CN104484872A - Interference image edge extending method based on directions - Google Patents
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Abstract
基于干涉图像条纹方向的边缘扩充方法，包括如下步骤：第一步：确定边界点方向：第二步：根据边缘等高线原理定义内部像素和外部像素并确定其位置：第三步：利用双线性插值确定已知像素与待填充像素的方程：第四步：根据第三步分别建立四个边界方向所有待填充像素的方程组，将方程组表示为矩阵形式，并通过求解矩阵的方法解出待填充的边缘像素值；第五步，将获得的边缘像素值填充到图像上，进行图像边缘扩充。
The edge expansion method based on the fringe direction of the interference image includes the following steps: the first step: determine the direction of the boundary point; the second step: define the inner pixel and the outer pixel according to the edge contour principle and determine their position; the third step: use the double Linear interpolation to determine the equations of the known pixels and the pixels to be filled: Step 4: Establish the equations of all pixels to be filled in the four boundary directions according to the third step, express the equations as a matrix, and solve the matrix Solve the edge pixel value to be filled; in the fifth step, fill the obtained edge pixel value on the image to expand the edge of the image.
Description
技术领域 technical field
本发明属于图像处理技术领域，具体涉及一种新的基于图像方向的干涉图像边缘扩充方法。 The invention belongs to the technical field of image processing, and in particular relates to a new image direction-based interference image edge extension method.
背景技术 Background technique
光学干涉技术提供非接触式、高精度测量，它运用在各种研究和应用领域中。干涉图像是这项技术的记录结果，为了增强精确度和鲁棒性，干涉图像需要在预处理阶段进行去噪处理。在多种干涉图像去噪技术中，在空域中基于偏微分方程的迭代和定向去噪技术是非常高效并且被广泛使用的。然而，如果使用传统的图像边缘填充，例如零填充或镜像填充，这种去噪技术会在图像边界引入误差。由于需要使用大量的迭代次数，误差将会从图像边界延伸至图像内部。为处理干涉图像边缘,一种基于迭代傅里叶变换的方法被提出来，它用向外推导干涉条纹来填充图像边界。然而，它要求干涉图像的光谱带是狭窄的，这并非在任何情况下都是成立的。由于干涉图像有干涉条纹这样的流式结构，沿着干涉条纹方向填充边界会有助于减少误差。因此，提出一种基于边缘方向的干涉图像边缘扩充。 Optical interferometry provides non-contact, high-precision measurements and is used in a variety of research and application fields. The interferometric image is the recorded result of this technique, and in order to enhance the accuracy and robustness, the interferometric image needs to be denoised in the preprocessing stage. Among various interferometric image denoising techniques, iterative and directional denoising techniques based on partial differential equations in the space domain are very efficient and widely used. However, if traditional image edge padding such as zero padding or mirror padding is used, this denoising technique introduces errors at the image boundaries. Due to the large number of iterations used, the error will extend from the image boundary to the image interior. To deal with interference image edges, a method based on iterative Fourier transform is proposed, which uses outward derived interference fringes to fill image boundaries. However, it requires that the spectral bands of the interference image be narrow, which is not true in every case. Since the interference image has a flow structure such as interference fringes, filling the boundary along the direction of the interference fringes will help reduce errors. Therefore, a kind of edge expansion of interference image based on edge direction is proposed.
发明内容 Contents of the invention
本发明要克服现有技术存在的缺点和不足，提出一种基于干涉图像条纹方向的图像边缘填充方法，包括如下基本步骤： The present invention will overcome the shortcomings and deficiencies of the prior art, and propose an image edge filling method based on the interference image fringe direction, including the following basic steps:
第一步：通过梯度方向法确定边界点方向θ(x,y),如下所示； Step 1: Determine the boundary point direction θ(x,y) by the gradient direction method, as shown below;
其中fσ是经过高斯除噪后的条纹图，fxσ和fyσ分别是fσ在x方向和y方向上的一阶偏导数。点(x,y)的方向θ(x,y)是其在周围区域[x-ε:x+ε,y-ε:y+ε,]中的方向均 值，ε表示周围区域的范围大小。 where f σ is the fringe pattern after Gaussian denoising, and f xσ and f yσ are the first-order partial derivatives of f σ in the x and y directions, respectively. The direction θ(x,y) of a point (x,y) is the mean value of its direction in the surrounding area [x-ε:x+ε,y-ε:y+ε,], and ε represents the size of the surrounding area.
第二步：根据边缘等高线原理定义内部像素和外部像素并确定其位置。对于边界像素f(x,y)，与它在同一等高线上的处于图像内部的内部像素f(xi,yi)与处于图像边界之外的外部像素f(xo,yo)可以表示为 Step 2: Define internal pixels and external pixels and determine their positions according to the principle of edge contours. For the boundary pixel f(x,y), the internal pixel f(x i ,y i ) inside the image and the external pixel f(x o ,y o ) outside the image boundary are on the same contour line It can be expressed as
f(xi,yi)＝f(xo,yo)＝f(x,y) (2) f(x i ,y i )=f(x o ,y o )=f(x,y) (2)
xi＝x-γ,yi＝y-η (3) x i ＝x-γ, y i ＝y-η (3)
xo＝x+γ,yo＝y+η (4) x o ＝x+γ, y o ＝y+η (4)
式中，γ和η分别表示内部像素和外部像素与边界像素的水平和垂直距离偏差。以外部像素为例，外部像素有以下性质： In the formula, γ and η represent the horizontal and vertical distance deviations of internal and external pixels and boundary pixels, respectively. Taking external pixels as an example, external pixels have the following properties:
ωx(x,y)γ+ωy(x,y)η＝0 (6) ω x (x,y)γ+ω y (x,y)η=0 (6)
式中，a(x,y)表示图像背景强度，b(x,y)表示振幅，表示相位，ωx(x,y)和ωy(x,y)分别表示相位在x方向和y方向上的一阶偏导数。由于方向θ(x,y)也可以被定义为: In the formula, a(x,y) represents the image background intensity, b(x,y) represents the amplitude, Represents the phase, and ω x (x,y) and ω y (x,y) represent the first-order partial derivatives of the phase in the x-direction and y-direction, respectively. Since the direction θ(x,y) can also be defined as:
θ(x,y)＝atan[ωx(x,y),-ωy(x,y)] (7) θ(x,y)=atan[ω x (x,y),-ω y (x,y)] (7)
γ和η可以用方向表示为: γ and η can be expressed in terms of directions as:
γ＝±αcosθ(x,y),η＝±αsinθ(x,y) (8) γ＝±αcosθ(x,y), η＝±αsinθ(x,y) (8)
α表示内部像素和外部像素与边界像素的距离。因为ωx(x,y)和ωy(x,y)一般未知，方向θ(x,y)由步骤一中方法求得。γ和η的正负±根据四个边界与自身的方向具有不同的定义，可以由下表确定： α represents the distance between the inner and outer pixels and the boundary pixels. Because ω x (x, y) and ω y (x, y) are generally unknown, the direction θ (x, y) is obtained by the method in step 1. The positive and negative ± of γ and η have different definitions according to the direction of the four boundaries and themselves, which can be determined by the following table:
第三步：利用双线性插值确定待填充像素方程。外部像素的双线性插值可以表示为 Step 3: Use bilinear interpolation to determine the pixel equation to be filled. Bilinear interpolation of external pixels can be expressed as
f(x+γ,y+η)≈(1-|γ|)(1-|η|)f(x,y)+|γ|(1-|η|)f[x+sign(γ),y] f(x+γ,y+η)≈(1-|γ|)(1-|η|)f(x,y)+|γ|(1-|η|)f[x+sign(γ) ,y]
+(1-|γ|)|η|f[x,y+sign(η)]+|γ||η|f[x+sign(γ),y+sign(η)] (9) +(1-|γ|)|η|f[x,y+sign(η)]+|γ||η|f[x+sign(γ),y+sign(η)] (9)
其中，当参数为正数或负数时sign取1或-1；根据不同的边界方向，f[x+sign(γ),y]与f[x+sign(γ),y+sign(η)]或者f[x,y+sign(η)]与f[x+sign(γ),y+sign(η)]是待填充的像素。f(x+γ,y+η)可以根据式(2)算得。 Among them, when the parameter is positive or negative, sign takes 1 or -1; according to different boundary directions, f[x+sign(γ),y] and f[x+sign(γ),y+sign(η) ] or f[x,y+sign(η)] and f[x+sign(γ),y+sign(η)] are the pixels to be filled. f(x+γ, y+η) can be calculated according to formula (2).
第四步：根据第三步分别建立四个边界方向所有待填充的边缘像素的方程组，将方程组表示为矩阵形式，并通过求解矩阵的方法解出待填充的边缘像素值； The fourth step: according to the third step, establish the equations of all the edge pixels to be filled in the four boundary directions, express the equations in matrix form, and solve the edge pixel values to be filled by solving the matrix;
第五步：将获得的边缘像素值填充到图像上，进行图像边缘扩充。 Step 5: Fill the obtained edge pixel values on the image to expand the edge of the image.
本发明的优点是：利用图像的现有信息进行图像变化的预测，实现更为精确的边缘填充。图像的现有信息以方向的形式巧妙简洁的表示出来。 The invention has the advantages of: using the existing information of the image to predict the change of the image and realize more accurate edge filling. The existing information of the image is cleverly and concisely expressed in the form of direction.
附图说明 Description of drawings
图1为本发明中定义的内部像素和外部像素。 Fig. 1 shows inner pixels and outer pixels defined in the present invention.
图2为本发明中涉及的等高线和图像方向。 Figure 2 shows the contour lines and image directions involved in the present invention.
图3为本发明中使用的双线性插值示意图。 Fig. 3 is a schematic diagram of bilinear interpolation used in the present invention.
图4为本发明方法结果示意图和与其他方法结果的比较示意图。 Fig. 4 is a schematic diagram of the results of the method of the present invention and a comparison diagram with the results of other methods.
具体实施方式 Detailed ways
在以下的描述中，结合附图和具体实施方法对本发明作进一步详细解释。然而，应该意识到，本发明不限于这种应用，而是可应用于许多其他类型和其他用途的图像处理中。 In the following description, the present invention is further explained in detail in conjunction with the accompanying drawings and specific implementation methods. However, it should be realized that the invention is not limited to this application, but is applicable to many other types and other uses of image processing.
本发明的基于干涉图像条纹方向的边缘扩充方法，包括如下基本步骤： The edge expansion method based on the interference image fringe direction of the present invention comprises the following basic steps:
步骤一：根据梯度方向法确定边界点方向。干涉图像可以表示为： Step 1: Determine the direction of the boundary point according to the gradient direction method. The interference image can be expressed as:
式中，f(x,y)表示像素点(x,y)像素值，a(x,y)表示图像背景强度，b(x,y)表示振幅，表示相位，n(x,y)表示加性噪声。唯一已知的只有f(x,y)。梯度法可以从带噪声的条纹图中准确地估计方向，如下所示； In the formula, f(x, y) represents the pixel value of the pixel point (x, y), a(x, y) represents the image background intensity, b(x, y) represents the amplitude, Represents the phase, and n(x,y) represents the additive noise. The only known one is f(x,y). Gradient methods can accurately estimate orientation from noisy fringe patterns as shown below;
其中fσ是经过高斯除噪后的条纹图，fxσ和fyσ分别是fσ在x方向和y方向上的一阶偏导数。点(x,y)的方向θ(x,y)是其在周围区域[x-ε:x+ε,y-ε:y+ε,]中的方向均值，ε表示周围区域的范围大小。 where f σ is the fringe pattern after Gaussian denoising, and f xσ and f yσ are the first-order partial derivatives of f σ in the x and y directions, respectively. The direction θ(x,y) of a point (x,y) is the mean value of its direction in the surrounding area [x-ε:x+ε,y-ε:y+ε,], and ε represents the size of the surrounding area.
步骤二：定义内部像素和外部像素并计算位置。如图1所示，图中的直线是通过边界点的等高线。左边的方块代表处于图像内部的内部像素，中间的方块代表边界像素，右边的方块代表处于图像边界之外的外部像素。内部像素和外部像素都是子像素。由于这三个像素位于同一等高线上，它们具有相同的像素值。对于边界像素f(x,y)，与它在同一等高线上的内部像素f(xi,yi)与外部像素f(xo,yo)可以表示为 Step 2: Define internal pixels and external pixels and calculate their positions. As shown in Figure 1, the straight lines in the figure are contour lines passing through the boundary points. Squares on the left represent interior pixels inside the image, squares in the middle represent border pixels, and squares on the right represent exterior pixels outside the border of the image. Both inner and outer pixels are sub-pixels. Since these three pixels lie on the same contour line, they have the same pixel value. For a boundary pixel f(x,y), the internal pixel f( xi ,y i ) and external pixel f(x o ,y o ) on the same contour line as it can be expressed as
f(xi,yi)＝f(xo,yo)＝f(x,y) (12) f(x i ,y i )=f(x o ,y o )=f(x,y) (12)
xi＝x-γ,yi＝y-η (13) x i = x-γ, y i = y-η (13)
xo＝x+γ,yo＝y+η (14) x o ＝x+γ, y o ＝y+η (14)
式中，γ和η分别表示内部像素和外部像素与边界像素的水平和垂直距离偏差。 In the formula, γ and η represent the horizontal and vertical distance deviations of internal and external pixels and boundary pixels, respectively.
如图2所示，是位于边界的等高线，在边界点附近区域内，可以假设a(x,y)和b(x,y)是常数，并且是线性的。因为同一等高线上的像素值相等，以外部像素为例，外部像素有以下性质： As shown in Figure 2, it is the contour line at the boundary. In the area near the boundary point, it can be assumed that a(x,y) and b(x,y) are constants, and is linear. Because the pixel values on the same contour line are equal, taking external pixels as an example, external pixels have the following properties:
ωx(x,y)γ+ωy(x,y)η＝0 (16) ω x (x, y) γ + ω y (x, y) η = 0 ( 16 )
式中ωx(x,y)和ωy(x,y)分别表示相位在x方向和y方向上的一阶偏导数。由于方向θ(x,y)也可以被定义为: where ω x (x, y) and ω y (x, y) represent the first-order partial derivatives of the phase in the x and y directions, respectively. Since the direction θ(x,y) can also be defined as:
θ(x,y)＝atan[ωx(x,y),-ωy(x,y)] (17) θ(x,y)＝atan[ω x (x,y),-ω y (x,y)] ( 1 7)
γ和η可以用方向表示为: γ and η can be expressed in terms of directions as:
γ＝±αcosθ(x,y),η＝±αsinθ(x,y) (18) γ＝±αcosθ(x,y), η＝±αsinθ(x,y) (18)
α表示内部像素和外部像素与边界像素的距离。根据实验数据表明，α取1时，获得的填充结果更佳，因此在此实施例中，α值取1。因为ωx(x,y)和ωy(x,y)一般未知，方向θ(x,y)由步骤一中方法即公式(11)求得。γ和η的正负±根据四个边界与自身的方向具有不同的定义，可以由下表确定： α represents the distance between the inner and outer pixels and the boundary pixels. According to the experimental data, when α is set to 1, the obtained filling result is better, so in this embodiment, the value of α is set to 1. Because ω x (x, y) and ω y (x, y) are generally unknown, the direction θ (x, y) is obtained by the method in step 1, namely formula (11). The positive and negative ± of γ and η have different definitions according to the direction of the four boundaries and themselves, which can be determined by the following table:
步骤三：利用双线性插值确定待填充像素值。如图3所示，左侧的方块列代表图像边界像素，中间的方块列代表外部像素，右侧的方块列代表待填充的像素。根据双线性插值，外部像素可以表示为 Step 3: Use bilinear interpolation to determine the pixel value to be filled. As shown in Figure 3, the square column on the left represents image border pixels, the middle square column represents external pixels, and the right square column represents pixels to be filled. According to bilinear interpolation, the outer pixels can be expressed as
f(x+γ,y+η)≈(1-|γ|)(1-|η|)f(x,y)+|γ|(1-|η|)f[x+sign(γ),y] f(x+γ,y+η)≈(1-|γ|)(1-|η|)f(x,y)+|γ|(1-|η|)f[x+sign(γ) ,y]
+(1-|γ|)|η|f[x,y+sign(η)]+|γ||η|f[x+sign(γ),y+sign(η)] (19) +(1-|γ|)|η|f[x,y+sign(η)]+|γ||η|f[x+sign(γ),y+sign(η)] (19)
其中，当参数为正数或负数时sign取1或-1。在式(19)中，等式左边是外部像素，它等于同一等高线上的边界像素和内部像素，是已知的。等式右边包含两个已知边界像素和两个未知的待填充像素。根据不同的边界方向，f[x+sign(γ),y]与f[x+sign(γ),y+sign(η)]或者f[x,y+sign(η)]与f[x+sign(γ),y+sign(η)]是待填充的像素。如图3所示,在相邻的外部像素的方程中,未知像素是重复出现的。对每一个外部像素都列出方程，可以得到n个方程，包含n+2个未知数，n是图 像的长或宽。可以使待填充的顶点像素等于原图的顶点像素，从而使方程与未知数相等，即可求解方程组。 Among them, sign takes 1 or -1 when the parameter is positive or negative. In Equation (19), the left side of the equation is the external pixel, which is equal to the boundary pixel and internal pixel on the same contour line, which is known. The right side of the equation contains two known boundary pixels and two unknown pixels to be filled. According to different boundary directions, f[x+sign(γ),y] and f[x+sign(γ),y+sign(η)] or f[x,y+sign(η)] and f[x +sign(γ),y+sign(η)] is the pixel to be filled. As shown in Figure 3, unknown pixels are repeated in the equations of adjacent outer pixels. List the equations for each external pixel, and you can get n equations, including n+2 unknowns, where n is the length or width of the image. The vertex pixels to be filled can be equal to the vertex pixels of the original image, so that the equations and unknowns are equal, and the equations can be solved.
步骤四：根据第三步分别建立四个方向上的方程组，将方程组表示为矩阵形式，并通过求解矩阵的方法解出待填充的边缘像素值。 Step 4: Set up equations in four directions according to the third step, express the equations in matrix form, and solve the edge pixel values to be filled by solving the matrix.
步骤五：将获得的边缘像素值填充到图像上，进行图像边缘扩充。 Step 5: Fill the obtained edge pixel values on the image to expand the edge of the image.
如图4所示，第一张图片为用本发明方法处理后的图片经过迭代降噪后的效果图，后两张分别用了零填充和镜像填充方法。可以明显观察到，用本发明方法处理后的图像经过降噪后，具有更好的效果。 As shown in Fig. 4, the first picture is the effect picture after iterative noise reduction of the picture processed by the method of the present invention, and the last two pictures use the zero filling and mirror filling methods respectively. It can be clearly observed that the image processed by the method of the present invention has a better effect after denoising.
本发明提供了一种图像边缘扩充方法的思路，具体实现该技术方案的方法和途径很多，以上所述仅是本发明的优选实施方式。应当指出，对于本技术领域的技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也应视为本发明的保护范围。 The present invention provides an idea of an image edge extension method, and there are many methods and ways to specifically realize the technical solution, and the above descriptions are only preferred implementation modes of the present invention. It should be pointed out that for those skilled in the art, some improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111370002A (en) * | 2020-02-14 | 2020-07-03 | 平安科技（深圳）有限公司 | Method and device for acquiring voice training sample, computer equipment and storage medium |
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| WO2024193305A1 (en) * | 2023-03-17 | 2024-09-26 | 山东云海国创云计算装备产业创新中心有限公司 | Image processing method, system, device, and storage medium |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105513073A (en) * | 2015-12-09 | 2016-04-20 | 浙江工业大学 | Direction-consistency-based discontinuous fringe image segmentation and boundary filling method |
| CN111370002A (en) * | 2020-02-14 | 2020-07-03 | 平安科技（深圳）有限公司 | Method and device for acquiring voice training sample, computer equipment and storage medium |
| CN112529013A (en) * | 2020-12-14 | 2021-03-19 | 北京集创北方科技股份有限公司 | Image recognition method, device, equipment and computer readable medium |
| WO2024193305A1 (en) * | 2023-03-17 | 2024-09-26 | 山东云海国创云计算装备产业创新中心有限公司 | Image processing method, system, device, and storage medium |
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