CN-116843919-B - RGB-D surface normal vector estimation method based on fractional differentiation

CN116843919BCN 116843919 BCN116843919 BCN 116843919BCN-116843919-B

Abstract

The invention discloses an RGB-D surface normal vector estimation method based on fractional differentiation, which comprises the steps of firstly converting a coordinate system of pixel points of an image, then screening neighborhood points of each point in the image, removing points with larger holes and errors, then solving algebraic expression of a solution vector by utilizing the characteristic that normal vectors are perpendicular to a plane where the pixel points are located, and finally solving by utilizing a fractional differentiation optimization gradient, thereby improving calculation accuracy of the surface normal vector.

Inventors

YUAN XIA
WU XINYI
ZHAO CHUNXIA

Assignees

南京理工大学

Dates

Publication Date: 20260512
Application Date: 20230630

Claims (5)

1. The RGB-D surface normal vector estimation method based on fractional differentiation is characterized by comprising the following steps: s1, converting a coordinate system of pixel points in an image, and converting two-dimensional pixel points in the image coordinate system into three-dimensional space points in a world coordinate system; step S2, screening neighborhood points of pixel points in the image, and removing hole points and neighborhood points with larger errors; s3, solving the normal vector of the surface of the pixel points in the image by utilizing the vertical relation between the normal vector and the plane where the pixel points are located; s4, converting the surface normal vector obtained by solving into a unit normal vector form under a spherical coordinate system; step S5, combining the definition of the image and mask convolution to construct the image The method comprises the steps of corresponding masks in negative x and y directions, and optimizing a gradient solving mode by combining fractional differentiation, wherein the method specifically comprises the following steps: Signal signal A kind of electronic device The order G-L fractional order derivative is defined as: Wherein, the Is in the range of And (2) and Is the step length; represents a gamma function defined as: for an image, the minimum scale is one pixel, so If (3) Pressing the button Divided by the difference in fractional differentiation can be expressed as: Wherein the method comprises the steps of Is calculated according to a function corresponding to the first Personal neighborhood value, for image The above extends to two dimensions, the first three terms are used to approximate the calculation, and the numerical realizations of fractional partial differentiation in the x and y directions are expressed as: By combining the definition of the image and mask convolution, one can construct both images Fractional differential corresponding mask in negative x and y directions to calculate difference between neighborhood point and current pixel point ; And step S6, traversing the depth image, and repeating the steps S2-S5 until the last pixel point of the image to obtain a complete surface normal vector result graph.
2. The method for estimating the RGB-D surface normal vector based on fractional differentiation according to claim 1, wherein the step S1 specifically comprises: For points in three-dimensional space Corresponding points in the image coordinate system The corresponding relation is as follows: Wherein K is a camera reference matrix, Is the center of the image and, And Respectively are Direction and direction The camera focal length in direction is in pixels.
3. The method for estimating the RGB-D surface normal vector based on fractional differentiation according to claim 1, wherein the step S2 specifically comprises: for any pixel point p in the image, marking 8 pixel points in the neighborhood as a set If the neighborhood point Is not 0, and Then the neighborhood pixel point is reserved Wherein Refers to one of the eight points of the neighborhood of pixel point p.
4. The method for estimating the RGB-D surface normal vector based on fractional differentiation according to claim 1, wherein the step S3 specifically comprises: For any point P in three-dimensional space The normal vector of the surface is recorded as Then there is a relationship: in combination with the relationship between the two-dimensional and three-dimensional coordinate systems, deducing: if the image is derived in the x-direction, i.e. a horizontal filter is used, the following equation can be obtained: if the y-direction derivative is applied to the image, i.e. a vertical filter, the following equation can be obtained: Combining the three formulas, the preparation method can obtain: thus, the surface normal vector is expressed as: 。
5. The method for estimating the RGB-D surface normal vector based on fractional differentiation according to claim 1, wherein the step S4 specifically comprises: The form of the usual unit normal vector is as follows: Bonding of And (3) with The expression of (2) is listed in The expression: For the following Through the 8 neighborhood of p, and the sum solution, namely, the solution is realized by using an average filter: Finally can be found The surface normal vector can be solved based on these two parameters.

Description

RGB-D surface normal vector estimation method based on fractional differentiation Technical Field The invention belongs to the field of computer vision, and particularly relates to an RGB-D surface normal vector estimation method based on fractional differentiation. Background With the widespread use of depth sensors, RGB-D data is becoming increasingly easier to acquire and apply to a wide variety of visual computing tasks. The depth image provides geometric information such as depth of field, shape, boundary and the like of a scene, and is well complementary with the RGB image, so that the scene understanding capability of the visual computing model is improved. Accordingly, research into depth information is also becoming more and more important. In the field of computer vision, image understanding is the most basic technique among them, and is also the most indispensable task link. Surface normals are a common visual feature when extracting features for semantic understanding of an image. The surface normals contain rich information and are highly interpretable and are therefore commonly used as auxiliary functions for other visual applications. The application of such auxiliary properties is often performed in an on-line manner at the front end of the overall functional framework, so that a higher accuracy and a faster speed of the calculation of the surface normals is required. The surface normal vector may be estimated from a color map, a three-dimensional point cloud, or a depth/disparity image. The color image may be implemented by a conventional method such as a photometric stereo method or a deep learning method, etc. For Lei Dadian cloud images, the obtained point cloud data is represented as a set of fixed point samples on the surface of a real object, so two solutions are generally available for solving the surface normal, namely, a curved surface reconstruction technology is adopted to obtain a curved surface corresponding to a sampling point from the obtained point cloud data set, and then the surface normal is calculated from a curved surface model, but the method has higher calculation precision but more calculation cost and time consumption, so that the surface normal is rarely adopted in practical application, and the other approach is adopted to approximate the surface normal from the point cloud data, namely, a problem of approximating the problem of solving the surface one point normal to the normal of a tangent plane of an estimated surface, namely, a least square plane fitting estimation problem is adopted, and the method is completed by solving the eigenvectors and eigenvalues of a covariance matrix created by the nearest neighbor point of an analysis query point, but also needs a large amount of calculation. Accordingly, recent studies are generally conducted on depth maps or disparity maps. Existing surface normal vector calculation methods can be generally divided into two categories, namely solving by using geometric algebra properties and solving by using deep learning neural network regression. The former is easily affected by noise of the image itself, and has strong dependence on the calculation form and the optimization mode adopted in the calculation process. The latter first requires a large number of manually labeled datasets as a basis, and training and final practice testing also requires a significant amount of time and computational cost. Disclosure of Invention The invention aims to provide a surface normal vector calculation method based on fractional differentiation. The technical scheme adopted for realizing the purpose of the invention is that the RGB-D surface normal vector estimation method based on fractional differentiation comprises the following specific steps: 1. converting a coordinate system of pixel points in the image from two-dimensional pixel points in the image coordinate system to three-dimensional space points in the world coordinate system; 2. Screening neighborhood points of pixel points in the image, and removing hole points and neighborhood points with larger errors; 3. for pixel points in an image, solving the surface normal vector of the pixel points by utilizing the perpendicular relation between the normal vector and the plane in which the pixel points are positioned 4. Converting the surface normal vector obtained by solving into a unit normal vector form under a spherical coordinate system; 5. constructing a mask corresponding to the image f (x, y) in negative x and y directions by combining the definition of the image and the mask convolution, and optimizing a gradient solving mode by combining fractional differentiation; 6. Traversing the depth image, and repeating the steps 2-5 until the last pixel point of the image to obtain a complete surface normal vector result graph. Compared with the prior art, the invention has the remarkable advantages that: (1) The problem of image noise caused by objective factors such as a camera is effe