Binary Feature Description of 3D Point Cloud Based on Retina-like Sampling on Projection Planes

: A binary feature description and registration algorithm for a 3D point cloud based on retina-like sampling on projection planes (RSPP) are proposed in this paper. The algorithm ﬁrst projects the point cloud within the support radius around the key point to the XY, YZ, and XZ planes of the Local Reference Frame (LRF) and performs retina-like sampling on the projection plane. Then, the binarized Gaussian density weight values at the sampling points are calculated and encoded to obtain the RSPP descriptor. Finally, rough registration of point clouds is performed based on the RSPP descriptor, and the RANSAC algorithm is used to optimize the registration results. The performance of the proposed algorithm is tested on public point cloud datasets. The test results show that the RSPP-based point cloud registration algorithm has a good registration effect under no noise, 0.25 mr, and 0.5 mr Gaussian noise. The experimental results verify the correctness and robustness of the proposed registration method, which can provide theoretical and technical support for the 3D point cloud registration application.


Introduction
In recent years, with the rapid development of three-dimensional (3D) point cloud sensor hardware, point cloud data has been widely used in unmanned driving [1], intelligent robot [2], surveying and mapping [3], remote sensing [4], and virtual reality [5]. Point cloud registration is a fundamental problem in 3D computer vision and photogrammetry. Given two groups of point clouds with overlapping information, the aim of registration is to find the transformation that best aligns the two groups of point clouds to the same coordinate system [6,7]. Point cloud registration plays a significant role in the above point cloud applications. Point cloud registration is generally achieved by matching point cloud feature descriptors. Although significant progress has been made in point cloud feature description and registration, several problems, such as sensitivity to noise [8] and large storage memory [9], still require further study. The measured point cloud usually contains much noise, and the memory of the mobile hardware platform is often limited. Therefore, it is urgent to develop a point cloud feature description and registration algorithm that is robust to noise and occupies less memory, which is of great significance to the practical application of the point cloud registration algorithm. Retina-like sampling has been successfully applied in the field of image registration, reducing the impact of the image registration algorithm on noise and improving image registration accuracy [10]. Inspired by this, this paper attempts to explore whether the retina-like sampling can improve point cloud registration accuracy. Binary feature descriptors have less memory than floatingpoint feature descriptors [11]. Therefore, to reduce the sensitivity of the cloud registration algorithm to noise, reduce descriptor storage memory and improve algorithm accuracy, combining the retina-like sampling technology and binary feature idea, this paper proposes a binary feature description and registration method based on retina-like sampling on projection planes according to the structural characteristics of the common 3D point cloud.

Binary Feature of Retina-like Sampling on Projection Planes
The binary feature description process of retina-like sampling on the projection planes is shown in Figure 1. Firstly, the key points are detected from the input point cloud. Secondly, the LRF is constructed at key points. Then, all points within the support radius are projected onto the XY, YZ, and XZ planes, retina-like sampling is performed on the projection planes, and the Gaussian density weight values at the sampling points are calculated. Finally, the weight values are binarized and encoded to form the RSPP feature descriptor.
[23] makes up for the limitations of LoVS on scale variation. Further based on LoVS features, Voxel-based Buffer-weighted Binary Descriptor (VBBD) [24] enhances the robustness of feature descriptors to boundary effects and density variations by introducing a Gaussian kernel function. Divisional Local Feature Statistics(DLFS) [25] divides a local space into several partitions along the projected radial direction and then performs statistics of one spatial and three geometric properties for each partition. Local Angle Statistics Histogram (LASH) [26] forms a description of local shape geometry by encoding its attribute as the angle between the normal vector of the point and the vector formed by the point and other points in its local neighborhood. Kernel Density Descriptor (KDD) [27] encodes information about the entire 3D space around feature points through kernel density estimation. Grid Normals Deviation Angles Statistics (GNDAS) [28] firstly divides the local surface into several grids evenly along the x-axis and y-axis of the LRF and then counts the deviation angle of the normal at grid points.

Binary Feature of Retina-Like Sampling on Projection Planes
The binary feature description process of retina-like sampling on the projection planes is shown in Figure 1. Firstly, the key points are detected from the input point cloud. Secondly, the LRF is constructed at key points. Then, all points within the support radius are projected onto the XY, YZ, and XZ planes, retina-like sampling is performed on the projection planes, and the Gaussian density weight values at the sampling points are calculated. Finally, the weight values are binarized and encoded to form the RSPP feature descriptor.

Key Points Detection
Key point detection is a basic and important step in point cloud registration. A key point detector has at least two requirements: high repeatability and good discrimination. At present, the widely used key point detectors include Harris 3D [29], 3D SURF [30], NARF [31], ISS [32], etc. Due to the good repeatability and high computational efficiency of the ISS key point detector [17], this paper selects the ISS key point detector. The specific process of ISS is as follows: (1) Assuming P is the input point cloud, an LRF is established for each point p i , and a search radius search r is set for all points;

Key Points Detection
Key point detection is a basic and important step in point cloud registration. A key point detector has at least two requirements: high repeatability and good discrimination. At present, the widely used key point detectors include Harris 3D [29], 3D SURF [30], NARF [31], ISS [32], etc. Due to the good repeatability and high computational efficiency of the ISS key point detector [17], this paper selects the ISS key point detector. The specific process of ISS is as follows: (1) Assuming P is the input point cloud, an LRF is established for each point p i , and a search radius r search is set for all points; (2) Determine all points in the area with p i as the center and r search as the search radius, and calculate the weight w ij of these points, whose expression is as follows: (3) Establish the covariance matrix cov(p i ) of p i : Machines 2022, 10, 984 4 of 16 (4) The eigenvalues of covariance matrix cov(p i ) are solved and arranged as λ 1 i , λ 2 i , λ 3 i from large to small, (5) Set the thresholds ε 1 and ε 2 , and select the p i point satisfying λ 2 i /λ 1 i < ε 1 and λ 3 i /λ 2 i < ε 2 as the key point

LRF Construction
A unique and stable LRF plays an essential role in the accuracy and stability of feature matching. Suppose p i is a key point in the input point cloud P, and the point set in the sphere with p i as the center and radius r LRF is defined as where q ij is other points around p i , and q ij − p i is the Euclidean distance between q ij and p i . Similar to reference [15], the distance weight covariance matrix Cov of feature points and neighborhood points are used to construct the LRF, and the matrix Cov is defined as follows: The eigenvalue decomposition is performed on matrix Cov. The eigenvector corresponding to the minimum eigenvalue is the normal vector n(p i ) at the key point, and the eigenvector corresponding to the maximum eigenvalue is the candidate X-axis direction X cand of the LRF. Since the direction of the feature vector has symbol uncertainty, the symbol ambiguity is eliminated by the following methods: Then, the constructed LRF is:

RSPP Descriptor
Some studies have shown that retina-like sampling has many successful cases in image feature matching, such as BRISK [33], FREAK [10], and DAISY [34]. These cases show that retina-like sampling can improve the accuracy of image registration. The original intention of this paper is to apply the idea of retina-like sampling to point cloud registration and explore its potential in improving the accuracy of point cloud registration. Therefore, a point cloud feature extraction method based on retina-like sampling on the projection plane is proposed in this paper, as shown in Figure 2. Firstly, all local points within a sphere of radius R centered on the key point are acquired in 3D space, as shown in Figure 2a. Secondly, the local point cloud is projected onto the XY, YZ, and XZ planes of the LRF, and the retina-like sampling points centered on the key point are established on each projection plane, as shown in Figure 2b. Then, we calculate and accumulate the Gaussian density weights of all points within the sampling radius to the feature sampling point, binarize the weight sum according to whether it is greater than the weight threshold and arrange the binarized weight sum of all feature sampling points in a fixed order to form a sub binary feature histogram, as shown in Figure 2c. Finally, the sub binary feature histograms of different projection planes are merged into the fused feature histogram, as shown in Figure 2d.
Gaussian density weights of all points within the sampling radius to the feature samplin point, binarize the weight sum according to whether it is greater than the weight threshol and arrange the binarized weight sum of all feature sampling points in a fixed order t form a sub binary feature histogram, as shown in Figure 2c. Finally, the sub binary featur histograms of different projection planes are merged into the fused feature histogram, a shown in Figure 2d. The schematic diagram of the retina-like sampling mode designed in this paper shown in Figure 3. The schematic diagram of the retina-like sampling mode designed in this paper is shown in Figure 3.  In Figure 3, the blue dot represents the sampling point, the red circle repre sampling area, the radius of the sampling circle of the same layer is the same, radius from the inside to the outside is 0 1 , , , n h h h ; the distance between the cen sampling circle of the same layer and the origin of the local coordinate system is t and the distance from the inside to the outside is 1 , , n r r ; n is the number of the sampling circle; The number of sampling circles in each layer is 0 It is assumed that for a specific sampling point p si , the point set in the cir In Figure 3, the blue dot represents the sampling point, the red circle represents the sampling area, the radius of the sampling circle of the same layer is the same, and the radius from the inside to the outside is h 0 , h 1 , . . . , h n ; the distance between the center of the sampling circle of the same layer and the origin of the local coordinate system is the same, and the distance from the inside to the outside is r 1 , . . . , r n ; n is the number of layers of the sampling circle; The number of sampling circles in each layer is N 0 , N 1 , . . . , N n and N 0 = 1.
It is assumed that for a specific sampling point p si , the point set in the circle with the sampling radius of h s is defined as C si = q sij , q sij − p si < h s . It is believed that each point in the sampling area impacts the feature description of the sampling point p si . The impact is represented by the sum of Gaussian density weights in this paper, as shown in the following formula: where σ s represents the sampling standard deviation, let σ s = h s /3 in this paper, and m si represents the number of points in the sampling area.
In order to enhance the robustness of feature description and improve the speed of feature matching, the weight sum is binarized, as shown in the following formula: The binary Gaussian density weight sum of the sampling points in each projection plane is arranged in a clockwise order from the inside out to obtain three sub binary histograms, and the three sub binary histograms are spliced to form a fused feature histogram.

Feature Matching
Suppose P s and P t represent the source point cloud and the target point cloud, respectively, their corresponding key point sets are {P s 1 , P s 2 , · · · , P s n } and P t 1 , P t 2 , · · · , P t m , and the corresponding feature descriptors of the key point sets are {f s In order to register the source point cloud and the target point cloud, the Hamming distance is used to describe the similarity between the two descriptors. Find the nearest feature descriptor through the following formula for the descriptor f s i of a key point in the source point cloud.
where H(·) represents the Hamming distance.
The corresponding matching key point pair P s i , P t j can be obtained through the descriptor matching point pair f s i , f t j . Since there will inevitably be mismatches in the registered key point pairs, to improve the registration accuracy, the Hamming distances of the descriptor matching pairs of all key points are sorted increasingly, and the smallest Kpairs of matching pairs are selected as the input of RANSAC to estimate the transformation matrix between two clouds finally.

Point Cloud Dataset
In order to prove the feasibility of the point cloud feature description and matching method based on retina-like sampling proposed in this paper, the commonly used Stanford 3D Scanning Repository [35][36][37][38] is selected as the input point cloud for algorithm verification. Most Stanford models in the Stanford 3D Scanning Repository are scanned with a Cyberware 3030 MS scanner. The Stanford models used in this paper include Stanford Bunny, Happy Buddha, Dragon, and Armadillo, as shown in Figure 4.

Evaluation Criteria
Recall vs. 1-Precision Curve (RP Curve) is widely used to evaluate the performance of point cloud feature descriptors [11,15,16]. Therefore, to quantitatively evaluate the performance of the proposed RSPP feature description and matching method, the RP curve is also adopted in this paper.

Point Cloud Dataset
In order to prove the feasibility of the point cloud feature description and matching method based on retina-like sampling proposed in this paper, the commonly used Stanford 3D Scanning Repository [35][36][37][38] is selected as the input point cloud for algorithm verification. Most Stanford models in the Stanford 3D Scanning Repository are scanned with a Cyberware 3030 MS scanner. The Stanford models used in this paper include Stanford Bunny, Happy Buddha, Dragon, and Armadillo, as shown in Figure 4.
where No. of represents "the number of". At the same time, to quantitatively evaluate the registration algorithm's accuracy, the registration accuracy index is used and defined as follows: In order to evaluate whether a pair of registration points p i , p j is correct, the root mean square error of the distance between the two coordinate positions d rmse is used as a criterion. If d rmse is less than the distance threshold ε rmse , it is a correct match; Otherwise, it is a wrong match. The d rmse is defined as follows: Machines 2022, 10, 984 8 of 16 where T i2j represents the real coordinate transformation matrix between two clouds. To sum up, the evaluation indicators used in this paper include the RP curve and accuracy. The larger the area under the RP curve and the higher the accuracy, indicating that the better the registration result is, the better the point cloud registration algorithm's performance.

Parameter Analysis
It can be seen from the above that the variable parameters involved in the calculation process of the binary feature based on retina-like sampling on the projection planes include the support radius R, the number of sampling layers n, the number of sampling circles per layer N 0 , N 1 , . . . , N n , the radius of the sampling circle h 0 , h 1 , . . . , h n , and the distance r 0 , r 1 , . . . , r n between the center of the sampling circle and the origin of the LRF.
For the convenience of expression, let where k h represents the radius coefficient of the sampling circle, and k i r represents the distance coefficient of the center of the sampling circle.
The parameter combination of the RSPP feature descriptor will significantly affect the performance of the descriptor. For example, when the support radius is large, but the number of sampling circles per layer is small, the performance of the descriptor will be poor. When the support radius is large and the number of sampling circles per layer is also large, the noise will seriously interfere with the performance of the descriptor. Therefore, finding an optimal combination of parameters is necessary to improve the performance of descriptors. To obtain the best parameter combination, take dragon data as an example to analyze the performance of the RSPP feature descriptor under different parameter combinations.

(1) Support radius
The support radius indicates the influence ability of point clouds around key points on the RSPP feature descriptors. The larger the support radius, the better the descriptors' distinguishability, but the requirements for the repeatability of the point cloud are higher. Therefore, it is necessary to find a suitable support radius. In order to analyze the impact of different support radii on the performance of the RSPP feature descriptor, the support radius is changed, and other parameters are fixed. The specific parameter combinations are shown in Table 1, where mr represents the mesh resolution of the point cloud. The RP curves of different support radii are shown in Figure 5. It can be seen from Figure 5 that the larger the support radius, the larger the area under the RP curve, which means that the larger the support radius, the better the performance of the feature descriptor. When the support radius is 60 mr, the performance of the RSPP feature descriptor is the best. The RP curves of different support radii are shown in Figure 5.

(2) Radius of sampling circle
The sampling circle radius coefficient indicates the impact of different sampling layers around the key points on the RSPP feature descriptor. The larger the sampling circle radius coefficient, the smaller the impact of the point cloud in the outer layer on the descriptor. It means that the farther away from the key points, the smaller the impact on the descriptor. In order to analyze the influence of the sampling circle radius on the performance of the RSPP feature descriptor, the sampling circle radius is changed, and other parameters are fixed. The specific parameter combinations are shown in Table 2. The RP curves of different radii of sampling circle are shown in Figure 6. It can be seen from Figure 5 that the larger the support radius, the larger the area under the RP curve, which means that the larger the support radius, the better the performance of the feature descriptor. When the support radius is 60 mr, the performance of the RSPP feature descriptor is the best.

(2) Radius of sampling circle
The sampling circle radius coefficient indicates the impact of different sampling layers around the key points on the RSPP feature descriptor. The larger the sampling circle radius coefficient, the smaller the impact of the point cloud in the outer layer on the descriptor. It means that the farther away from the key points, the smaller the impact on the descriptor. In order to analyze the influence of the sampling circle radius on the performance of the RSPP feature descriptor, the sampling circle radius is changed, and other parameters are fixed. The specific parameter combinations are shown in Table 2. The RP curves of different radii of sampling circle are shown in Figure 6. It can be seen from Figure 6 that when the radius coefficient h k of the sampling circle is taken as 1.1 or 1.2, the performance of the RSPP feature descriptor is the best. In this paper, h k is taken as 1.2.

(3) Sampling layers
The number of sampling layers indicates the fineness of RSPP feature descriptors. It can be seen from Figure 6 that when the radius coefficient k h of the sampling circle is taken as 1.1 or 1.2, the performance of the RSPP feature descriptor is the best. In this paper, k h is taken as 1.2.

(3) Sampling layers
The number of sampling layers indicates the fineness of RSPP feature descriptors. The larger the number of sampling layers, the richer the point cloud details described by RSPP. In order to analyze the influence of the sampling layers on the performance of the RSPP feature descriptor, the number of sampling layers is changed, and other parameters are fixed. The specific parameter combinations are shown in Table 3. The RP curves of different sampling layers are shown in Figure 7.  The RP curves of different sampling layers are shown in Figure 7. It can be seen from Figure 7 that when the number of sampling layers n is 4 and 5, the performance of the RSPP feature descriptor is similar. n is taken as 5 to increase the feature description ability of the descriptor in this paper.
Based on the above analysis, the combination of parameters shown in Table 4 can better exert the performance of the RSPP feature descriptor.

Performance Analysis
To intuitively verify the performance of the proposed RSPP feature descriptor, the RSPP is compared with the commonly used point cloud feature descriptors, including 3DSC, SHOT, FPFH, TOLDI, and RCS. The performance of these feature descriptors under noiseless and noisy conditions is analyzed, respectively. In addition, to keep the test conditions consistent, the support radius of all feature descriptors is taken as 60 mr, as shown in Table 5.  It can be seen from Figure 7 that when the number of sampling layers n is 4 and 5, the performance of the RSPP feature descriptor is similar. n is taken as 5 to increase the feature description ability of the descriptor in this paper.
Based on the above analysis, the combination of parameters shown in Table 4 can better exert the performance of the RSPP feature descriptor. Table 4. Parameter combination adopted in this paper.

Performance Analysis
To intuitively verify the performance of the proposed RSPP feature descriptor, the RSPP is compared with the commonly used point cloud feature descriptors, including 3DSC, SHOT, FPFH, TOLDI, and RCS. The performance of these feature descriptors under noiseless and noisy conditions is analyzed, respectively. In addition, to keep the test conditions consistent, the support radius of all feature descriptors is taken as 60 mr, as shown in Table 5.
It can be seen from Table 5 that the binary RSPP descriptor occupies the slightest memory, which is very helpful for mobile platform applications.

(1) Performance analysis without noise
Point cloud feature extraction and matching are performed on the point cloud data of the Stanford Models without adding noise. The RP curve is shown in Figure 8. It can be seen from Table 5 that the binary RSPP descriptor occupies the slightest memory, which is very helpful for mobile platform applications.

(1) Performance analysis without noise
Point cloud feature extraction and matching are performed on the point cloud data of the Stanford Models without adding noise. The RP curve is shown in Figure 8. As can be seen from Figure 8, under noise-free conditions, the RP curve of the RSPP for the Bunny and Armadillo datasets is superior to other feature descriptors, and the RP curve of the RSPP for the Buddha and Dragon datasets is close to the RP curve of FPFH and is better than other feature descriptors.

(2) Performance analysis with noise
To compare the sensitivity of different point cloud feature descriptors to noise, the performance of different feature descriptors is tested when the Gaussian noise standard deviations are 0.25 mr and 0.5 mr, and their RP curves are shown in Figures 9 and 10, respectively. As can be seen from Figure 8, under noise-free conditions, the RP curve of the RSPP for the Bunny and Armadillo datasets is superior to other feature descriptors, and the RP curve of the RSPP for the Buddha and Dragon datasets is close to the RP curve of FPFH and is better than other feature descriptors.

(2) Performance analysis with noise
To compare the sensitivity of different point cloud feature descriptors to noise, the performance of different feature descriptors is tested when the Gaussian noise standard deviations are 0.25 mr and 0.5 mr, and their RP curves are shown in Figures 9 and 10, respectively. It can be seen from Figures 9 and 10 that under the conditions of 0.25 mr and 0.5 mr Gaussian noise, the RP curves of RSPP on the test dataset are better than other feature descriptors, indicating that RSPP has good robustness against noise.
To quantitatively evaluate the accuracy of the registration algorithm, the registration accuracy of different feature descriptors under the conditions of Figure 8 to Figure 10 is calculated, as shown in Table 6. The two top accuracy values under different datasets in the table are displayed in bold. The distance threshold ε rmse for judging whether a pair of registration points are correctly matched is 3 mr.
It can be seen from Table 6 that the proposed RSPP feature descriptor has good registration accuracy on different datasets and under different noise conditions, which verifies the accuracy and reliability of the RSPP-based point cloud registration algorithm proposed in this paper.
To intuitively show the effect of point cloud registration, Figure 11 shows  It can be seen from Figures 9 and 10 that under the conditions of 0.25 mr and 0.5 mr Gaussian noise, the RP curves of RSPP on the test dataset are better than other feature descriptors, indicating that RSPP has good robustness against noise.
To quantitatively evaluate the accuracy of the registration algorithm, the registration accuracy of different feature descriptors under the conditions of Figure 8 to Figure 10 is calculated, as shown in    It can be seen from Figure 11 that after the point cloud registration algorithm based on RSPP, the original point cloud and the registered point cloud basically coincide. Furthermore, even in the case of partial data missing and a low point cloud coincidence rate, a good registration effect can still be achieved, which intuitively verifies the performance of the registration algorithm based on the RSPP proposed in this paper. It can be seen from Figure 11 that after the point cloud registration algorithm based on RSPP, the original point cloud and the registered point cloud basically coincide. Furthermore, even in the case of partial data missing and a low point cloud coincidence rate, a good registration effect can still be achieved, which intuitively verifies the performance of the registration algorithm based on the RSPP proposed in this paper.

Conclusions
This paper proposes a binary feature description called RSPP and an RSPP-based 3D point cloud registration algorithm to reduce the sensitivity to point cloud noise. The primary process of feature description and registration algorithm is as follows. Firstly, the key points of the input point cloud are detected, and the corresponding LRF is established. Secondly, the point cloud within the support radius around the key point is projected to the XY, YZ, and XZ planes of the LRF, and a retina-like sampling mode is established on each projection plane. At the same time, the Gaussian density weight value at the sampling point is calculated and binarized. Then, the binary Gaussian density weight value at all sampling points is encoded to obtain the RSPP feature descriptor. Finally, coarse registration of the point cloud is performed based on the RSPP descriptor, and the RAN-

Conclusions
This paper proposes a binary feature description called RSPP and an RSPP-based 3D point cloud registration algorithm to reduce the sensitivity to point cloud noise. The primary process of feature description and registration algorithm is as follows. Firstly, the key points of the input point cloud are detected, and the corresponding LRF is established. Secondly, the point cloud within the support radius around the key point is projected to the XY, YZ, and XZ planes of the LRF, and a retina-like sampling mode is established on each projection plane. At the same time, the Gaussian density weight value at the sampling point is calculated and binarized. Then, the binary Gaussian density weight value at all sampling points is encoded to obtain the RSPP feature descriptor. Finally, coarse registration of the point cloud is performed based on the RSPP descriptor, and the RANSAC algorithm is used to optimize the registration result. The performance of the proposed algorithm is tested and verified on the public Stanford 3D Scanning Repository point cloud dataset. The results show that compared with some typical point cloud feature descriptors, the RSPP-based point cloud registration algorithm has a relatively good registration effect on the test 3D point cloud datasets under noise-free, 0.25 mr, and 0.5 mr Gaussian noise conditions. It indicates that the proposed RSPP-based point cloud registration algorithm has lower sensitivity to noise, and its overall performance is better than other comparative methods. At the same time, even in the case of partial data missing and a low point cloud coincidence rate, a good registration effect can still be achieved. Furthermore, a binary RSPP feature descriptor occupies 31 bytes of memory, which is significantly smaller than other mentioned classical descriptors and has good mobile hardware application potential. The results verify the correctness and robustness of the proposed point cloud registration method, which can provide theoretical and technical support for 3D point cloud registration applications.