高速角點(diǎn)檢測的機(jī)器學(xué)習(xí)

1、Machine learning for high-speed corner detection高速角點(diǎn)檢測的機(jī)器學(xué)習(xí)Edward Rosten and Tom DrummondDepartment of Engineering, Cambridge University, UKAbstract Where feature points are used in real-time frame-rate applications, a high-speed feature detector is necessary. Feature detectors such as SIFT (DoG), H

2、arris and SUSAN are good methods which yield high quality features, however they are too computationally intensive for use in real-time applications of any complexity. Here we show that machine learning can be used to derive a feature detector which can fully process live PAL video using less than 7

3、% of the available processing time. Bycomparison neither the Harris detector (120%) nor the detection stage of SIFT (300%) can operate at full frame rate.摘要當(dāng)實(shí)時(shí)幀速率應(yīng)用中檢測特征點(diǎn)時(shí)，我們必須采用一種高速特征探測器。當(dāng)探測高質(zhì)量特征時(shí)，使用特征探測器例如SIFT (DoG)（尺度不變特征轉(zhuǎn)換），Harris（角點(diǎn)檢測），SUSAN（SUSAN角點(diǎn)檢測算法）是好的方法，然而他們?cè)趯?shí)時(shí)處理復(fù)雜圖形的應(yīng)用中，數(shù)據(jù)量計(jì)算量太大。我們?cè)谶@篇文章中

4、展示的機(jī)器學(xué)習(xí)能夠驅(qū)動(dòng)一種特征探測器，這種方法可以完全處理實(shí)時(shí)PAL制式視頻，比起現(xiàn)可行的方法可以減少7%的處理時(shí)間。通過比較，Harris探測（120%的時(shí)間）或者SIFT（300%的時(shí)間）都不能以全幀速率運(yùn)行。Clearly a high-speed detector is of limited use if the features produced are unsuitable for downstream processing. In particular, the same scene viewed from two different positions should yield

5、 features which correspond to the same real-world 3D locations1. Hence the second contribution of this paper is a comparison corner detectors based on this criterion applied to 3D scenes. This comparison supports a number of claims made elsewhere concerning existing corner detectors. Further, contra

6、ry to our initial expectations, we show that despite being principally constructed for speed, our detector significantly outperforms existing feature detectors according to this criterion.明顯地，一個(gè)高速探測器的使用是會(huì)受限制的如果特征的產(chǎn)生與下一步處理不匹配。特別的，從倆個(gè)不同的位置看相同的場景得到的特征應(yīng)該與真實(shí)世界三維實(shí)物相吻合。因此這篇文章的第二個(gè)貢獻(xiàn)是，提出了一個(gè)基于上述準(zhǔn)則的3D場景角比較探測器。

7、這種比較支持許多其他現(xiàn)有角點(diǎn)探測器的功能。此外，與我們最初的期望相反，我們發(fā)現(xiàn)，盡管我們創(chuàng)造這種探測器主要是為了提高運(yùn)算速度，然而就針對(duì)上述準(zhǔn)則，我們的探測器明顯優(yōu)于其他現(xiàn)存特征檢測器。1 Introduction Corner detection is used as the first step of many vision tasks such as tracking,SLAM (simultaneous localisation and mapping), localisation, image matching and recognition. Hence, a large numb

8、er of corner detectors exist in the literature. With so many already available it may appear unnecessary to present yet another detector to the community; however, we have a strong interest in real-time frame rate applications such as SLAM in which computational resources are at a premium. In partic

9、ular, it is still true that when processing live video streams at full frame rate, existing feature detectors leave little if any time for further processing, even despite the consequences of Moores Law.引言角點(diǎn)檢測是許多視覺工作的第一步，例如跟蹤、SLAM（同步定位與測圖）、定位、圖像匹配和識(shí)別。因此文獻(xiàn)中大量介紹角點(diǎn)檢測器。已經(jīng)有如此多的角點(diǎn)探測存在，我們也許沒有必要把另一個(gè)探測器呈現(xiàn)給社會(huì)

10、。然而，我們有強(qiáng)烈的興趣針對(duì)實(shí)時(shí)幀速率應(yīng)用，例如SLAM，在這里面計(jì)算資源是非常珍貴的。特別地，盡管摩爾定律的結(jié)果證明可以，但當(dāng)我們?cè)谝匀珟俾侍幚硪曨l直播流時(shí)，現(xiàn)有的特征檢測器幾乎沒有留出時(shí)間來進(jìn)行深沉次的處理。 Section 2 of this paper demonstrates how a feature detector described in earlier work can be redesigned employing a machine learning algorithm to yield a large speed increase. In addition, the

11、 approach allows the detector to be generalised, producing a suite of high-speed detectors which we currently use for real-time tracking 2 and AR label placement 3.在文章的第二部分證明了，通過使用機(jī)器學(xué)習(xí)算法，在早期的工作中應(yīng)用的特征檢測器可以被重新設(shè)計(jì)，從而達(dá)到一個(gè)速度的提升。此外，這種方法允許檢測器被廣泛推廣，生成一系列高速探測器，我們目前將他們用于實(shí)時(shí)跟蹤和AR標(biāo)簽位置To show that speed can been o

12、btained without necessarily sacrificing the quality of the feature detector we compare our detector, to a variety of well-known detectors. In Section 3 this is done using Schmids criterion 1, that when presented with different views of a 3D scene, a detector should yield (as far as possible) corners

13、 that correspond to the same features in the scene. Here we show how this can be applied to 3D scenes for which an approximate surface model is known.為了說明我們的探測器在獲得速度的提升的同時(shí)，沒有犧牲特征探測器的質(zhì)量，我們將我們的探測器和一系列知名的探測器做了比較。在第三部分，我們通過使用施密德的標(biāo)準(zhǔn)來完成對(duì)比，當(dāng)展現(xiàn)三維場景的不同角度，探測器應(yīng)該服從（盡可能）角，這些角符合場景中相同的特征。這里我們展示這種探測器如何被應(yīng)用于3D場景中，模型表

14、面是近似已知的。1.1 Previous workThe majority of feature detection algorithms work by computing a corner response function (C) across the image. Pixels which exceed a threshold cornerness value (and are locally maximal) are then retained.Moravec 4 computes the sum-of-squared-differences (SSD) between a patc

15、h around a candidate corner and patches shifted a small distance in a number of directions. C is then the smallest SSD so obtained, thus ensuring that extracted corners are those locations which change maximally under translations.Harris5 builds on this by computing an approximation to the second de

16、rivative of the SSD with respect to the shift .The approximation is: （1）先前的工作大多數(shù)特征檢測算法在檢測圖像時(shí)，是計(jì)算一個(gè)角響應(yīng)函數(shù)（C）。像素點(diǎn)超過一個(gè)角點(diǎn)門限值（是局部最大值）就被保存下來。Moravec 在候補(bǔ)角點(diǎn)和周圍的小塊像素值之間計(jì)算平方差之和（SSD），這些小的像素塊在不同方向上都有，且只移動(dòng)一點(diǎn)點(diǎn)距離(灰度方差)。C取SSD算法最小值，從而保證提取的角點(diǎn)是那些沿著各個(gè)方向改變最大的點(diǎn)。Harris算法是計(jì)算一個(gè)相對(duì)于移位的SSD的二階導(dǎo)數(shù)的近似值。近似值是 （1）where denotes averagi

17、ng performed over the image patch (a smooth circular window can be used instead of a rectangle to perform the averaging resulting in a less noisy, isotropic response). Harris then defines the corner response to be （2）上述公式中表示像斑的平均值，一個(gè)光滑的圓形窗口可以代替一個(gè)矩形，從而來執(zhí)行平均值，導(dǎo)致小的噪聲產(chǎn)生。然后Harris定義角響應(yīng)為： （2）This is large

18、if both eigenvalues of H are large, and it avoids explicit computation of the eigenvalues. It has been shown6 that the eigenvalues are an approximate measure of the image curvature.C值是大的如果倆個(gè)H的特征值是大的，并且避免了直接計(jì)算特征值。已經(jīng)證明特征值可以大約測試出圖像曲率Based on the assumption of affine image deformation, a mathematical an

19、alysis led Shi and Tomasi7 conclude that it is better to use the smallest eigen value of H as the corner strength function: （3）A number of suggestion have 5,7,8,9 been made for how to compute the corner strength from H and these have been all shown 10 to be equivalent to various matrix norms of H 基于

20、圖像仿射變換的假設(shè)，經(jīng)過數(shù)學(xué)的推導(dǎo)分析，Shi and Tomasi證明最好是使用H的最小特征值做為角強(qiáng)度函數(shù)： （3）關(guān)于怎樣使用H計(jì)算角強(qiáng)度，許多建議已經(jīng)被提出，這些結(jié)果都和H不同的矩陣范數(shù)相等。 Zheng et al.11 perform an analysis of the computation of H, and find some suitable approximations which allow them to obtain a speed increase by computing only two smoothed images, instead of the thr

21、ee previously required.Lowe 12 obtains scale invariance by convolving the image with a Difference of Gaussians (DoG) kernel at multiple scales, retaining locations which are optima in scale as well as space. DoG is used because it is good approximation for the Laplacian of a Gaussian (LoG) and much

22、faster to compute. An approximation to DoG has been proposed which, provided that scales are apart,speeds up computation by a factor of about two, compared to the striaght forward implementation of Gaussian convolution 13. Zheng et al.分析了H的計(jì)算結(jié)果，并且找到了一些合適的近似值，這些值允許我們只計(jì)算倆個(gè)平滑像素，因?yàn)槿〈酥暗娜齻€(gè)數(shù)據(jù)，所以計(jì)算速度上獲得了提

23、升。Lowe得到了尺度不變性通過使用多級(jí)高斯差分來卷積像素，保留的位置既是尺度上的最優(yōu)化，又是空間的最優(yōu)解。DoG（高斯差分）被使用因?yàn)樗芎芎玫慕朴?jì)算出LoG（高斯拉普拉斯算子）并且計(jì)算的更快。DoG的一個(gè)近似值已經(jīng)被提出，證明尺度是分離，計(jì)算速度得到提升是通過倆個(gè)因素實(shí)現(xiàn)的，相比于直接用高斯卷積來計(jì)算。It is noted in 14 that the LoG is a particularly stable scale-space kernel.Scale-space techniques have also been combined with the Harris approac

24、h in 15 which computes Harris corners at multiple scales and retains only those which are also optima of the LoG response across scales.在14這篇文章中指出LoG（高斯拉普拉斯算子）是一個(gè)特別穩(wěn)定的多級(jí)空間的核。 在15中多級(jí)空間技術(shù)已經(jīng)結(jié)合了Harris算法，文章在多級(jí)計(jì)算Harris角并且保留LoG多級(jí)間響應(yīng)的最優(yōu)值。 Recently, scale invariance has been extended to consider features whi

25、ch are invariant to affine transformations 14,16,17.An edge (usually a step change in intensity) in an image corresponds to the boundary between two regions. At corners of regions, this boundary changes direction rapidly. Several techniques were developed which involved detecting and chaining edges

26、with a view to finding corners in the chained edge by analysing the chain code18, finding maxima of curvature 19,20,21, change in direction 22or change in appearance23. Others avoid chaining edges and instead look for maxima of curvature24 or change in direction 25 at places where the gradient is la

27、rge.最近，尺度不變性已經(jīng)擴(kuò)展到考慮一些特性，這些特性對(duì)仿射轉(zhuǎn)換不會(huì)發(fā)生改變的。圖像的邊緣（通常會(huì)有一個(gè)階躍性的強(qiáng)度改變）是和倆個(gè)區(qū)域的邊界相融合的。在區(qū)域的角落里，邊沿方向改變非常的快。有幾種技術(shù)已經(jīng)被開發(fā)，這些技術(shù)包括探測和鏈接邊緣，通過分析鏈碼，在被鏈接的邊緣用尋找角，找到曲率最大值，改變方向，或者改變外表。其他避免鏈接邊緣和取而代之尋找曲率的最大值或者在梯度大的地方改變方向。Another class of corner detectors work by examining a small patch of an image to see if it “l(fā)ooks” like a

28、corner. Since second derivatives are not computed, a noise reduction step (such as Gaussian smoothing) is not required. Consequently, these corner detectors are computationally efficient since only a small number of pixels are examined for each corner detected. A corollary（推論） of this is that they t

29、end to perform poorly on images with only large-scale features such as blurred images（模糊圖像）. The corner detector presented in this work belongs to this category.另一類角探測器工作時(shí)，檢測圖像的一小塊，來驗(yàn)證它是否像一個(gè)角。因?yàn)槎A導(dǎo)數(shù)沒有被計(jì)算出來，降噪這一步（例如高斯平滑）就是不需要的。結(jié)果這些角探測器計(jì)算特別有效率因?yàn)槊總€(gè)角探測器僅僅只需檢測小數(shù)量的像素。一個(gè)推論是這些角探測器運(yùn)行效果很差當(dāng)這些圖片僅有大數(shù)量級(jí)的特征例如模糊圖像。

30、在這篇文章中展示的角探測器就是屬于這個(gè)領(lǐng)域的。 The method presented in 26 assumes that a corner resembles a blurred wedge, and finds the characteristics of the wedge (the amplitude, angle and blur) by fitting it to the local image. The idea of the wedge is generalised in 27, where a method for calculating the corner stren

31、gth is proposed which computes self similarity by looking at the proportion of pixels inside a disc whose intensity is within some threshold of the centre (nucleus) value. Pixels closer in value to the nucleus receive a higher weighting. This measure is known as the USAN (the Univalue Segment Assimi

32、lating Nucleus). A low value for the USAN indicates a corner since the centre pixel is very different from most of its surroundings. A set of rules is used to suppress（抑制） qualitatively（質(zhì)量上） “bad” features, and then local minima of the, SUSANs, (Smallest USAN) are selected from the remaining candida

33、tes.在26中展示的方法假設(shè)角像一個(gè)模糊的楔形，并且通過局部圖像擬合來尋找楔形的特征（幅度，角度，和模糊度）。楔形的概念在27中有所概括，在這篇文章中提出一種計(jì)算角強(qiáng)度的方法，這種方法是通過計(jì)算光盤中像素的比例來計(jì)算自相似性地，他們的強(qiáng)度是在中心值閾值內(nèi)的。像素值離中心值更接近的占更高的權(quán)值。這種測量就是著名的USAN（同值收縮核區(qū)）算法。USAN的值低能證明是一個(gè)角因?yàn)橹行南袼厥桥c周圍環(huán)境非常不同的。一系列的規(guī)則被用來抑制質(zhì)量上差的點(diǎn)，并且標(biāo)出SUSANs,最小的值，最小的USAN被選出來從剩下的候選者。Trajkovic and Hedley28 use a similar idea:

34、a patch is not self-similar if pixels generally look different from the centre of the patch. This is measured by considering a circle. is the pixel value at the centre of the circle, and and are the pixel values at either end of a diameter line across the circle. The response function is defined as

35、(4)Trajkovic and Hedley使用了相似的觀點(diǎn)，如果像素是大體上與中心圖像塊不同的,小塊圖像就是不自相似的。這個(gè)可以通過一個(gè)圓進(jìn)行測量。就是圓中心像素值，并且和是圓直徑倆個(gè)端點(diǎn)的像素值。響應(yīng)函數(shù)被定義為 (4)This can only be large in the case where there corner. The test is performed on a Bresenham circle. Since the circle is discretized（離散）, linear or circular interpolation is used in betwee

36、n discrete orientations in order to give the detector a more isotropic （各向同性的）response. To this end, the authors present a method whereby the minimum response function at all interpolated（插值） positions between two pixels can be efficiently computed. Computing the response function requires performin

37、g a search over all orientations, but any single measurement provides an upper bound（上限） on the response. To speed up matching, the response in the horizontal and vertical directions only is checked. If the upper bound on the response is too low, then the potential corner is rejected. To speed up th

38、e method further,this fast check is first applied at a coarse scale.僅當(dāng)這個(gè)地方是角點(diǎn)的情況下C值是大的。這個(gè)測試是可以執(zhí)行在一個(gè)Bresenham圓上。因?yàn)閳A是離散的，線性，或者圓差值被用在不同的方向是為了給探測器一個(gè)各向同性的響應(yīng)。為此，作者提出了一個(gè)方法可以有效地計(jì)算出倆個(gè)像素間插值位置響應(yīng)函數(shù)的最小值。計(jì)算響應(yīng)函數(shù)需要對(duì)不同方向進(jìn)行計(jì)算，但是任何角度的測量結(jié)果都能為響應(yīng)提供一個(gè)上限值。為了加快匹配速度，我們僅僅檢查水平方向和豎直方向上響應(yīng)的值。如果響應(yīng)的上限值太低，那么潛在的角點(diǎn)是會(huì)被拒絕的。為了加快方法的速度，快速檢

39、查先在粗略的尺度上運(yùn)行一下。圖1.12是對(duì)一個(gè)圖像的角點(diǎn)測試，高亮度的正方形就是角點(diǎn)檢測中的像素。像素P是候選角點(diǎn)的中心，虛線標(biāo)出的弧穿過12個(gè)連續(xù)的像素，比p更亮的，都超過的門限值。A fast radial（徑向） symmetry transform is developed in 29 to detect points. Points have a high score when the gradient（梯度） is both radially symmetric, strong, and of a uniform sign along the radius（半徑）. The sca

40、le can be varied by changing the size of the area which is examined for radial symmetry.為了檢測角點(diǎn)，在29中介紹了一個(gè)快速徑向同步變換的方法。當(dāng)這些點(diǎn)梯度值是徑向?qū)ΨQ的，值高的并且沿著半徑是不統(tǒng)一的，那這些點(diǎn)分就會(huì)很高。通過改變鏡像面積，規(guī)?？梢允强勺兊?。An alternative method of examining a small patch of an image to see if it looks like a corner is to use machine learning to cla

41、ssify patches of the image as corners or non-corners. The examples used in the training set determine the type of features detected. In 30, a three layer neural（神經(jīng)） network is trained to recognise corners where edges meet at a multiple of 45, near to the centre of an 8 8 window. This is applied to i

42、mages after edge detection and thinning. It is shown how the neural net learned a more general representation and was able to detect corners at a variety of angles.檢查一小塊圖像是否像一個(gè)角，一個(gè)可行的方法是使用機(jī)器學(xué)習(xí)的方法，把圖像分類，分成是角點(diǎn)和非角點(diǎn)。在訓(xùn)練集中使用的例子決定了特征檢測的類型。在文章30中，一個(gè)三層的神經(jīng)網(wǎng)絡(luò)被訓(xùn)練來識(shí)別角，這些角有許多45度的角，在88窗口中心的附近。在邊緣檢測和變稀少完成后，圖像中就會(huì)應(yīng)用

43、這個(gè)神經(jīng)網(wǎng)絡(luò)。這個(gè)方法也證明了神經(jīng)單元是怎樣學(xué)習(xí)一個(gè)更廣泛的表像，并且能在各個(gè)角度探測角度。2 High-speed corner detection高速角探測2.1 FAST: Features from Accelerated Segment TestFAST：加速段檢測的特征The segment test criterion operates by considering a circle of sixteen pixels around the corner candidate p. The original detector 2,3 classifies p as a corner

44、 if there exists a set of n contiguous pixels in the circle which are all brighter than the intensity of the candidate pixel Ip plus a threshold t, or all darker than Ip t, as illustrated in Figure 1. n was chosen to be twelve because it admits a high-speed test which can be used to exclude a very l

45、arge number of non-corners: the test examines only the four pixels at 1, 5, 9 and 13 (the four compass directions). If p is a corner then at least three of these must all be brighter than Ip + t or darker than Ip t. If neither of these is the case, then p cannot be a corner. The full segment test cr

46、iterion can then be applied to the remaining candidates by examining all pixels in the circle. This detector in itself exhibits high performance, but there are several weaknesses:段檢測標(biāo)準(zhǔn)運(yùn)行通過檢測圓上16個(gè)像素點(diǎn)，這些點(diǎn)都是在候選角點(diǎn)p的附近。在23中介紹的原始探測器劃分p點(diǎn)做為角的標(biāo)準(zhǔn)是：如果在圓中存在n個(gè)連續(xù)的像素點(diǎn)，這n個(gè)點(diǎn)的亮度全部比Ip+t大或者是都比Ip-t暗，圖1中證明的就是這種檢測方法。n取值是1

47、2因?yàn)樗梢栽试S一個(gè)高速的測試，這可以被用來排除許多數(shù)量的非角點(diǎn)：測試時(shí)僅僅測4個(gè)像素點(diǎn)，1,5,9和13（4個(gè)垂直方向）。如果p是一個(gè)角點(diǎn)，那么這4個(gè)值中至少3個(gè)亮度值必須大于Ip + t或者小于Ip t。如果不符合這些要求，那么p就不能是一個(gè)角。完整的分段測試可以被用于接受的所有候選點(diǎn)，通過檢測圓上的所有點(diǎn)。這種檢測有很好的性能，但是有一些缺點(diǎn)： 1. The high-speed test does not generalise well for n 12.2. The choice and ordering of the fast test pixels contains implic

48、it assumptionsabout the distribution of feature appearance.3. Knowledge from the first 4 tests is discarded.4. Multiple features are detected adjacent to one another.1. 當(dāng)n 12時(shí)不能拒絕許多候選點(diǎn)。檢測出來的角點(diǎn)不是最優(yōu)的，這是因?yàn)樗男适且揽拷屈c(diǎn)外形的排列和分布的。前4次的檢測信息被遺棄了相鄰的多個(gè)特征點(diǎn)會(huì)被檢測到2.2 Machine learning a corner detector機(jī)器學(xué)習(xí)的角探測器Here we

49、 present an approach which uses machine learning to address the first three points (the fourth is addressed in Section 2.3). The process operates in two stages. In order to build a corner detector for a given n, first, corners are detected from a set of images (preferably from the target application

50、 domain) using the segment test criterion for n and a convenient threshold. This uses a slow algorithm which for each pixel simply tests all 16 locations on the circle around it.For each location on the circle , the pixel at that position relative to p (denoted by ) can have one of three states: （5）

51、這里我們想出一個(gè)方法，使用機(jī)器學(xué)習(xí)語言來來處理前三點(diǎn)，（第四點(diǎn)將在2.3部分來闡述）。處理操作分倆部，為了建立一個(gè)角探測器,在n值給定的情況下，第一步檢測一系列圖片的角（最好是來至目標(biāo)應(yīng)用的區(qū)域）為了n使用段檢測標(biāo)準(zhǔn)并且一個(gè)合適的門限。使用一個(gè)慢速的算法使得每個(gè)像素簡單的檢測圓附近的所有16個(gè)位子。這16個(gè)像素中的每一個(gè)像素（假設(shè)為），可以有下面三種狀態(tài)中的一種 （5）Choosing an x and computing for all (the set of all pixels in all training images) partitions P into three subsets

52、, Pd, Ps, Pb, where each p is assigned to。Let Kp be a boolean variable which is true if p is a corner and false otherwise.Stage 2 employs the algorithm used in ID331 and begins by selecting the x which yields the most information about whether the candidate pixel is a corner,measured by the entropy

53、（熵）of Kp.選擇一個(gè)x并且計(jì)算P中所有p點(diǎn)的值（所有圖像的像素的集合），將所有的P分成三個(gè)子集：Pd, Ps, Pb, ，每一個(gè)p是被分配到中。定義Kp為布爾變量，如果p是角，Kp是真的，否則是假的。第二步是使用了ID3算法并且開始選擇x，x服從大多數(shù)信息關(guān)于候選的像素是否是一個(gè)角點(diǎn)，測量的標(biāo)準(zhǔn)就是Kp的熵值。 The entropy of K for the set P is:集合P的K的熵值如下計(jì)算 （6）The choice of x then yields the information gain:選擇X然后服從信息增益 （7）Having selected the x whic

54、h yields the most information, the process is applied recursively（遞歸） on all three subsets i.e. xb is selected to partition Pb in to Pb,d, Pb,s,Pb,b, xs is selected to partition Ps in to Ps,d, Ps,s, Ps,b and so on, where each x is chosen to yield maximum information about the set it is applied to. T

55、he process terminates when the entropy of a subset is zero. This means that all p in this subset have the same value of Kp, i.e. they are either all corners or all non-corners. This is guaranteed to occur since K is an exact function of the learning data.已經(jīng)選出了服從大多素信息的x，處理過程中對(duì)三個(gè)子集應(yīng)用遞歸，也就是說xb是被選出來的，為了

56、將Pb分割到Pb,d, Pb,s,Pb,b, xs是被選來將Ps分成Ps,d, Ps,s, Ps,b等等。那里每個(gè)x是被選來服從應(yīng)用的集合的最大信息量。當(dāng)子集的熵值是零時(shí)，處理結(jié)束。這就意味著子集中的所有p有相同的Kp值，也就是它們要么全是角點(diǎn)，或者全部不是。這就保證了角點(diǎn)的出現(xiàn)，因?yàn)镵是一個(gè)額外的功能函數(shù)關(guān)于學(xué)習(xí)資料。This creates a decision tree which can correctly classify all corners seen in the training set and therefore (to a close approximation) cor

57、rectly embodies（表現(xiàn);象征;包括;包含） the rules of the chosen FAST corner detector. This decision tree is then converted into C-code, creating a long string of（一長串的） nested（嵌套） if-then-else statements which is compiled and used as a corner detector. For full optimisation（優(yōu)化）, the code is compiled twice, once

58、 to obtain profiling data on the test images and a second time with arcprofiling enabled in order to allow reordering optimisations. In some cases, two of the three subtrees may be the same. In this case, the boolean test which separates them is removed.可以創(chuàng)造一個(gè)決策樹，決策樹可以正確的將訓(xùn)練集中的所有角進(jìn)行分類，因此能夠正確的表示FAST角

59、點(diǎn)探測器的規(guī)則。然后決策樹轉(zhuǎn)換為C代碼，創(chuàng)造一長串的嵌套if-then-else的算法，然后編譯和并用做角探測器。為了更加優(yōu)化，代碼會(huì)被編譯倆次，一次是為了獲得分析測試圖像后得到的數(shù)據(jù)，而第二次編譯允許重新將最優(yōu)化值重新排序。在一些例子中，三分之二的子樹將是一樣的。在這種特例中，分離子樹的布爾測試將會(huì)被移除。Note that since the data contains incomplete coverage of all possible corners,the learned detector is not precisely the same as the segment test

60、detector. It would be relatively straightforward to modify（修改） the decision tree to ensure that it has the same results as the segment test algorithm, however, all feature detectors are heuristic（啟發(fā)式） to some degree, and the learned detector is merely a very slightly different heuristic to the segme