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II. OVERVIEW OF PHOTON-COUNTING LASER ALTIMETRY

【綜述】光子計數(shù)激光測高儀

????????Photon-counting laser altimetry records the time position of each individual received photon. Then, the surface elevation of illuminated area can be derived by calculating photon travel time and knowing the altitude of the sensor. Two sources of simulated ICESat-2 data are used in this letter.

Photon-counting[?f??t?n]：光子計數(shù)

laser altimetry[?le?z?(r) ??lt?mi?t?(r)]：激光高度計

elevation[?el??ve??n]：海拔

illuminated[??lu?m?ne?t?d]：

derive[d??ra?v]：獲得

altitude[??lt?tju?d]：海拔高度

simulated[?s?mjule?t?d]：模擬的

????????光子計數(shù)激光測高儀哪亿，會記錄每個接收到光子的時間位置。接著讨阻，通過計算光子的運動時間钝吮，了解傳感器的海拔高度，可以得到被照射區(qū)域的表面高度。本文使用了兩種模擬ICESAT-2數(shù)據(jù)链患。

A. First Principle Simulation of Photon-Counting Laser Altimetry

光子計數(shù)激光測高的第一原理模擬

? ??????The first data set is based on the first principle simulation of photon-counting laser altimetry. As mentioned in our previous letter [15], the transmitter and receiver are modeled using a model of the ICESat-2 ATLAS instrument. The laser beam is characterized as circular Gaussian with a diameter of 10 m on the ground.

transmitter[tr?nz?m?t?(r)]：發(fā)射機

ATLAS： Advanced Topographic Lidar Altimetry System 先進地形激光測高系統(tǒng) 【onboard ICESat-2】

laser beam[?le?z?(r) bi?m]：激光束

be characterized[?k?r?kt?ra?z] as：被認(rèn)為，被描述

diameter[da???m?t?(r)]：直徑

? ? ? ? 第一組數(shù)據(jù)集基于光子計數(shù)激光測高的第一原理模擬贸毕。根據(jù)之前的論文[15]明棍，發(fā)射器與接收器均按照ICESat-2上的ATLAS結(jié)構(gòu)建模寇僧。激光束的特征為嘁傀，地面直徑1/e2 10米细办。

Meanwhile, the temporal shape of laser photons is modeled with a Gaussian distribution with a 1-ns full-width at half-maximum pulsewidth. Laser along-track sampling is 0.7 m based on the latest ICESat-2 design. The number of mean received photoelectrons per shot for typical ice sheets is set as 2.04 for a weak spot and 8.17 for a strong spot [16]. A 3-D synthetic surface is also generated using fractal techniques. Here, the created terrain has a size of 1024 × 1024 m, with a resolution of 1 m.

pulse width：脈沖寬度

Gaussian distribution：高斯分布

temporal[?temp?r?l]：時間的笑撞，短暫的

sampling[?sɑ?mpl??]：n.?抽樣

along-track：沿軌道

photoelectrons ：光電子

synthetic[s?n?θet?k]：合成的

fractal[?fr?ktl] technique：分形技術(shù)

terrain[t??re?n]：地形

resolution[?rez??lu??n]：正式?jīng)Q定茴肥，分辨率

同時炉爆，用一個半最大脈沖寬度為1-ns全寬的高斯分布，來模擬激光光子的時間形狀逼裆。根據(jù)最新ICESat-2的設(shè)計胜宇，激光沿軌采樣為0.7m桐愉。針對典型的冰原从诲，每一次拍攝的平均光電子數(shù)為2.04（針對弱拍攝）與8.17（針對強拍攝）系洛。3D合成表面由分形技術(shù)生成略步。創(chuàng)建的地形尺寸為1024×1024 m趟薄，分辨率為1 m杭煎。

For the surface reflectance model, an analytical snow bidirectional reflectance distribution function presented by Kokhanovsky and Breon [17] in a slightly modified notation is used here. Laser wavelength λ is set as 532 nm with χ = 2.54 × 10?9. Meanwhile, parameter M is set to be 5.5 × 10?8, with a = 1.247, b = 1.186, and c = 5.157, based on Kokhanovsky’s letter [17]. The snow grain size is 200 μm.

reflectance[r??flekt?ns]：反射

bidirectional[?ba?d??rek??nl] ：雙向的

notation[n???te??n]：符號

wavelength：波長

grain[ɡre?n]：顆粒

針對地面反射模型玫鸟，由Kokhanovsky and Breon [17]提出的雪雙向反射分布函數(shù)在這里應(yīng)用犀勒。激光波長λ設(shè)為532 nm贾费，χ=2.54×10?9褂萧。同時导犹，根據(jù)Kokhanovsky的文章[17]，參數(shù)m設(shè)置為5.5×10?8卷雕，a=1.247漫雕，b=1.186浸间，c=5.157魁蒜。雪粒大小為200μm梅惯。

????????In addition, noise is added to the point cloud with uniform random distribution. With a noise rate of 2 MHz, an ICESat-2 point cloud of 0.1-s flight (700-m distance on the ground) over test 3-D synthetic scene is plotted in Fig. 1.?

uniform[?ju?n?f??m]：n.制服；adj.統(tǒng)一的脚作。

? ? ? ? 此外球涛，通過隨即均勻分配亿扁，在點云中增加噪點从祝。圖1顯示牍陌，在3D合成場景中员咽，一個噪聲率2兆赫的ICESat-2點云飛行0.1秒（距地面700米）贝室。

圖1

B. High-Altitude MABEL Data Set

The second source of simulated ICESat-2 data is from MABEL [18]. The test data (L2A) were collected in WI, USA, on September 26, 2012, where lots of canopy-covered ground are present, as shown in Fig. 2.

canopy-covered ground[?k?n?pi]：冠層覆蓋地面

第二種模擬ICESat-2 data數(shù)據(jù)來自于MABEL[18]怀泊。測試數(shù)據(jù)(L2A)于2012年9月26日在美國WI收集霹琼。在WI收集到大量的樹冠覆蓋地面枣申，如圖2所示忠藤。

圖2

III. METHODOLOGY

B. Modified DBSCAN

????????The key idea of DBSCAN is that, for each point of a cluster, the neighborhood of a given radius has to contain at least a minimum number of points, i.e., the density in the neighborhood has to exceed some threshold. The shape of a neighborhood is determined by the choice of a distance function for two points p and q, denoted by dist(p, q). Two parameters mentioned here are an Eps-neighborhood of a point, defined by dist(p, q) ≤ Eps, and the minimum number of points (MinPts) in that Eps-neighborhood [14].

density[?dens?ti]：密度

exceed[?k?si?d]：v.超過

denote [d??n??t]：v.表示

????????DBSCAN的主要思想是尖阔，簇中的每一個點介却，在給定半徑內(nèi)至少有minimum個點齿坷。也就是說永淌，該點鄰近范圍內(nèi)的密度必須超過某個閾值遂蛀。鄰近范圍的形狀取決于距離函數(shù)的選擇李滴，關(guān)鍵點在于p與q悬嗓，用dist(p, q)表示裕坊。提到的這兩個參數(shù)周瞎，決定了該點的Eps領(lǐng)域范圍声诸，需要滿足dist(p, q) ≤ Eps彼乌。同時慰照，在該Eps領(lǐng)域范圍內(nèi)毒租，有至少MinPts個點墅垮。

????????For a data set in two dimensions, the distance between two points p(tp, hp) and q(tq, hq) is defined as

公式1

where t represents delta_time in Fig. 1, which can be considered as an along-track distance, and h represents elevation. tscale and hscale are used for normalization so that the points in the test data set have comparable order over t- and h-axes. Hence, dist(p, q) is now unitless.

unitless：無單位的

????????對于二維數(shù)據(jù)集算色，點p(tp, hp)與q(tq, hq)之間的距離可以表示為公式1剃允。其中斥废，t表示圖1中的delta_time牡肉，可以理解成沿軌距離。h表示高度饲窿。tscale和hscale用于標(biāo)準(zhǔn)化逾雄，以便測試數(shù)據(jù)集中的點在T軸和H軸上具有可比較的順序鸦泳。因此做鹰，dist（p钾麸，q）現(xiàn)在是無單位的饭尝。

????????In our algorithm, since most of the clusters (surface returns) have higher density in the horizontal than the vertical direction, it is reasonable to modify the shape of search area accordingly. Therefore, the distance between points p(tp, hp) and q(tq, hq) is now modified as

公式2

horizontal[?h?r??z?ntl]：水平的

vertical[?v??t?kl]：垂直的

? ? ? ? 在我們的算法中芋肠，由于絕大多數(shù)簇（地表返回的）在水平方向有比垂直方向更高的密度奈惑，因此相應(yīng)地改變搜索區(qū)域的形狀是合理的肴甸。距離表示公式修改如公式2所示原在。

????????As can be seen in Fig. 3, the search area is modified as an ellipse with centroid p, major axis with length 2a, and minor axis with length 2b, while a > b. Due to the change in search area, points in the horizontal direction have more weight with respect to the search area center than points in the vertical direction. Therefore, continuous points in a roughly horizontal direction are more likely to be classified as belonging to the cluster. That is also the same as in the detection of ground for MABEL lidar point clouds.

圖3

?with respect to：關(guān)于庶柿、至于

roughly[?r?fli]：大約

????????由圖3看到，搜索區(qū)域變成了一個橢圓审残，中心點為p搅轿，長軸長2a璧坟，短軸長2b（a>b）沸柔。由于搜索區(qū)域的改變褐澎，水平方向上的點相較于垂直方向上的工三，有更高的權(quán)重俭正。因此掸读，在大致水平方向上的連續(xù)點儿惫，更容易被劃分成屬于這一簇肾请。這同樣適用于MABEL雷達(dá)點云對地面的勘測結(jié)果隔显。

C. Estimation of Clustering Parameters

????????As the ellipse shape is determined by a and b in (2), two parameters are needed for modified DBSCAN implementation: MinPts and Eps. Here, we develop a simple but effective heuristic way to determine the two parameters. For simplicity, Eps = 2 is used all the time so that only MinPts will be modified. It can be done by estimating the average point density within the search ellipse.

heuristic[hju?r?st?k]：啟發(fā)式的

simplicity[s?m?pl?s?ti]：簡單

? ? ? ?在公式2中括眠， 橢圓的形狀由參數(shù)a與b決定哺窄。兩個參數(shù)MinPts與Eps，在改進后的DBSCAN中很重要奸柬。我們使用了一個簡單但是有效的方法去決定這兩個參數(shù)。簡單起見桌粉，Eps=2被廣泛應(yīng)用铃肯，因而只有MinPts需要被改變押逼。這可以通過估算一個橢圓區(qū)域內(nèi)的平均點云密度實現(xiàn)挑格。

? ? ? ? 1）A partition of points from the test data set is first extracted. This example covers a flight time of δt and an elevation range of δh. The area S of this sample data set is

公式3

partition[pɑ??t??n]：分割

extracted[?k?str?kt?d]：提取

? ? ? ? 首先雾消，從測試數(shù)據(jù)集中提取一個點分區(qū)仪或。它覆蓋的飛行時間為δt范删，高度范圍為δh。則該樣本數(shù)據(jù)集的區(qū)域S可表示為公式3添忘。

????????2) ?For an ellipse with dist(p, q) = Eps, its area s1 is

公式4

where a = 0.5 and b = 0.2. Hence, the number of ellipses within the example data set is roughly estimated as S/s1.

? ? ? ? 當(dāng)該橢圓dist(p, q) = Eps時搁骑，其區(qū)域面積s1可表示為公式4。其中乏冀，a=0.5辆沦，b=0.2肢扯。因此蔚晨，數(shù)據(jù)集中橢圓的數(shù)量可估計為S/s1蛛株。

????????3）The number of points in the example data set is found to be N . Therefore, the average point density (ρ) within the search ellipse can be calculated

公式5

? ? ? ? 數(shù)據(jù)集中的點數(shù)量為N欢摄。因此怀挠，一個搜索橢圓區(qū)域內(nèi)的平均點密度(ρ)可按照公式5計算。

????????4) To better estimate ρ, more than one of the example data sets are extracted from the test data set, processed through steps 1) to 3), and then averaged. In the proposed clustering method, the point density for clusters should be higher than the average density of the whole data set. MinPts can be empirically estimated as

公式6

proposed：提議吞滞，打算

empirically[?m?p?r?kl] ：經(jīng)驗性的

? ? ? ? 為了更好的估算ρ，選取多個樣本數(shù)據(jù)集重復(fù)進行步驟一至步驟三佩捞，然后取平均值。在提出的聚類方法中蕾哟，聚類的點密度要比整個數(shù)據(jù)集的平均密度ρ高一忱。按經(jīng)驗，MinPts估計為公式6谭确。

Practically, we can always start with the minimum integer larger than 4ρ and increase by one gradually. For the simulated photon-counting lidar data sets as in Fig. 1, ρ ≈ 0.3, and MinPts = 4 is finally applied. For the MABEL data sets as in Fig. 2, ρ ≈ 3.7, and MinPts = 16 is used. This proposed clustering algorithm can be quickly implemented and adaptive to photon-counting lidar data sets with different point densities.

Practically[?pr?kt?kli]：實際上

實際上帘营，我們一般從大于4ρ的最小整數(shù)開始琼富，然后逐一增加仪吧。圖一模擬的光子計數(shù)雷達(dá)數(shù)據(jù)，應(yīng)用ρ ≈ 0.3鞠眉，MinPts = 4薯鼠。圖二的MABEL數(shù)據(jù)集，應(yīng)用ρ ≈ 3.7械蹋，MinPts = 16出皇。提出的聚類算法可以改進應(yīng)用于各種不同點密度的光子計數(shù)雷達(dá)數(shù)據(jù)。

IV. PERFORMANCE AND EVALUATION

????????Our algorithm is tested using the aforementioned two sets of photon-counting laser altimeter data. In the first principle simulation, parameter p in the filter for generating the 3D synthetic surface is 2.0 [15]. The noise rate is set as 2 MHz. As can be seen in Fig. 4, surface returns can be reliably classified as ground returns using the proposed algorithm. A quantitative evaluation on the performance of the proposed method is presented later.

aforementioned[??f??men??nd]：前面提到的

synthetic[s?n?θet?k]：合成的

quantitative [?kw?nt?t?t?v]：定量性的

? ? ? ? 利用之前提到的兩組光子計數(shù)激光測高數(shù)據(jù)哗戈，對該算法進行測試郊艘。在第一原則模擬中，用于生成三維合成曲面的1/f^p濾波器的參數(shù)p為2.0唯咬。噪聲率設(shè)為2兆赫纱注。由圖4看出，使用該算法胆胰，surface returns可以可靠地被歸類為ground returns狞贱。隨后對該方法的性能進行了定量評價。

圖4

????????This density-based clustering approach is also tested for the MABEL data set. For the experimental data set, the classification result is shown in Fig. 5, which demonstrates that the proposed algorithm is capable of detecting both canopy and ground surface. The adaptive nature of our proposed algorithm allows it to work on a variety of surfaces and with data from a variety of photon-counting lidars. More classification results using the proposed algorithm for surface detection are presented in another letter [20], where point clouds of photon-counting lidar collected from different scenes and atmospheric conditions are studied.

experimental[?k?sper??mentl]：實驗性的

demonstrates[?dem?nstre?ts]：v.證明

atmospheric?conditions[??tm?s?fer?k]：大氣條件

????????這種基于密度的聚類方法同樣被應(yīng)用于MABEL數(shù)據(jù)集蜀涨。實驗數(shù)據(jù)集的分類結(jié)果如圖5所示瞎嬉，這也證明了該算法同時適用于檢測冠層與地表。該算法的自適應(yīng)性質(zhì)允許它在各種表面上工作厚柳，能夠使用來自各種光子計數(shù)激光雷達(dá)的數(shù)據(jù)氧枣。使用該算法檢測表面的更多分類結(jié)果在文章[20]中有說明，其中研究了從不同場景和大氣條件下收集的光子計數(shù)激光雷達(dá)的點云别垮。

圖5

????????To quantitatively evaluate the performance of the proposed algorithm, ground truth information is required. From the synthetic terrain, a 2-D profile of illuminated terrain can be directly extracted, which contains ground elevation versus flight distance or time. Note that the laser footprint has a radius of 5 m. Hence, due to the variance of ground within the circular laser footprint, it is hard to designate the returning photon to a specific location within the illuminated area.

terrain [t??re?n]：地形便监，地勢

profile[?pr??fa?l]：概述，簡介碳想，側(cè)面輪廓

illuminated[??lu?m?ne?t?d] ：被照明的

versus[?v??s?s]：與...相對

designate[?dez?ɡne?t] ：指定

? ? ? ? 為了定量評測該算法的性能茬贵，需要地面真實信息。從合成地形中移袍，我們可以直接提取到一個被照射地形的二維剖面解藻，其中包含地面高度與飛行距離或者時間。請注意葡盗，激光足跡的半徑為5m螟左。因此，由于在一個圓形激光足跡中地表的變化觅够，我們很難把返回的光子指定到被照射區(qū)域中的一個確定位置胶背。

A statistical method is then necessary to define a region for accuracy evaluation. Here, an upper/lower boundary along the 2-D ground truth is created with a specific height above/below the terrain profile. The two boundaries enable a window which can be regarded as the criterion of true surface returns. Therefore, each photon is assigned to an elevation with respect to flight distance and can be categorized as surface returns if it is within the contour “window.” A height of 10 cm, which is close to the expected elevation bias standard deviation for ICESat-2, is chosen for performance assessment [15], [16].

statistical[st??t?st?kl]：統(tǒng)計學(xué)的

region[?ri?d??n]：區(qū)域

with respect to ：關(guān)于

criterion[kra??t??ri?n]：n.標(biāo)準(zhǔn)

categorize[?k?t?ɡ?ra?z] ：分類

bias[?ba??s]：偏向

deviation[?di?vi?e??n]：偏離

需要一個統(tǒng)計學(xué)的方法來定義準(zhǔn)確評估的區(qū)域。于是喘先，沿二維地面實況創(chuàng)建上／下邊界钳吟，在地形剖面上／下有一個確定高度。兩個邊界組成的窗口窘拯，可以被認(rèn)為是正確地面返回的標(biāo)準(zhǔn)红且。因此坝茎，每個光子都被分配到一個與飛行距離有關(guān)的高度，并且如果它在輪廓“窗口”內(nèi)暇番，則可以被歸類為表面返回嗤放。選擇高度10cm來進行性能評估，這個高度接近ICESat-2預(yù)期高度偏向標(biāo)準(zhǔn)偏離的值壁酬。

? ??????In addition, the statistical indicators known as recall and precision are computed. Recall R is the fraction of true signal points that are successfully enclosed within the contour window. Precision P is the fraction of true signal points from all points enclosed within the detected contours. They are defined as follows [21]:

indicators[??nd?ke?t?z] ：指標(biāo)

fraction[?fr?k?n]：少量次酌，分?jǐn)?shù)

contour [?k?nt??(r)] ：輪廓

? ? ? ? 另外，計算了作為統(tǒng)計指標(biāo)的召回率和準(zhǔn)確度舆乔。R=被預(yù)測為地面返回且成功落在窗口內(nèi)的點的數(shù)量／所有落在窗口內(nèi)的信號點的總數(shù)岳服，P=被預(yù)測為地面返回且成功落在窗口內(nèi)的點的數(shù)量／被預(yù)測為是地面返回點的總數(shù)。這些在文章[21]中定義希俩。

公式7

where TP , FP , and FN represent the numbers of true positives (hit), false positives (false alarm)m and false negatives (miss), respectively. To be more specific, true positives represent points that are enclosed in the contour window being detected as surface returns, and false positives represent points that are not enclosed in the contour window being detected as surface returns. For better estimation, the proposed algorithm is evaluated for five sets of point clouds, each of which was collected by different test tracks (as shown in Fig. 6).

respectively[r??spekt?vli]：分別地

其中TP表示將正類預(yù)測為正類數(shù)吊宋，F(xiàn)P將負(fù)類預(yù)測為正類數(shù)（誤報），F(xiàn)N表示將正類預(yù)測為負(fù)類數(shù)（漏報）斜纪。更詳細(xì)的說贫母，TP表示落在框內(nèi)且被預(yù)測為是地面返回的點數(shù)，F(xiàn)P表示沒落在框內(nèi)卻被預(yù)測為是地面返回的點數(shù)盒刚。為了更好地估計腺劣，對五組點云進行了評估，每個點云由不同的測試軌道收集因块。（如圖六所示）

圖6

????????For each track, a statistical indicator is calculated to find TP, FP, and FN, respectively. As can be seen in Fig. 7, the contour window is labeled as a black dashed line. Returns classified as ground and enclosed inside the window are TP (Hit), and those not enclosed inside the window are FP (False Alarm). Mean- while, classified noise enclosed inside the window is FN (Miss).

dashed line[d??t]：虛線

? ? ? ? 針對每一個軌道橘原，計算一個統(tǒng)一指標(biāo)去找到TP, FP和FN。如圖7所示涡上，輪廓窗口標(biāo)記為黑色虛線趾断。被預(yù)測為地面返回且落在窗口內(nèi)的是TP (Hit)。被預(yù)測為地面返回但未落在窗口內(nèi)的是FP (False Alarm)吩愧。同時芋酌，被預(yù)測為噪點但落在窗口內(nèi)的是FN (Miss)。

圖7

????????In order to use a single performance measure that will allow for comparison of results, the harmonic mean of recall and precision will be used

公式8

For all five tracks, the F-measure value is calculated, respectively, and then averaged. Thus, uncertainty caused by ground surface variation will be mitigated. The result of F-measure versus surface roughness parameter p is shown in Fig. 8. Note that, as p increases, the synthetic terrain becomes less rough [15] and the F-measure increases significantly from 0.58 to 0.86. Therefore, the proposed algorithm has better performance on a smoother surface.

harmonic mean[hɑ??m?n?k mi?n]：調(diào)和平均數(shù)

roughness [r?fn?s] ：粗糙

? ??????為了使用一個允許結(jié)果比較的單一性能度量雁佳，將使用召回和精度的調(diào)和平均值脐帝。分別計算這五組軌跡的F-measure值，并選取平均數(shù)糖权。F-測量值與表面粗糙度參數(shù)P的對比結(jié)果如圖8所示堵腹。注意，隨著P值的增加星澳，合成地形變得不那么粗糙[15]疚顷，F(xiàn)值從0.58顯著增加到0.86。因此，該算法在光滑表面上具有較好的性能腿堤。

圖8

? ??????In addition, the impact of noise rate is studied. Noise rate varies based on atmospheric and solar conditions: 0.5 MHz simulates nighttime acquisitions, while 2 and 5 MHz represent daytime acquisitions with clear sky and hazy atmosphere, respectively [19]. As we increase the noise rate from 0.5 to 5 MHz, the F-measure maintains an average of 0.8 (blue curve in Fig. 9), and the elliptical DBSCAN algorithm is seen to be robust. However, it is shown that lower noise rate will lead to slightly better detection performance.

nighttime[?na?tta?m]：夜間

acquisition[??kw??z??n]：獲得阀坏，采集

robust[r???b?st]：強健的

????????此外，還研究了噪聲率的影響释液。噪聲率根據(jù)大氣和太陽條件而變化：0.5兆赫模擬夜間采集全释，而2兆赫和5兆赫分別代表晴空和朦朧大氣的白天采集[19]装处。當(dāng)我們將噪聲率從0.5兆赫增加到5兆赫時误债，f-測量保持0.8的平均值（圖9中的藍(lán)色曲線），并且橢圓DBSCAN算法被認(rèn)為是穩(wěn)健的妄迁。然而寝蹈，研究表明，較低的噪聲率會使檢測性能稍有改善登淘。

圖9

? ??????Meanwhile, the improvement of ground detection accuracy is studied using the proposed elliptical DBSCAN over the conventional circle DBSCAN method. For comparison, all parameters used in the proposed algorithm remain the same for the circle DBSCAN method, except that in (2), in which a = b = 0.5 is used to change the search area to a circle. The result of ground detection accuracy using circle DBSCAN is plotted in red color in Fig. 9. With a low noise rate (around 1 MHz), both reach the F-measure of around 0.8. As the noise rate increases, the ground detection accuracy is significantly improved while using elliptical DBSCAN method. This quantitative plot also shows that the proposed method using elliptical DBSCAN has better performance despite the solar noise rate. Note that this conclusion works for photon-counting laser altimeter data whose point density of surface returns is higher than the background noise. If the surface return rate is too low to visually distinguish surface returns from noise, it is difficult to achieve good performance of the proposed algorithm.

conventional[k?n?ven??nl]：常規(guī)的

同時箫老，在常規(guī)圓DBSCAN方法的基礎(chǔ)上，利用該橢圓DBSCAN方法對提高地面探測精度進行了研究黔州。比較而言耍鬓，除了（2）中的參數(shù)外，該算法中使用的所有參數(shù)對圓DBSCAN方法保持不變流妻，其中a=b=0.5用于將搜索區(qū)域更改為圓牲蜀。使用圓DBSCAN的地面檢測精度結(jié)果，用紅色繪制在圖9中绅这。在低噪聲率（1兆赫左右）下涣达，兩者都達(dá)到了0.8左右的F測量值。隨著噪聲率的增加证薇，采用橢圓DBSCAN方法可以顯著提高地面檢測精度度苔。這定量圖也表明，在太陽噪聲率較高情況下浑度，橢圓DBSCAN具有更好的性能寇窑。注意，這個結(jié)論適用于光子計數(shù)激光高度計數(shù)據(jù)箩张，其表面回波的點密度高于背景噪聲。如果表面返回率太低横漏，無法從視覺上區(qū)分表面返回和噪聲熟掂，則很難實現(xiàn)該算法的良好性能。

V. CONCLUSION

????????In this letter, a density-based algorithm has been proposed for classifying photon-counting lidar point clouds as surface or noise returns. In consideration of finding surface returns more accurately from the lidar point cloud, the area shape of a data point search for its nearest neighbors was modified to be an ellipse to match general characteristics of terrain or vegetation. This adaptive clustering method was then implemented and tested on photon-counting lidar altimetry data. Validation showed that surface and canopy can be expected to be observable using the proposed algorithm during the ICESat-2 mission. Performance measurement demonstrated that this method has better performance for smoother surfaces and lower noise rate conditions.

????????本文提出了一種基于密度的光子計數(shù)激光雷達(dá)點云分類算法素跺。為了從激光雷達(dá)點云中，更準(zhǔn)確地找到地表回波指厌，將最近鄰點數(shù)據(jù)點搜索的面積形狀修改為橢圓，以匹配地形或植被的一般特征踩验。然后對光子計數(shù)激光雷達(dá)測高數(shù)據(jù)進行了自適應(yīng)聚類測試。驗證結(jié)果表明牡借，在ICESAT-2任務(wù)中袭异，利用該算法可以觀測到地表和樹冠。性能測試結(jié)果表明御铃，該方法在光滑表面和低噪聲條件下具有較好的性能碴里。

????????Future work will consider the following issues. First, in our current work, only objects which have high density in horizontal direction were studied. We will develop a definition to extend the approach for more complicated objects such as steep crevasses in photon-counting point cloud. Second, more realistic lidar data sets will be studied to evaluate the proposed algorithm performance for more complicated terrains and atmospheric conditions. Third, additional tests will be performed to quantify the algorithm performance in detecting both vegetation canopy and ground in dense forests.

steep crevasses [sti?p kr??v?s?z]：陡峭的裂縫

quantify[?kw?nt?fa?]：量化

????????今后的工作將考慮以下問題。首先上真，在我們目前的工作中咬腋，只研究水平方向具有高密度的物體。我們將發(fā)展一個定義來擴展對更復(fù)雜物體的方法谷羞，例如光子計數(shù)點云中的陡峭裂縫帝火。其次，將研究更真實的激光雷達(dá)數(shù)據(jù)集湃缎，以評估所提出的算法在更復(fù)雜的地形和大氣條件下的性能犀填。第三，將進行額外的測試嗓违，量化算法在密林植被冠層和地面檢測中的性能九巡。

個人總結(jié)

一、DBSCAN算法改進

1. 原DBSCAN算法

（1）概述

某樣本在eps距離內(nèi)有至少MinPts個樣本蹂季，則該樣本可以成為核樣本冕广。通過找到一個核樣本，找到其附近的核樣本偿洁，再找到附近核樣本的附近的核樣本撒汉。遞歸尋找。形成一個高密度區(qū)域涕滋。

（2）核樣本的鄰域

半徑為Eps的圓睬辐，當(dāng)時，說明q在p的鄰域內(nèi)。

（3）Dist(p,q)定義

Fig.1

如圖Fig.1所示溯饵，二維數(shù)據(jù)集侵俗，存在點p(tp, hp)與q(tq, hq)丰刊，t表示delta_time啄巧，h表示Elevation棵帽。

Dist(p,q)可以表示為：

公式1

其中逗概，tscale和hscale用于標(biāo)準(zhǔn)化逾苫，以便測試數(shù)據(jù)集中的點在T軸和H軸上具有可比較性铅搓。

2. 改進DBSCAN算法

（1）概述

????????由于本實驗中，絕大多數(shù)簇在水平方向有比垂直方向更高的密度嫩舟，因此播玖，Eps鄰域范圍由圓改進為橢圓蜀踏。

（2）核樣本的鄰域

????????橢圓掰吕。同樣局待，當(dāng)時燎猛，說明q在p的鄰域內(nèi)重绷。

（3）Dist(p,q)定義

Fig.2

????????Dist(p,q)可以表示為：

公式2

????????則根據(jù)愤钾，可推導(dǎo)出橢圓公式為：

????????可知，該橢圓長軸長為伙菊，短軸長為

二镜硕、改進DBSCAN算法的參數(shù)估算

1. Eps

????????Eps兴枯，取用常見數(shù)值2

2. MinPts

（1）總面積：

（2）一個橢圓的面積：

????其中财剖，a=0.5躺坟，b=0.2【論文中并沒有給出選取值的理由】

（3）總點數(shù)：

（4）一個橢圓內(nèi)的平均點數(shù)：

（5）多次計算，求取平均值得到最終值匣摘。MinPts需滿足：

3. 實驗選取值

????????MinPts值音榜，從大于4ρ的最小整數(shù)開始赠叼，逐一增加。模擬光子計數(shù)雷達(dá)數(shù)據(jù)瞬场，應(yīng)用ρ ≈ 0.3贯被，MinPts = 4彤灶。MABEL數(shù)據(jù)集幌陕，應(yīng)用ρ ≈ 3.7搏熄，MinPts = 16搬卒。

三、定量評測改進算法的性能

1. 定義True Surface Returns

????????沿二維地面實況失暴，創(chuàng)建上／下邊界逗扒，高度為10cm。兩個邊界組成的窗口肃续，可以被認(rèn)為是True Surface Returns的標(biāo)準(zhǔn)刽酱。因此棵里，如果一個光子，在輪廓“窗口”內(nèi)典蝌，則可以被歸類為Surface Returns赠法。圖Fig.3中砖织，黑色虛線即為輪廓窗口侧纯。

Fig.3

2. 計算Recall、Precision娜氏、F-Measure

? ? ? ? 選取五條軌跡贸弥。針對每一個軌道绵疲，計算TP, FP和FN盔憨。如圖Fig.3所示郁岩，輪廓窗口標(biāo)記為黑色虛線问慎。被預(yù)測為地面返回且落在窗口內(nèi)的是TP (Hit)蝴乔。被預(yù)測為地面返回但未落在窗口內(nèi)的是FP (False Alarm)薇正。同時挖腰，被預(yù)測為噪點但落在窗口內(nèi)的是FN (Miss)审轮。

? ? ? ? 根據(jù)公式計算Recall疾渣、Precision榴捡、F-Measure：

???

? ??????分別計算這五組軌跡的F-measure值吊圾，并選取平均數(shù)项乒。

3. 實驗結(jié)果一：F-Measure與表面粗糙度參數(shù)P的關(guān)系

????????F-Measure與表面粗糙度參數(shù)P的對比結(jié)果，如Fig.4所示趁尼。隨著P值的增加，合成地形變得不那么粗糙啃憎，F(xiàn)值從0.58顯著增加到0.86悯姊。因此贩毕，該算法在光滑表面上具有較好的性能先壕。

Fig.4

4. 實驗結(jié)果二：F-Measure與噪聲率

????????噪聲率根據(jù)大氣和太陽條件而變化：0.5MHz模擬夜間采集，2MHz和5MHz分別代表晴空和朦朧大氣的白天采集[19]集绰。

????????當(dāng)我們將噪聲率從0.5MHz增加到5MHz時栽燕，F(xiàn)-Measure保持0.8的平均值（Fig.5中的藍(lán)色曲線）碍岔，因此該橢圓DBSCAN算法被認(rèn)為是穩(wěn)健的蔼啦。除此之外询吴，研究發(fā)現(xiàn)猛计，較低的噪聲率會使檢測性能稍有改善奉瘤。

Fig.5

5. 實驗結(jié)果三：對比改進前后的DBSCAN算法

????????圓DBSCAN算法中，更改參數(shù)a=b=0.5成肘，用于將搜索區(qū)域更改為圓砚偶。其余參數(shù)不變染坯。使用圓DBSCAN的地面檢測精度結(jié)果单鹿，用紅色繪制在圖Fig.5中仲锄。

????????在低噪聲率（1兆赫左右）下，兩者都達(dá)到了0.8左右的F-Measure是趴。隨著噪聲率的增加唆途，采用橢圓DBSCAN方法可以顯著提高地面檢測精度。 這定量圖也表明温赔，在太陽噪聲率較高情況下鬼癣，橢圓DBSCAN具有更好的性能拜秧。

????????注意章郁，該結(jié)論適用于其表面回波的點密度高于背景噪聲聊替。如果表面返回率太低培廓，無法從視覺上區(qū)分表面返回和噪聲肩钠，則很難實現(xiàn)該算法的良好性能蔬将。