness ranges. It can flexibly perform appropriate compression of extremely dark areas to suppress noise and protective mapping of extremely bright areas to prevent overexposure.
[0050] This application demonstrates excellent detail enhancement and artifact suppression capabilities. Through localized modeling and transformation, it effectively avoids the negative effects of global or coarse-scale operations, resulting in a more natural transition. Since the polynomial model is built within a local neighborhood, it essentially models the spatial relationships between pixels. Therefore, its enhancement process is "informed," better able to identify and enhance true edges and textures, rather than blindly amplifying noise.
[0051] This application exhibits excellent color fidelity. It strictly adheres to the processing principle of "processing brightness first, then transferring color." Color information is transferred through proportional scaling, ensuring a controllable proportional relationship between color saturation changes and brightness changes. This maximizes the preservation of the original image's hue and color relationships, avoiding severe color cast problems. Attached Figure Description
[0052] To more clearly illustrate the technical solution of this application, the accompanying drawings used in the technical description will be briefly introduced below.
[0053] Figure 1A flowchart of the method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding provided in this application. Detailed Implementation
[0054] The following detailed description provides further details on specific implementation methods.
[0055] like Figure 1 As shown, this application provides a method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding, including:
[0056] Step 1: Acquire the interference fringe image collected by the coherent dispersive spectroscopy imaging device, and convert the image to a perceptibly uniform brightness space to provide a basic brightness channel L that conforms to the perceptual characteristics of the human eye for all subsequent processing, ensuring the perceptual naturalness of the enhancement effect.
[0057] Step 2: Transform the local brightness distribution of the image into a polynomial coefficient expression. Gradient guidance enables the algorithm to adaptively focus on detailed regions, providing the mathematical object P for the subsequent root transformation. p (z).
[0058] Step 3: Transform the static polynomial coefficient representation into a dynamic, iterable root state space. Perform one iteration based on the Durand-Kerner algorithm:
[0059]
[0060] In the formula, r i (k) P(r) represents the approximate value of the k-th root after the i-th iteration. i (k) ) denotes a polynomial, where the denominator is the product of the differences between all other roots and the currently considered root.
[0061] Step 4: By applying a nonlinear transformation function, the brightness distribution of the low-contrast interference fringe image is mapped to the target range of the high-contrast interference fringe image, thereby expanding the dynamic range and reshaping the contrast. The formula is as follows:
[0062]
[0063] In the formula, r i ' is a new set of roots with expanded dynamic range, i is the degree of the adaptive polynomial, T() is the nonlinear transformation, α is the steepness of the control curve, β is the center point of the control curve, and κ is an exponential factor.
[0064] Step 5: Decode the result after root space transformation into a new perceptual brightness map with high dynamic range to achieve high-contrast interference fringe image brightness reconstruction. The formula is as follows:
[0065]
[0066] In the formula, Z is the unknown, and ri' (i = 1, 2, ..., N) p The result is obtained from the previous formula;
[0067] Step 6: Perform color space transfer, and while maintaining color consistency, transfer color information from the low-contrast interference fringe image domain to the high-contrast interference fringe image domain.
[0068] Example
[0069] This embodiment provides a detailed description of the implementation steps of the above method. The interference fringe image contrast enhancement method based on the polynomial root-finding principle in this embodiment includes the following steps:
[0070] Step 1: Acquire the interference fringe image collected by the coherent dispersive spectroscopy imaging device, use the standard brightness extraction formula, and introduce gamma correction to linearize the brightness value, converting the image to a perceived uniform brightness space.
[0071] Y linear = 0.2126*R + 0.7152*G + 0.0722*B
[0072]
[0073] In the formula, γ is the gamma value approximating sRGB. Here, L represents the basic brightness channel that conforms to the characteristics of human eye perception, ensuring the naturalness of the enhancement effect; its value range is [0,1]. This shows the brightness distribution of the entire image after processing.
[0074] Step 2: Transform the local brightness distribution of the image into a polynomial coefficient representation. The gradient information of an image reflects the richness of detail. High gradient regions (edges, textures) require higher local contrast. Therefore, this application does not construct a global polynomial for the entire image, but rather adaptively constructs a low-order polynomial for each pixel neighborhood based on the gradient information within a local window.
[0075] Consider the brightness value L(x,y) of each pixel in the image as the root of an Nth-degree complex coefficient polynomial P(z). Assuming the image has M pixels, the degree of the polynomial is N≥M.
[0076] Calculate the perceived brightness gradient map based on the Sobel operator:
[0077]
[0078] This formula is an expression based on the Sobel operator for calculating the perceived brightness gradient map;
[0079] For the center pixel p, define a 5x5 local window W(p).
[0080] Then the degree N of the adaptive polynomial p for:
[0081] N p =base N +floor(λ*avg Gradient (W(p)))
[0082] In the formula, base N The base number of iterations is 3; avg Gradient (...) represents the average gradient value within the calculation window; λ is a hyperparameter controlling the strength of the gradient's influence on its degree, with a value of 2.2; floor is the floor function. Higher-degree polynomials are used in high-texture regions to capture more complex local brightness relationships.
[0083] For N within window W(p) p Each pixel, their brightness value The polynomial P constructed for pixel p p The roots of (z). According to the fundamental theorem of algebra, this polynomial can be written as:
[0084]
[0085] In the formula, This is the brightness value. The coefficient of the first term, N represents the coefficients of the polynomial. p Let Z be the number of pixels, and Z be the independent variable of the polynomial.
[0086] For numerical stability, assume the leading coefficient coefficients of the polynomial We can use Vieta's formulas to find the root L i It can be calculated directly.
[0087] For example, for a cubic polynomial:
[0088] P p (z)=(z-r1)(z-r2)(z-r3)=z 3 -(r1+r2+r3)z 2 +(r1r2+r1r3+r2r3)z-r1r2r3
[0089] Therefore, the coefficients are c1 = -(r1 + r2 + r3), c2 = (r1r2 + r1r3 + r2r3), and c3 = r1r2r3.
[0090] This transforms the local brightness distribution of the image into a polynomial coefficient expression. Gradient guidance enables the algorithm to adaptively focus on detailed regions, providing the mathematical object P for the subsequent root transformation. p (z).
[0091] Step 3: Perform one iteration based on the Durand-Kerner algorithm to transform the static polynomial coefficient representation into a dynamic, iterable root state space:
[0092]
[0093] In the formula, r i (k) P(r) represents the approximate value of the k-th root after the i-th iteration. i (k) ) denotes a polynomial, where the denominator is the product of the differences between all other roots and the currently considered root.
[0094] Using the original luminance root set As the initial value for iteration Ensure that the algorithm converges in the initial state.
[0095] Step 4: Map the brightness distribution of the low-contrast interference fringe image to the target area of the high-contrast interference fringe image. After obtaining the perturbation root set... Applying a monotonically increasing, adjustable nonlinear transformation function T(·) to the root yields a new set of roots r with expanded dynamic range. i In the space of polynomial roots, the distribution of brightness values is manipulated directly and explicitly. The nonlinear transformation T directly maps the brightness distribution [0,1] of the low-contrast interference fringe image to the target range [L] of the high-contrast interference fringe image. min HDR,L max HDR enables the expansion of dynamic range and the reshaping of contrast.
[0096]
[0097] In the formula, α is the steepness of the control curve (tensile strength); β is the center point of the control curve (the brightness at the center of the stretching point); and κ is an exponential factor used to fine-tune the symmetry of the curve.
[0098] Step 5: Reconstruct the brightness of the high-contrast interference fringe image. The transformed root r i ' is a new polynomial Q p Find the roots of (z). Find this new polynomial Q. p(z) Values near the original center pixel brightness are used to determine the brightness value of the high-contrast interference fringe image after the center pixel p is transformed. The result after root space transformation is then decoded into a new perceptual brightness map with high dynamic range.
[0099]
[0100] By calculating the brightness value L of the original center pixel using the new polynomial p The function value at point p is taken and scaled to obtain the new brightness value L' of the center pixel p. p .
[0101] L' p =η*|Q p (L p )|
[0102] In the formula, η is a normalization factor used to map the values to the target high-contrast interference fringe image range. Since r i 'Is Q' p The root of (z), Q p (L p The value of ) measures L p The "distance" relative to the new root set, after non-linear scaling, can well reflect the position of point p in the new dynamic range.
[0103] Step 6: Color Space Transfer of Interference Fringe Image. While maintaining color consistency, color information is transferred from the low-contrast interference fringe image domain to the high-contrast interference fringe image domain. A classic color scaling method is used:
[0104] C out =C in *(L' p / L linear )σ,C∈R,G,B
[0105] In the formula, C in It represents the original color channel values in the linear RGB color space; L linear It is a linear brightness calculated using gamma values approximating sRGB; L' p σ represents the linear brightness of the reconstructed high-contrast interference fringe image; σ is a color saturation control parameter (σ = 1.2). σ = 1 indicates strict scaling, preserving the original colors to the greatest extent; σ > 1 enhances saturation, while σ < 1 reduces saturation. C out This is the high-contrast interference fringe image obtained after algorithm processing.
[0106] This application proposes an innovative framework for converting low-contrast interference fringe images to high-contrast interference fringe images based on the inverse Durand-Kerner polynomial root-finding principle. This framework cleverly maps the image brightness distribution to a set of polynomial roots, performing a highly controllable nonlinear transformation within the root space, thereby achieving precise dynamic range expansion and contrast enhancement.
[0107] The above description is only a specific embodiment of this application, but the protection scope of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the protection scope of this application.
Claims
1. A method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding, characterized in that, include: Step 1: Acquire the interference fringe image, convert the image to a perceptually uniform brightness space, and provide a basic brightness channel; Step 2: Transform the local brightness distribution of the image into a polynomial coefficient expression to provide a mathematical object for the subsequent root transformation; Step 3: Transform the static polynomial coefficient representation into a dynamic, iterable root state space; Step 4: By applying a nonlinear transformation function, the brightness distribution of the low-contrast interference fringe image is mapped to the target range of the high-contrast interference fringe image; Step 5: Re-decode the result after root space transformation into a new perceptual brightness map with high dynamic range; Step 6: Perform color space transfer, and while maintaining color consistency, transfer color information from the low-contrast interference fringe image domain to the high-contrast interference fringe image domain.
2. The method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding as described in claim 1, characterized in that, In step 1, the interference fringe image acquired by the coherent dispersive spectroscopy imaging device is obtained. A standard brightness extraction formula is used, and gamma correction is introduced to linearize the brightness values, transforming the image into a perceptually uniform brightness space. The formula is as follows: Y linear =0.2126*R+0.7152*G+0.0722*B In the formula, γ is the gamma value of approximately sRGB, and RGB are the three dimensions of the luminance space.
3. The method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding according to claim 1, characterized in that, In step 2, the brightness value L(x,y) of each pixel in the image is regarded as the root of an Nth-degree complex coefficient polynomial P(z); assuming the image has M pixels, the degree of the polynomial N≥M; Calculate the perceived brightness gradient map based on the Sobel operator; For the center pixel p, define a 5*5 local window W(p); Then the degree N of the adaptive polynomial p for: N p =base N +floor(λ*avg Gradient (W(p))) In the formula, base N Based on the number of times; avg Gradient (...) represents the average gradient value within the calculation window; λ is a hyperparameter that controls the strength of the gradient's influence on the order of iterations; floor is the floor function. For N within window W(p) p Each pixel, brightness value The polynomial P constructed for pixel p p The roots of (z) are given by the polynomial written as: In the formula, This is the brightness value. The coefficient of the first term, N represents the coefficients of the polynomial. p Let Z be the number of pixels, and Z be the independent variable of the polynomial.
4. The method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding according to claim 3, characterized in that, First term coefficient coefficients of the polynomial Using Vieta's formulas from the root L i Calculated.
5. The method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding according to claim 3, characterized in that, base N The value is 3, and λ is 2.
2.
6. The method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding according to claim 1, characterized in that, In step 3, an iteration is performed based on the Durand-Kerner algorithm to transform the static polynomial coefficient representation into a dynamic, iterable root state space. The iterative formula is as follows: In the formula, r i (k) Let P(r) be the approximate value of the k-th root after the i-th iteration. i (k) () is a polynomial; Using the original luminance root set As the initial value for iteration 7. The method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding according to claim 1, characterized in that, In step 4, after obtaining the perturbation root set Applying a monotonically increasing, adjustable nonlinear transformation function T(·) to the root yields a new set of roots r with expanded dynamic range. i '.
8. The method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding according to claim 7, characterized in that, The nonlinear transformation T maps the brightness distribution [0,1] of the low-contrast interference fringe image to the target range [L] of the high-contrast interference fringe image. min HDR,L max HDR achieves expanded dynamic range and reconstructed contrast. The adaptive S-curve function formula used is as follows: In the formula, α represents the steepness of the control curve, β represents the center point of the control curve, and κ represents the exponential factor.
9. The method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding according to claim 8, characterized in that, Through the new polynomial Q p (z) The value near the original center pixel brightness determines the brightness value of the high-contrast interference fringe image after the transformation of the center pixel p, and the new polynomial Q p The expression for (z) is: By calculating the brightness value L of the original center pixel using the new polynomial p The function value at point p is taken and scaled to obtain the new brightness value L' of the center pixel p. p : The p =η*|Q p (L p )| In the formula, η is the normalization factor, and Q p (L p ) for L p The function value at that location.
10. The method for enhancing the contrast of interference fringe images based on the principle of polynomial root finding according to claim 1, characterized in that, The color scaling method used in step 6, after algorithm processing, yields a high-contrast interference fringe image C. out for: C out =C in *(L’ p / L linear ) σ ,C∈R,G,B In the formula, C in L represents the original color channel values in the linear RGB color space. linear This is the linear luminance calculated using gamma values approximating sRGB; L' p σ represents the linear brightness of the reconstructed high-contrast interference fringe image; σ is the color saturation control parameter.