We designed a cart-type bird’s eye perspective data acquisition equipment constructed from aluminum profiles, using a structure that reaches forward for depth camera mounting, which allows for ample movement space between the pig and the equipment. The equipment’s up aluminum boom arm is adjustable both vertically and horizontally, facilitating data collection at various heights and ranges, and includes a platform for placing a computer. Equipment includes a Microsoft Surface Book 2, an Orbbec Femto Bolt camera (TOF), and an outdoor portable battery which can supply power to the computer and camera, as illustrated in Figure 2A.

During point cloud acquisition, a resolution of 512 × 512 was utilized with a wide field of view of 120° × 120°, the camera’s optical axis was oriented vertically downwards. We collected data at three heights of 1,680, 1,780, and 1,880 mm (where height refers to the vertical distance from the camera’s protective window to the ground surface), the data stream operated at a frame rate of 30 fps, with the data acquisition program set to capture data every second. During data collection, we tried to keep the pig within the camera’s field of view as much as possible.The real situation of data collection is shown in Figure 2B.

The DPFFS algorithm was developed in the Microsoft Visual Studio 2019 using C++ programming language, employed the point cloud library (PCL) 1.11.1 version of the point cloud library and the Orbbec SDK 1.9.5 Release version. The point cloud was loaded using a K-D Tree structure to speed up the process of nearest neighbor searching. The computer configuration for the algorithm design was as follows: CPU - Intel(R) Core(TM) i5-9300H, RAM - 8.00 GB, GPU - GTX 1650, Windows 11. The algorithm did not use a deep learning network and did not require dataset training. To obtain high-density original pig body point clouds or to swiftly extract simplified point clouds with almost unchanged features, we selected three sets of voxel downsampling parameters to assess the algorithm’s execution speed. The equipment parameters involved in the experiment are presented in Table 1.

The data acquisition for this study was conducted at a fattening pig farm in Longyao, Xingtai City, Hebei Province, China. During this period, a total of 40 different Duroc x Large White crossbred pigs were selected for data collection, ranging in age from 3 to 5 months. The data collection used the push-cart equipment that followed the pigs while maintaining a distance from them. In total, 1,000 sets of polygon file format (PLY) format point clouds were collected, encompassing individuals with different ages (based on body weight) and various movement postures. Among these datasets, 13 sets were considered to be erroneous due to pig moves out of the field of view. As the exposure errors lead to severe depth information and point cloud loss, these erroneous point clouds were removed from the overall dataset, leaving 987 sets of data, sows accounted for 70%, while boars constituted 30%, with body weights ranging from a minimum of 60.0 kg to a maximum of 102.3 kg. The detailed information of the data is provided in Table 2. The postures and sizes of pig body point cloud varied, with some mixed with environmental noise, while others remained unaffected by noise interference except for ground point cloud disturbances.

In the wide field-of-view depth imaging system of a TOF camera, the spatial structure of the acquisition space presents a conical influenced by the geometric characteristics of the perspective mirror. Areas of the ground farther from the camera optical center exhibit larger X-Y plane areas, and these points tend to cluster within small segments along the Z direction. Therefore, the principle of module 1 involves slicing the point cloud continuously, tallying the number of points within each slice, and ultimately identifying slices containing peak point count as “ground noise” for removal using a pass-through filter. Previous section calculated a standardized coordinate system point cloud P, using P as input, traversing the point cloud index, obtaining the maximum value Z_max of the Z-axis, which is realistically the lowest point on the ground, defining Δ_Z = 1,000, equivalent to 1,000 mm, Z_max - Δ_Z is defined as the lower limit and Z_max as the upper limit for a spatial pass-through filter. This procedure defined a rectangular spatial region with a height of 1,000 mm and filtered out all noise points with Z values exceeding 1,000 mm. The purpose of this procedure is to eliminate non-critical areas, particularly noise points above the spatial region, thereby optimizing the spatial distribution of the point cloud data. This facilitates focusing on key features around the pig’s body and the ground for subsequent denoising modules. The target point cloud in the space region P_s is calculated by the following Equation, P_i is the point in P where the value of the Z value falls within the region of space, $$ \forall $$ P_i = (X_i, Y_i, Z_i), i represents index, from 0 to n (total number of points).

(3) $$ P_s=\bigcup_{P_i\in P}\left \{ P_i(X_i,Y_i,Z_i)|\left \{P_i\in P|Z_{\mathrm{max}}-\Delta _Z\le Z_i\le Z_{\mathrm{max}}\right \} \right \} $$

The starting and ending interval of the Z-axis for the target point cloud P_s are now [Z_max - Δ_Z, Z_max]. Within this interval, a cyclic program and pass-through filter are employed to generate slices, each with a span value D_Z of 100, corresponding to 100 mm in reality (the impact of varying D_Z values is discussed in the discussion section). Subsequently, starting from the coordinate value Z_max - Δ_Z, continuous slicing is performed along the Z-axis direction until reaching Z_max + D_Z. When the span of the last slice does not meet 100, it necessitates including some empty values in the point cloud. The following Equation (4) is utilized to calculate the number of points N within each slice.Function I is defined such that the result is 1 when the Z-axis of P_i satisfies the condition and 0 otherwise. I represents slice’s index, which can be dynamically calculated from different values of Z_max. For example if I = 3, N₃ represents the number of points in the third slice of D_Z thickness, interval is [(Z_max - Δ_Z) - (3*D_Z), (Z_max - Δ_Z) - (3*D_Z) + D_Z].

(4) $$ N_I=\sum_{i=1}^n I\left \{ P_i(X_i,Y_i,Z_i)|(Z_{\mathrm{max}}-\Delta _Z)-(I*D_Z)\le Z_i\le (Z_{\mathrm{max}}-\Delta _Z)-(I*D_Z)+D_Z \right \} $$

The number of points within each slice is tallied, resulting in a quantity distribution characteristic shown in Figure 4A, which represents the correspondence between point cloud slices and the number of points within each slice. In Figure 4B, which represents the characteristic distribution chart of point cloud quantities within one point cloud set, the number of points within a slice reaches a peak at positions closer to the ground, corresponding to larger coordinates. To validate this observation, 10 additional sets of point clouds were randomly selected, and their distribution of features exhibited a similar pattern, as shown in Figure 4C. This method can be utilized for ground point cloud localization and denoising purposes.

After obtaining the peak value, a slice with a span value D_Z is determined to contain ground noise points within the target space. The starting Z-axis value of the slice is set as d_z, calculated by the algorithm, and the ending coordinate value equal to the starting coordinate plus the span: d_z + D_Z, interval equals to [d_z, d_z + D_Z]. Considering significant noise near the ground and the limitation of small slice spans in encompassing all ground noise points, the range of the pass-through filter is further extended into [d_z - $$ \frac{D_Z}{2} $$, d_z + $$ \frac{3}{2} $$D_Z] during the actual filtering stage to enhance ground removal efficacy. This extension involves filtering out additional portions above and below the target space by $$ \frac{D_Z}{2} $$ units. The point cloud set without ground noise S₁, is obtained using the following Equation (5), where d_z is the dynamically calculated starting Z-axis value, which varies for point clouds at different heights:

(5) $$ S_1=\bigcup_{P_i\in P_s}\left \{ P_i(X_i,Y_i,Z_i)|d_z-\frac{D_Z}{2}\le Z_i\le Z_{\mathrm{max}}-\Delta _Z\right \} $$

Under the current experimental conditions, point cloud data for slatted floor have not been obtained. However, in practical applications, to ensure the comfort of animals standing and lying down, gap dimensions should be smaller than those of the floor section. Additionally, the point cloud density captured by a single consumer-grade depth camera does not meet industrial standards. Therefore, during point distribution statistics, the characteristics should correspond to those of an actual cement floor. This assumption needs further discussion and validation when real-world data become available.

Following the filtration of ground noise, the point cloud set S₁ still exhibits significant noise redundancy, primarily manifested as clusters of outliers comprising non-critical objects such as railings, ancillary facilities of the pig pens, walls, parts of the data acquisition equipment, and suspended dust particles. Consequently, the consideration arises to further constrain the target region to a smaller rectangular space to reduce scene complexity. The camera position defines the viewpoint origin from which the point cloud is generated, with geometric constraints referencing it as the coordinate point. Based on the movement of the pig’s body within the field of view, a bounding box is computed. From the spatial origin coordinate position A0(0, 0, 0) of the camera, A1(0, 0, Z_max - Δ_Z) is designated as the localized starting point. A bounding box with dimensions length Δ_X = 2,000 mm, width: Δ_Y = 2,000 mm, and height: Δ_Z = 1,000 mm is selected. These dimensions are determined based on the movement range of the largest pig in the experiment. Point cloud data points lying outside this geometric boundary, where the pig’s body would exceed the specified dimensions, are classified as erroneous. The target point cloud set S₂ is calculated by the following Equation:

(6) $$ S_{2}=\bigcup_{P_{i} \in S_{1}}\left\{P_{i}\left(X_{i}, Y_{i}, Z_{i}\right) \left\lvert\, \forall P_{i}\left\{\left(\begin{array}{c} A 1(X)-\frac{\Delta_{X}}{2} \leq X_{i} \leq A 1(X)+\frac{\Delta_{X}}{2}, \\ A 1(Y)-\frac{\Delta_{Y}}{2} \leq Y_{i} \leq A 1(Y)+\frac{\Delta_{Y}}{2}, \\ d_{z}-D_{Z} \leq Z_{i} \leq A 1(Z) \end{array}\right)\right\}\right.\right. $$

The point cloud data acquired by depth camera is exceedingly voluminous, demanding significant computational resources and long processing times. Voxel downsampling is employed to effectively reduce the data volume while ensuring the integrity of the target point cloud features. In this study, three sets of voxel downsampling parameters are selected to obtain point clouds of varying densities and analyze the runtime of the DPFFS algorithm. To facilitate the observation and differentiation of point cloud features within subsequent illustrations, no downsampling operation is conducted on the point clouds within the figures except for the final results. Bounding boxes are computed within the point cloud set, discretized into small voxels, each cube of the same size is defined as voxel V, and the centroid (X_c, Y_c, Z_c) within each V is calculated to obtain the simplified point cloud P_c after sampling. m represents the number of points within each voxel V. This chapter selects V values of 10, 20, and 30 mm for algorithmic time evaluations.

(7) $$ P_{c}=\bigcup_{(X_c,Y_c,Z_c) \in V}(X_c,Y_c,Z_c) $$

(8) $$ \left (X_{c}=\frac{\sum_{i=1}^{m} X_{i}}{m}, Y_{c}=\frac{\sum_{i=1}^{m} Y_{i}}{m}, Z_{c}=\frac{\sum_{i=1}^{m} Z_{i}}{m} \right ) $$

(9) $$ (X_i,Y_i,Z_i)\in V $$

In order to segment the target pig body from environmental noise, this study considers designing an identification method to transform target extraction into a binary classification task, dividing points into noise set or pig body set based on their distinct features. The perceptual box is a three-dimensional spatial cropping model based on pose constraints, its essence lies in using axis-aligned oriented bounding boxes to delineate the regions of interest for target objects in complex scenes, enabling noise suppression. Therefore, by employing the concept of perceptual boxes, perceptual spaces are constructed where point cloud features can be differentiated, each space contains few points and has high computational efficiency. To better observe the features of pig bodies and noise points, several point cloud sets of heavily interfered and noise closely adhered with pig body’s points, as well as undisturbed typical point cloud sets, are selected for analysis. As shown in Figure 6, the point cloud data corresponding to the black pig body points exhibits a uniform, dense, and smooth “single-layer” structural characteristic, this type of structure demonstrates continuity and consistency within a spatial segment along the Z-axis, with low variance. Conversely, the other two types of points exhibit more extreme characteristics in the Z-direction and the X-Y plane, The green noise region represents noise such as walls, inner and outer walls of feed troughs, and parts of the data acquisition equipment, specifically, in the Z-coordinate axis direction, these points span a large range, are densely distributed, and exhibit significant longitudinal clustering properties. The blue noise region represents noise like railings, window sills, and the bottoms of feed troughs, in this case, points exhibit a small span along the Z-coordinate axis but are densely distributed within a small neighborhood in the X-Y plane, showing distinct lateral clustering properties. The remaining yellow region comprises scattered outlier points with less prominent features. By using the concept of perceptual boxes to construct spatial structures sensitive to both longitudinal and lateral feature distributions, a task of noise points and pig bodies identification and classification can be conducted. However, during the construction process, it is not possible to construct only a single perceptual space. This is because at the boundaries of different regions, the points within the perceptual space exhibit composite features. Consequently, the two-dimensional and three-dimensional perceptual spaces and corresponding geometric constraints were ultimately constructed to amplify the distribution characteristic differences between the pig body and noise. For the point cloud noise in the green and blue regions in Figure 6 it is necessary to calculate the intra-point Z-axis spans and statistical quantities within the perceptual spaces and select appropriate threshold values to avoid misidentification and erroneous filtering of point clouds not affected by noise, as shown in Figure 6F. For the remaining sparse yellow outlier points, they can be filtered out during the utilization of clustering algorithms without requiring specific attention.

Based on the characteristics of noise points, a 3D “cylindrical” perceptual space was designed for the identification and filtering of noise points exhibiting large Z-axis spans and significant point clustering features, such as walls, inner and outer walls of feed troughs, etc. The size of the constructed perceptual space is determined based on the trade-off between computational speed and effectiveness. If the perceptual space is excessively large, the corresponding neighborhood search radius will also increase, resulting in slower computational speeds and the potential erroneous filtering of point clouds unaffected by noise. Conversely, selecting a space that is too small may lead to suboptimal filtering effects, making it challenging to remove noise adhering to the pig body point cloud. Specific parameter selections are detailed in the discussion section. The point cloud is loaded using the K-D Tree structure, traversing all points within the set S₂. Each point is considered as the center point for neighborhood radius search and perceptual spaces construction, as the PCL does not directly offer a cylindrical search method within the K-D Tree structure. A cylindrical space, denoted as σ, with a radius r of 10 mm and a height h of 200 mm is constructed by code to impose geometric constraints. Within the search radius r_s, all inner points P_i falling within the spatial constraint σ are counted. And the maximum and minimum Z values of these inner points are recorded to calculate the count parameter C and span parameter D. A threshold is then set for binary classification, where center points classified as noise are filtered out. The search radius r_s is computed based on the constructed radius r, and the search region is the circumscribed sphere of σ. By using a radius search, a greater number of points can be encompassed in the computation, the defined cylindrical space and constraint serve to amplify the span differences in the Z-direction of inner points. Furthermore, from a top-down perspective, a circular shape at the boundaries between the two types of points contains fewer shared adhesion regions, thereby mitigating potential severe disruptions to the edges of the pig body point clouds.

Traversing each point in S₂ as construction center point (X_Central, Y_Central, Z_Central), search radius r_s and the mathematical set form of σ can be calculated by the following Equations (10) and (11), respectively:

(10) $$ r_s=\sqrt{(r)^2+(\frac{h}{2})^2} $$

(11) $$ \sigma =\bigcup_{P_{i} \in S_{2}}\left\{P_{i}\left(X_{i}, Y_{i}, Z_{i}\right) \left\lvert\, \begin{array}{c} \sqrt{(X_i-X_{Central})^2+(Y_i-Y_{Central})^2}\le r, \\ Z_{Central}-\frac{\mathrm{h}}{2}\le Z_i\le Z_{Central}+\frac{\mathrm{h}}{2} \end{array}\right.\right \} $$

where σ represents the neighborhood point set that within the geometric constraint. An indicator function I is defined such that the result is 1 when P_i within the set σ and 0 otherwise. The count parameter C is ultimately calculated, where C₀ in the equation represents the initial value of 0, and n denotes the number of points in the point cloud:

(12) $$ C=C_0+\sum_{i=1}^n I(P_i(X_i,Y_i,Z_i)\in \sigma ) $$

The span parameter D is calculated by Equation (13):

(13) $$ D=\max_{P_i(X_i,Y_i,Z_i)\in \sigma}Z_i-\min_{P_i(X_i,Y_i,Z_i)\in \sigma}Z_i $$

where i represents the index of inner points, $$ \max_{P_i(X_i,Y_i,Z_i)\in \sigma} $$Z_i represents the maximum Z value of the inner points, and $$ \min_{P_i(X_i,Y_i,Z_i)\in \sigma} $$Z_i represents the minimum Z value of the inner points.

Figure 7 illustrates the construction principle of the cylindrical perceptual spaces and the method for determining inner points, which exhibits different characteristics between the pig body point cloud and the noise point cloud. When the blue cylinder σ₁ is constructed at a noise point, the inner points tend to cluster vertically, with the maximum span difference nearly equal to the height h, denoted as Δ_Z1 in Figure 7. In contrast, for the green cylinder σ₂ constructed on a single layer of the pig body point cloud, the inner points are sparser with smaller Z differences, indicated as Δ_Z2 in Figure 7. It is evident from the figure that Δ_Z1 is significantly greater than Δ_Z2, consequently, the count parameter C and span parameter D for σ₁ are both greater than those for σ₂. By combining C and D as filtering criteria, the removal of center points is executed when the inner points of σ satisfy C ≥ 50 and D ≥ 50 mm.

In summary, the method flow is to traverse the point cloud, selecting the current index point as the construction center point (X_Central, Y_Central, Z_Central) based on its actual coordinates X_Central, Y_Central and Z_Central, followed by the construction of a perceptual space and geometric constraint. The coordinates of all inner points within the constraint are calculated. If the C and D criteria are met, the center point is removed from the point cloud, otherwise, it is skipped. This process continues iteratively until all index points have been traversed. The pseudocode of the program logic design is depicted in Figure 8.

The 3D perceptual spatial filtering method is unable to handle point clouds exhibiting clustering characteristics in the X-Y plane direction. Consequently, a 2D “circular” perceptual region was devised to address this limitation. Within the plane resulting from the dimension reduction projection of the point cloud, this method identifies and eliminates noise characterized by a small Z-direction span but a significant concentration of points within a short height neighborhood, such as railings, window sills, and trough bottoms. When constructing the 2D circular perceptual region ρ, the dimensions should be larger to encompass a larger number of points. This facilitates the amplification of feature differences for better distinction between noise and pig body point, and helps mitigate false filtering. The potential for erroneous filtering arises from point cloud sets that are not affected by noise, primarily representing the pig’s body. Additionally, the natural posture of the pig results in a smaller Z-direction span of the point cloud at the pig’s back edge, a smaller ρ value may lead to the mis-filtering of these edges. Therefore, a construction diameter of 100 mm was selected for ρ to cover a larger lateral area of the pig’s back during side projection.

In the preceding section, the point cloud set S_3D was calculated. Subsequently, with its point cloud X coordinates set to 0, all points were projected onto the Y-Z plane as shown in Figure 9A. Utilizing the K-D Tree structure, the point cloud was loaded and traversed, conducting a nearest neighbor radius search with each point cloud serving as a construction center point. Following the data transformation into 2D, the search region coincided with the perceptual region, enabling the direct construction of geometric constraint ρ using the search radius. While r was chosen to be 50 mm, the process involved counting all inner points P_i falling within the perceptual region ρ, simultaneously recording the maximum and minimum Z values of these inner points to derive the count parameter C and span parameter D. The rationale for selecting a circular rather than a rectangular geometric constraint lies in the circular shape’s better alignment with the search region, offering a larger area of coverage. In contrast, choosing a rectangular constraint would result in the search area being the circumscribed circle of the rectangle, potentially causing point omissions at the edges.

Traversing each point in S_3D as construction center point (0, Y_Central, Z_Central), the mathematical set form of ρ can be calculated by the following Equation:

(14) $$ \rho =\bigcup _{P_i\in S_{3\mathrm{D}}}\left \{ P_i(0,Y_i,Z_i)|\sqrt{(Y_i-Y_{Central})^2+(Z_i-Z_{Central})^2}\le r \right \} $$

In the above equation, ρ represents the neighborhood point set that within the geometric constraint. The same indicator function I is used to calculate the count parameter C. While C₀ in the equation represents the initial value of 0, and n denotes the number of points in the point cloud:

(15) $$ C=C_0+\sum_{i=1}^n I(P_i(0,Y_i,Z_i)\in \rho ) $$

The span parameter D is calculated:

(16) $$ D=\max_{P_i(0,Y_i,Z_i)\in \rho}Z_i-\min_{P_i(0,Y_i,Z_i)\in \rho}Z_i $$

i represents the index of inner points, $$ \max_{P_i(0,Y_i,Z_i)\in \rho} $$Z_i represents the maximum Z value of the inner points, and $$ \min_{P_i(0,Y_i,Z_i)\in \rho} $$Z_i represents the minimum Z value of the inner points. Then continue to project the point cloud to the X-Z plane as in Figure 9B, and similarly calculate C and D. Twice 2D filtering can remove most of the noisy points such as the railings, window sill surfaces, and the bottom of the trough, only a small number of sparse point clusters remain.

Figure 9 illustrates the two projection steps and the construction method of the circular perceptual region ρ, the inner points in space still exhibit different characteristics. When constructing the blue region ρ₁, the inner points demonstrate a small Z-direction span and clustering in the X-Y direction, denoted as Δ_Z1. Conversely, for the green region ρ₂, the pig’s back exhibits a certain curvature, allowing ρ₂ to encompass more points. The Z difference for ρ₂ exceed ρ₁, as indicated by Δ_Z2 being greater than Δ_Z1. The combined conditions of C and D are employed for filtering, specifically, when the inner points of ρ satisfy C ≥ 20 and D ≤ 40 mm, center point will be removed.

In summary, the method flow is to project S_3D onto the Y-Z plane, traversing the point cloud, selecting the current index point as the construction center point (0, Y_Central, Z_Central) with Y_Central and Z_Central representing the actual coordinates of the point. Subsequently, perceptual regions are constructed, calculating the coordinates of all inner points within the region. If these points satisfy the criteria C and D, the center point is removed from the point cloud, otherwise, it is skipped. This process continues iteratively until all index points have been traversed, then the remaining points are projected onto the X-Z plane, and the aforementioned steps are repeated. Finally, all remaining points are matched with the S₂ set, and the corresponding Y and X coordinates of points with identical coordinates are assigned their original values. The pseudocode of the program logic design is depicted in Figure 10.

To evaluate the dynamic noise removal effect of module 1 on ground noise, point cloud datasets collected at three different heights of 1,680, 1,780, and 1,880 mm were selected for comparative experiments. By analyzing the distribution characteristics of point cloud quantities within Z-direction slices, we observed that the original point cloud data exhibited significant peak in point distribution in the vicinity of the ground before filtering, as shown in Figure 11A. The slice region containing the counting-peak (ground noise) was effectively eliminated after filtering, concurrently filtering out point clouds from non-critical areas above the pig body as shown in Figure 11B. The experiment showed that module 1 of the DPFFS algorithm can achieve adaptive dynamic filtration of ground noise at different heights, exhibiting a high level of processing efficiency.

Significant differences in noise interference levels existed among different point cloud groups, compounded by variations in pig weights and sizes, resulting in distinct size and density distributions of clusters within the point cloud. Consequently, the algorithm needed to simultaneously satisfy two key requirements under a unified parameter configuration: (1) effectively denoise point clouds with high noise interference levels and (2) avoid excessive filtration of point clouds with low noise interference levels. To objectively quantify the denoising performance and robustness of the algorithm, the denoising rate (DR) was introduced as a core evaluation metric. The 6 sets of point clouds were utilized shown in Figure 6 for filtration experiments, where the sixth set F [Figure 6F] had zero noise points and was excluded from DR calculations. Noise points were segmented using Cloud Compare software to obtain the total number of noise points before filtration: N_S, while the total number of noise points after algorithmic filtration was defined as N_P. The quantity of points correctly filtered out was determined as N_S - N_P. DR was then calculated using the following Equation:

(20) $$ DR=\frac{N_S-N_P}{N_S}\times 100\% $$

As shown in Table 3, the first through third groups of point clouds were heavily influenced by noise interference, characterized by a regular geometric distribution of noise points. Consequently, the algorithm exhibited a higher DR in these instances. In contrast, the fifth group of point clouds had low noise density and less distinct features (as shown in Figure 6), resulting in a relatively lower DR. The fourth group of point clouds exhibited the most complex noise structure, characterized primarily by irregular surface distributions. The number of noise points significantly exceeded that of the pig body point cloud, resulting in the lowest DR among all groups. In summary, the algorithm effectively reduced the number of noise points in heavily interfered point cloud groups to below the number of pig body points, while maintaining lower DRs for groups with less interference to avoid false filtering. The experimental results indicated that module 2 possessed filtering capabilities for different noise intensities.

The final clustered results after filtering were shown in Figure 12.