dataesr/scientific-paragraphs-categorization huggingface dataset:
One method is to compress the input image to a fixed size as in the  [9] ,  [10]. Another method crops part of the image area, such as  [11]. Both of these image processing methods are very convenient. Nevertheless, the compress-image method results in a loss of detection accuracy. The crop-image method can only be used with an existing dataset and acquisition environment. Changes in camera model, spatial position, and scaling require researchers to redesign the system. We observe that the HR images obtained by autonomous vehicles contain some areas without pedestrians. We named this area a Non-Pedestrian Area (NPA). We find that there is a relationship between the region size of NPA in the image and the environmental parameters. The environmental parameters contain camera height, camera pitch angle, camera vertical field of view (FOV), the distance between the pedestrian and the camera, pedestrian height and vertical resolution of the image.
Therefore, we propose the Non-Pedestrian Area Estimation (NPAE) algorithm to describe the relationship between the two factors. Afterwards, the NPAE algorithm can estimate the NPA based on the environmental parameters. Once the NPA is acquired, we remove the non-pedestrian area from the HR image and then send the processed image to the subsequent pedestrian detector. We first design an experiment to verify the correctness of the NPAE algorithm. Then, the algorithm acceleration performance is tested on the JAAD dataset both on the GPU platform and the CPU platform. Finally, the performance of the algorithm in extreme cases is tested on the Caltech dataset which has a plentiful variety of scenarios. Among them, the JAAD dataset contains two types of high-resolution images, 1920 × 1080 pixels and 1280 × 720 pixels.
b: IMAGE CROPPING Image cropping is also a very widely used method. The usual method is to crop the region of interest (RoI) in the image. For example, the image area affected by pincushion distortion effect is cropped in the KITTI dataset  [11]. The image resolution is cropped from 1392 × 512 pixels to 1242 × 375 pixels, a reduction of 34. 65% pixels. Reducing the number of pixels will reduce the amount of computation and therefore accelerate the detection process. The advantage of the image cropping method is that it is quick and easy to understand. The disadvantage is that when there is less cropping, the acceleration is less effective. When there is too much cropping, the target will be cropped. Therefore, it is necessary to get all the data first, count the target distribution and then manually adjust the cropping area.
2) CALTECH DATASET The dataset has the images with low resolution (LR) of 640 × 480 pixels. The Caltech dataset does not contain HR images. However, it contains a rich set of scenes and is widely adopted by existing methods. Thus this LR image dataset is used for comparison experiments. Both the JAAD dataset and the Caltech dataset have a frame rate of 30 fps. For the selected dataset, we will count the distribution of pedestrians. Therefore, it is necessary to select one of the pedestrian's attribute parameters as the statistical object. We define that the pedestrian bounding box is located by two points, P1 and P2, as shown in Figure  1. Where P1 = (P1 x , P1 y ) indicates the top-left vertex, P2 = (P2 x , P2 y ) indicates the right bottom vertex. Since pedestrians will appear at random locations, P1 x ∈ [0, X max ], P2 x ∈ [0, X max ].
P2 represents the bottom boundary of the pedestrian bounding box, so we need to find NPA bottom in the lower half of the image. NPA bottom does not exist in the three sets of images with different resolutions in Figure  2 (b), 2(d) and 2(f). This situation is not a coincidence. For a better view, the camera is usually set up on top of the autonomous vehicle. Hence h c = h v , where h c is the camera height and h v is the vehicle height. In general, vehicle height h v and pedestrian height h p have h v > h p /2. Then h c > h p /2, which means that the area where pedestrian appears in the image is more towards the bottom. This is the reason why NPA only exists at the top of the image. In this paper, we use NPA to refer to NPA top. From the analysis of the dataset, we can see that NPA is present.
B. NON-PEDESTRIAN AREA ESTIMATION FOR SINGLE IMAGE Our goal is to find suitable non-pedestrian areas for all images in the dataset. The situation in the dataset is more complicated. It contains a large number of pedestrians, with different camera postures and different collection equipment. Therefore, we first try to find the optimal NPA for a single image. Then we will discuss how to find a common applicable NPA on the dataset. To accurately estimate the non-pedestrian area in a single image, it is necessary to analyze the highest position of the pedestrian bounding box P1 point in the image. As shown in Figure  3 (a), there are three pedestrians, Ped 1 , Ped 2 and Ped 3. The distance between camera and pedestrian is d 1 , d 2 and d 3 , respectively. Ped 1 is on the vertical centre line of the image, d 1 is perpendicular to the plane of the image.
After recording and inputting the required parameters of equation (  1 ), the NPAE algorithm can be verified by comparing the calculated value of NPA with the actual value. Since the dataset does not contain the required environmental parameter, a validation experimental platform is built. The parameters in the validation experimental platform are: The height of the pedestrian h p is 1. 90 m. The camera height h c is 1. 17 m. The vertical resolution of the image px v is 1080 pixels. The camera vertical FOV α is 52 degrees. The camera pitch angle γ is set at 0. 5 degrees, 3. 5 degrees, and 10 degrees in sequence. The distance between the pedestrian and the camera d pc is set at 2. 0 m, 2. 5 m, 3. 0 m, 3. 5 m, and 4. 0 m in sequence. The vertical coordinate of the P1 point of the pedestrian bounding box P1 y is manually measured.
C. NON-PEDESTRIAN AREA ESTIMATION FOR MULTIPLE IMAGES NPAE algorithm is designed to find the non-pedestrian area for the dataset. There is a difference between applying the NPAE algorithm to a dataset and applying the algorithm to a single image. When using the NPAE algorithm on a dataset, all six environment parameters need to be set to constants. In this way, the NPAE algorithm can uniformly remove nonpedestrian areas for the images in the dataset based on the set environmental parameters. However, the situation is further complicated by the large number of images contained in the dataset. The six environmental parameters used by NPAE need to be revisited.
6) PEDESTRIAN-CAMERA DISTANCE d pc According to subsection III-A, the smaller pedestrian-camera distance for pedestrians with the same height determines the value of NPA. Although pedestrians may appear at any location, the d pc will usually not be 0 due to the vehicle width. We refer to the average size of cars and set pedestrian-camera distance d pc = 1. 2 m. The camera vertical FOV, vertical resolution, camera height, and camera pitch angle obtained from the dataset along with the predefined pedestrian height and pedestriancamera distance are the environmental parameters required for the NPAE algorithm. The NPA value for the dataset can be obtained by entering these parameters into equation  (1). Taking into account the following special conditions may encounter: 1) The pedestrian height is higher than the assumed value.
The processing does not have any effect on the pedestrian detection results. This is the most common state. II: P1 y_new < 0 and P2 y_new < 0. In this case, some pedestrians in the original images will be removed. This type of pedestrian is usually located above certain objects. There is no way that the autonomous vehicle can hurt this type of pedestrian. We found this type of pedestrian in the Caltech dataset, as shown in Figure  4(a). Pedestrians on the overpass are not the targets we are interested in. Dealing with such pedestrian target is a waste of processing resources. Therefore, eliminating such pedestrian targets will not affect the pedestrian detection accuracy. III: P1 y_new < 0 and P2 y_new > 0. In this case, some part of the pedestrian will be removed. To cause this, pedestrians have to be close enough to the camera and the camera's angle of view should be small enough.
We only found some samples in the Caltech dataset, as shown in Figure  4 (b). The area above the pedestrian's head in the red box will be partially removed, but the remaining pedestrian image still occupies a large area in the image. Due to problems such as object occlusion and pedestrian overlap, the pedestrian detector should have the ability to detect part of the pedestrian. Missing some part of the pedestrian image will not cause the detection result to fail. Based on the above analysis, we conclude that the NPAE algorithm does not have a negative impact on the pedestrian detection results.
a: JAAD The JAAD dataset is developed by York University. It has various weather conditions such as sunny, cloud, rain and snow. It is collected from three cities with complex traffic scenarios and a large number of pedestrians. 2786 pedestrians are labelled in a total of 389545 bounding boxes. JAAD dataset has 336 videos with a resolution of 1920 × 1080 pixels and 10 videos with a resolution of 1280 × 720 pixels. The frame rate is 30 fps, which leads to a total of 82032 frames. There are 79812 frames with the resolution of 1920 × 1080 pixels. 63850 frames are used for training and 15962 frames are used for testing. There are 2220 frames with the resolution of 1280 × 720 pixels. 1776 frames are used for training and 444 frames are used for testing.
b: CALTECH Caltech dataset is developed by the California Institute of Technology. The dataset contains a large number of image frames, challenging low resolution (LR) images and images of occluded targets. The dataset consists of 10 hours of video with 2300 pedestrians marked. There are over 350000 bounding boxes. The resolution of the image is 640×480 pixels and the frame rate is 30 fps. 146622 frames in total are adopted in the experiment. 122185 frames are used for training and 24437 frames are used for testing. Although our goal is to accelerate high resolution image pedestrian detection, experiments on low resolution images are still valuable. The Caltech dataset has an equal number of pedestrian bounding boxes as the JAAD dataset. However, the situation in the Caltech dataset is more complex due to the different environmental parameters set.
2) PARAMETERS FOR NPAE There are six environmental parameters: camera height h c , camera pitch angle γ , camera vertical FOV α, pedes-triancamera distance d pc , pedestrian height h p , vertical resolution px v. According to  [31] , for JAAD with a resolution of 1920 × 1080: Vertical resolution px v = 1080 pixels. Considering the car shudder, the Camera pitch angle γ is varied between [-1 • , 1 • ]. The adjusted environmental parameters can be used to derive the corresponding NPA for each dataset according to equation  (1). The NPA interval for JAAD 1920 × 1080 is between NPA γ =-1 and NPA γ =1. We take the minimum value, so NPA = 405 pixels. To facilitate the experiment, the value of NPA is modified using equation  (7). NPA mod = NPA -(NPA mod 10) (7) Equation (  7 ) is not obligatory. The purpose of using this operation is simply to make the experimental comparison clearer.
B. EXPERIMENTS Experiments are performed separately on high resolution (HR) images and low resolution (LR) images. The purpose of the experiments on HR images is to measure the performance of the NPAE algorithm acceleration. The experiments on LR images focus on the robustness of the NPAE algorithm in complex situations. To compare the effects of detection acceleration, we designed comparison experiments for each resolution image. In general, the experiments are compared with two other image data optimization acceleration methods. The image compression method compresses the image to the same resolution as the NPAE-processed image. Since the NPAE algorithm is essentially an image cropping method, we compare the results of acceleration with different degrees of cropping. We also count the number of pedestrian targets affected by the image cropping method.
There are two categories, targets that are partially cropped (PR) and targets that are completely removed (CR). The evaluation metric used in this paper is the Average Precision (AP)  [33]. It is a typical object detection task evaluation metric. We record the runtime of pedestrian detection accelerated by different image data optimization methods. The CPU experimental platform is Intel Xeon W-2104 with 16GB RAM. The GPU experimental platform is Nvidia Quadro P5000. Most of the current pedestrian detection algorithms are based on deep learning. The common platforms for deep learning frameworks are CPU and GPU, therefore our experiments focus on these two platforms. The exper-imental results on the high resolution images are shown in Table  2  and Table  3. We train RetinaNet using three resolution images obtained from two datasets.
Algorithm 1 Use NPAE Algorithm to Accelerate Pedestrian Detection Input: Environmental parameters: Obtained from the input image collection environment. Images: Data collected under the same camera settings. Output: Pedestrian bounding boxes. 1: Calculate NPA value: Input environmental parameters to the NPAE algorithm. 2: Crop images: Crop all images according to the NPA value. The original image size is (H,W), and the cropped image size is (H-NPA, W). 3: Calculate pedestrian bounding box: The cropped images are sent to the pedestrian detector to get the pedestrian bounding boxes. In Table  2 , RetinaNet is the baseline. The detection result has 84. 80% average precision (AP). It takes RT G = 175. 7 milliseconds to process an image on the GPU, which means 5. 69 frames per second (FPS G ). On the CPU, the time to detect an image RT C is 4307.
The partially cropped pedestrian target number is recorded as Ped PC , and the completely removed pedestrian is labeled as Ped CR. In terms of acceleration, the speed increases as the degree of shearing increases. In terms of detection accuracy, it first remains constant and then decreases. The inflexion point occurs around the NPA value estimated by the NPAE algorithm. The Ped PC and Ped CR values also show an inflexion point around the NPA value. This pattern means that more and more pedestrian area information is lost as the cropping range exceeds the NPA value. This results in a decrease in detection accuracy. The same conclusion can be drawn from the experimental results on the JAAD 1280 × 720 dataset in Table  3. On the GPU platform, the proposed NPAE algorithm increases the detection speed by 39.
V. CONCLUSION In this paper, we present an algorithm for accelerating pedestrian detection with high resolution images, named Non-Pedestrian Area Estimation (NPAE). Based on six environmental parameters, the NPAE algorithm can accurately estimate the non-pedestrian areas in the dataset. Therefore, the proposed algorithm crops the image more accurately compared to other image data optimization methods. Because the image area is reduced and the target information is preserved, the pedestrian detector gains acceleration while maintaining accuracy. Two high resolution images, 1920 × 1080 and 1280 × 720, and two different computing platforms, GPU and CPU, are used for the experiments. In the GPU platform, the detection speed is increased by 46. 92% and 39. 19%, respectively. In the CPU platform, the detection speed is increased by 52.
17% and 60. 78%, respectively. All experiments have shown that the proposed algorithm does not affect the detection accuracy. A low resolution dataset is used to confirm the robustness of the NPAE algorithm. The NPAE algorithm performs better compared to traditional image data optimization methods. Image compression usually results in a loss of detection accuracy. Compared to NPAE algorithm, image compression loses 23. 10% of average precision on 1920 × 1080 resolution, 37. 94% on 1280 × 720, and 8. 97% on 640 × 480. Image cropping cannot be calculated to obtain the optimal size of the cropping area, so it is difficult to accurately balance detection accuracy and detection speed. The NPAE algorithm has four advantages: 1). It accelerates detection without loss of accuracy, 2). It can be used on a of computing platforms, 3).
Otolith Shape Analysis A calibrated high-resolution image (3200 dpi) of the proximal face of the whole left and right sagittal otolith was obtained using a scanner with reflected light. Within this process, a fixed single magnification was used to ensure as high a resolution as possible. Images were processed using the image analysis system TNPC (Digital processing for calcified structures, version 7) with the sulcus acusticus facing up. In order to compare left and right otolith shapes, mirror images of left otoliths were used. An elliptic Fourier analysis (e. g. ,  [33] ) was carried out on each otolith contour delineated and extracted after image binarization. All EFDs were obtained using TNPC 7 software. For each otolith, the first 99 elliptical Fourier harmonics (H) were extracted and normalised with respect to the first harmonic and were thus invariant to otolith size, rotation, and starting point of contour description  [34].
This type of analysis was carried out for all individuals and then separately for each sampling location. pRDA is an extension of multiple regression to multivariate response data and an extension of PCA  [36] , combined with permutation tests (marginal effect, type II  [37] ) on the selected PCs matrix. To visualise differences in otolith shape between the right and left sides, an average otolith shape of each side group was rebuilt based on EFDs of the averaged shape. To evaluate DA amplitude, average left and right shapes were rebuilt based on EFDs averaged for each side at the level of all individuals and for each sampled location. DA amplitude was then computed as the percentage of non-overlapping surface between the reconstructed right and left otolith average shapes relative to the total area they covered after superposition.
2016; Beutler et al. 2016). These approaches may be subject to limits including a limited relative galaxy bias (samples in a single-tracer survey usually do not differ much in the galaxy bias), and a limited overlapping area (most galaxy surveys are designed to be complementary to each other, in terms of the sky coverage and/or redshift range)  (Wang & Zhao 2020). Fortunately, the extended Baryon Oscillation Spectroscopic Survey (eBOSS) project has provided such an opportunity for a proper multi-tracer analysis. Targeted for both Luminous Red Galaxies (LRG) and Emission Line Galaxies (ELG) at  ∈ [0. 6, 1. 1] in a large overlapping patch of sky, the eBOSS Data Release (DR) 16 provided a total of ∼ 550, 000 spectra for the multi-tracer analysis, which is the largest sample for such an analysis to date.
This is the natural motivation for this work. In this analysis, we develop new methods for a joint BAO and RSD analysis using the DR16 LRG and ELG sample, and pay particular attention to the mitigation of possible systematics. The paper is structured as follows. In Section 2, we describe the observational and simulated datasets used in this analysis, and in Section 3, we present the method, followed by mock tests and main result of this work in Section 4, before conclusion and discussion in Section 5. This work is one of a series of papers presenting results based on the final eBOSS DR16 samples. The multi-tracer analysis of the same galaxy sample is performed in configuration space to complement this work  (Wang et al. 2020). For the LRG sample, produced by  Ross et al. (2020) , the correlation function is used to measure BAO and RSD in  Bautista et al.
The eBOSS DR16 LRG and ELG samples Being part of the Sloan Digital Sky Survey-IV (SDSS-IV) project  (Blanton et al. 2017) , the eBOSS survey  (Dawson et al. 2016; Zhao et al. 2016 ) started in 2014 using the 2. 5-metre Sloan telescope  (Gunn et al. 2006 ) at the Apache Point Observatory in New Mexico. The LRG targets are selected using optical and infrared imaging data over the entire SDSS imaging footprint. The optical imaging data are taken from the SDSS I/II  (York et al. 2000)  and III  (Eisenstein et al. 2011)  surveys in five passbands: , , , , , while the infrared data is provided by the Wide Field Infrared Survey Explorer (WISE) survey  (Wright et al. 2010 ). The ELG targets, however, are not selected using the SDSS imaging observations. Instead, the , ,  bands of the DECam Legacy Survey (DECaLS)  (Dey et al.
The simulated mock samples A large number of mock samples, each of which has the same clustering property of the eBOSS DR16 sample, are required to estimate the data covariance matrix. In this analysis, we use the Extended Zel'dovich (EZ) mocks, which consist of 1000 realisations, produced following the prescription in  Zhao et al. (2020) ;  Chuang et al. (2015)  The number of total realisations of the EZmocks we have, which is 2000 for the LRG and ELG (1000 for each), is sufficient given the total number of data points (including those for the cross-power spectrum multipoles) we used, which is 208, for a joint LRG and ELG analysis 1. To reflect the actual situation of the eBOSS observations, observational systematics, including the depth-dependent radial density, angular photometric systematics, fibre collision, redshift failure, etc.
( 16 ) 6 It is true that this is a toy model for the angular systematics, but this captures the primary systematics in the eBOSS ELG sample, as we demonstrate in the mock test. -1 0 0 Eliminating  () from Eqs. (  15 ) and (  16 ), we obtain the following relation, 0 1 0 0 N G C , P k ∆( k ) [ h -2 M p c 2 ] N G C , Q k [ h M p c -1 ] 0. 0 1 0. 1 -1 0 0 0 1 0 0 S G C , P 0. 0 1 0. 1 0. 3 S G C , Q 𝑄 obs ℓ = 𝑄 true ℓ , (17) where  ℓ is the chained power spectrum multipoles, 𝑄 ℓ ≡ 𝑃 ℓ -𝐴 ℓ 𝑃 ℓ+2 , (18) and 𝐴 ℓ ≡ (2ℓ + 1)L ℓ (0) (2ℓ + 5)L ℓ+2 (0). ( 19 ) Unlike the observed  ℓ , the observed  ℓ is immune to the angular systematics, as demonstrated by Eq. (  17 ), thus is a better quantity to use for data analysis. For the first three multipoles of , Eq. (  18 ) means, 𝑄 0 𝑄 2 𝑄 4 = 1 -𝐴 0 0 0 0 1 -𝐴 2 0 0 0 1 -𝐴 4 𝑃 0 𝑃 2 𝑃 4 𝑃 6 (20) To reconstruct  from , a truncation in  ℓ is necessary, otherwise the above matrix equation is not invertible.
The radial integral constraint Due to the ignorance of the true selection function of the galaxy survey, which is needed for a clustering analysis, the redshift distribution of actual observations, (), is used instead as the selection function for analysis. This can in principle bias the final measurement of BAO and RSD parameters if not accounted for. The resultant bias, quantified as the radial integral constraint (RIC), is recently investigated in de Mattia & Ruhlmann-Kleider (2019), and corrected for in the theoretical model for the power spectrum in the eBOSS DR16 ELG analysis  (de Mattia et al. 2020). In this work, we take a different approach, namely, subtracting the RIC component from the data directly. In practice, we analyse two sets of EZmocks, with different treatments of the randoms so that one has the RIC effect, while the other does not.
The power spectrum multipoles Figures 4 and 5 show the measurement of power spectrum multipoles  ℓ and Q ℓ for the LRG and ELG samples in the NGC and SGC, respectively. The shaded bands illustrate the measurements (68% CL uncertainty around the averaged power spectra) from 1000 realisations of the EZmocks, and the data points with error bars are from the DR16 galaxy sample. Although measurements of the auto power spectrum in  ℓ are presented and extensively discussed in Gil-  Marín et al. (2020) and de Mattia et al. (2020)  for the LRG and ELG samples, respectively, they are included here for completeness, which is helpful for presenting and discussing the measurement of  ℓ and the cross power spectrum. As expected, we see that  ℓ generally has larger uncertainties compared to  ℓ , because  ℓ+2 , which is less well determined than  ℓ , is involved in  ℓ.