クラス
class	cv::ppf_match_3d::ICP
	このクラスは，反復的な最近接点(ICP) アルゴリズムの非常に効率的でロバストなバージョンを実装しています。タスクは，ノイズの多いターゲットデータに対して，3Dモデル（または点群）を登録することです．亜種は、特定のテストの後、私自身がまとめたものです。タスクは、雑然としたシーンの中で、部分的でノイズの多い点群を迅速にマッチングさせることです。精度を維持しつつ、性能を重視していることがわかります。この実装は、Tolga Birdal氏のMATLAB実装をベースにしています。http://www.mathworks.com/matlabcentral/fileexchange/47152-icp-registration-using-efficient-variants-and-multi-resolution-scheme主な貢献は以下の通りです。[【詳解】（英語］

class	cv::ppf_match_3d::Pose3D
	クラスは、ポーズの保存を可能にする。データ構造は、四元数と行列形式の両方を格納します。ポーズを操作するためのさまざまなヘルパーメソッドとともに、IO機能をサポートしています。[【詳解】（英語］

class	cv::ppf_match_3d::PoseCluster3D
	複数のポーズ（参照Pose3Dを参照）がグループ化されると（同じ変換に寄与すると）、ポーズクラスタが発生します。このクラスは、このようなポーズ群のための一般的なコンテナです。これらのポーズの保存、読み込み、IOの実行が可能です。[【詳解】（英語］

struct	cv::ppf_match_3d::THash
	構造体、ハッシュテーブルのノードを保持する[【詳解】（英語］

class	cv::ppf_match_3d::PPF3DDetector
	3Dモデルの読み込みとマッチングを行うクラスです。典型的な使用例です。[【詳解】（英語］

struct	cv::ppf_match_3d::hashnode_i

struct	cv::ppf_match_3d::HSHTBL_i

型定義
typedef Ptr< Pose3D >	cv::ppf_match_3d::Pose3DPtr

typedef Ptr< PoseCluster3D >	cv::ppf_match_3d::PoseCluster3DPtr

typedef struct cv::ppf_match_3d::THash	cv::ppf_match_3d::THash
	構造体、ハッシュテーブルのノードを保持する

typedef uint	cv::ppf_match_3d::KeyType

typedef struct cv::ppf_match_3d::hashnode_i	cv::ppf_match_3d::hashnode_i

typedef struct cv::ppf_match_3d::HSHTBL_i	cv::ppf_match_3d::hashtable_int

関数
CV_EXPORTS_W Mat	cv::ppf_match_3d::loadPLYSimple (const char *fileName, int withNormals=0)
	PLYファイルの読み込み[【詳解】（英語］

CV_EXPORTS_W void	cv::ppf_match_3d::writePLY (Mat PC, const char *fileName)
	PLYファイルへの点群の書き込み[【詳解】（英語］

CV_EXPORTS_W void	cv::ppf_match_3d::writePLYVisibleNormals (Mat PC, const char *fileName)
	デバッグ用に使用され、法線ベクトルの先端を赤い点で表示して点群をPLYファイルに書き込む[【詳解】（英語］

Mat	cv::ppf_match_3d::samplePCUniform (Mat PC, int sampleStep)

Mat	cv::ppf_match_3d::samplePCUniformInd (Mat PC, int sampleStep, std::vector< int > &indices)

CV_EXPORTS_W Mat	cv::ppf_match_3d::samplePCByQuantization (Mat pc, Vec2f &xrange, Vec2f &yrange, Vec2f &zrange, float sample_step_relative, int weightByCenter=0)

void	cv::ppf_match_3d::computeBboxStd (Mat pc, Vec2f &xRange, Vec2f &yRange, Vec2f &zRange)

void *	cv::ppf_match_3d::indexPCFlann (Mat pc)

void	cv::ppf_match_3d::destroyFlann (void *flannIndex)

void	cv::ppf_match_3d::queryPCFlann (void *flannIndex, Mat &pc, Mat &indices, Mat &distances)

void	cv::ppf_match_3d::queryPCFlann (void *flannIndex, Mat &pc, Mat &indices, Mat &distances, const int numNeighbors)

Mat	cv::ppf_match_3d::normalizePCCoeff (Mat pc, float scale, float Cx, float Cy, float Cz, float MinVal, float *MaxVal)

Mat	cv::ppf_match_3d::transPCCoeff (Mat pc, float scale, float Cx, float Cy, float Cz, float MinVal, float MaxVal)

CV_EXPORTS_W Mat	cv::ppf_match_3d::transformPCPose (Mat pc, const Matx44d &Pose)

CV_EXPORTS_W void	cv::ppf_match_3d::getRandomPose (Matx44d &Pose)

CV_EXPORTS_W Mat	cv::ppf_match_3d::addNoisePC (Mat pc, double scale)

CV_EXPORTS_W int	cv::ppf_match_3d::computeNormalsPC3d (const Mat &PC, CV_OUT Mat &PCNormals, const int NumNeighbors, const bool FlipViewpoint, const Vec3f &viewpoint)
	任意の点群の法線を計算する computeNormalsPC3d は，平面フィットの手法を用いて，局所的な法線をスムーズに計算します．法線は、最小の固有値に対応する共分散行列の固有ベクトルによって得られます。PCNormalsにNx6の行列が指定された場合、新たな割り当ては行われず、既存のメモリが上書きされます。[【詳解】（英語］

static uint	cv::ppf_match_3d::next_power_of_two (uint value)
	2の次のべき乗に切り上げる[【詳解】（英語］

hashtable_int *	cv::ppf_match_3d::hashtableCreate (size_t size, size_t(*hashfunc)(uint))

void	cv::ppf_match_3d::hashtableDestroy (hashtable_int *hashtbl)

int	cv::ppf_match_3d::hashtableInsert (hashtable_int hashtbl, KeyType key, void data)

int	cv::ppf_match_3d::hashtableInsertHashed (hashtable_int hashtbl, KeyType key, void data)

int	cv::ppf_match_3d::hashtableRemove (hashtable_int *hashtbl, KeyType key)

void *	cv::ppf_match_3d::hashtableGet (hashtable_int *hashtbl, KeyType key)

hashnode_i *	cv::ppf_match_3d::hashtableGetBucketHashed (hashtable_int *hashtbl, KeyType key)

int	cv::ppf_match_3d::hashtableResize (hashtable_int *hashtbl, size_t size)

hashtable_int *	cv::ppf_match_3d::hashtable_int_clone (hashtable_int *hashtbl)

hashtable_int *	cv::ppf_match_3d::hashtableRead (FILE *f)

int	cv::ppf_match_3d::hashtableWrite (const hashtable_int hashtbl, const size_t dataSize, FILE f)

void	cv::ppf_match_3d::hashtablePrint (hashtable_int *hashtbl)

詳解

Note about the License and Patents

The following patents have been issued for methods embodied in this software: "Recognition and pose determination of 3D objects in 3D scenes using geometric point pair descriptors and the generalized Hough Transform", Bertram Heinrich Drost, Markus Ulrich, EP Patent 2385483 (Nov. 21, 2012), assignee: MVTec Software GmbH, 81675 Muenchen (Germany); "Recognition and pose determination of 3D objects in 3D scenes", Bertram Heinrich Drost, Markus Ulrich, US Patent 8830229 (Sept. 9, 2014), assignee: MVTec Software GmbH, 81675 Muenchen (Germany). Further patents are pending. For further details, contact MVTec Software GmbH (info@.nosp@m.mvte.nosp@m.c.com).

Note that restrictions imposed by these patents (and possibly others) exist independently of and may be in conflict with the freedoms granted in this license, which refers to copyright of the program, not patents for any methods that it implements. Both copyright and patent law must be obeyed to legally use and redistribute this program and it is not the purpose of this license to induce you to infringe any patents or other property right claims or to contest validity of any such claims. If you redistribute or use the program, then this license merely protects you from committing copyright infringement. It does not protect you from committing patent infringement. So, before you do anything with this program, make sure that you have permission to do so not merely in terms of copyright, but also in terms of patent law.

Please note that this license is not to be understood as a guarantee either. If you use the program according to this license, but in conflict with patent law, it does not mean that the licensor will refund you for any losses that you incur if you are sued for your patent infringement.

Introduction to Surface Matching

Cameras and similar devices with the capability of sensation of 3D structure are becoming more common. Thus, using depth and intensity information for matching 3D objects (or parts) are of crucial importance for computer vision. Applications range from industrial control to guiding everyday actions for visually impaired people. The task in recognition and pose estimation in range images aims to identify and localize a queried 3D free-form object by matching it to the acquired database.

From an industrial perspective, enabling robots to automatically locate and pick up randomly placed and oriented objects from a bin is an important challenge in factory automation, replacing tedious and heavy manual labor. A system should be able to recognize and locate objects with a predefined shape and estimate the position with the precision necessary for a gripping robot to pick it up. This is where vision guided robotics takes the stage. Similar tools are also capable of guiding robots (and even people) through unstructured environments, leading to automated navigation. These properties make 3D matching from point clouds a ubiquitous necessity. Within this context, I will now describe the OpenCV implementation of a 3D object recognition and pose estimation algorithm using 3D features.

Surface Matching Algorithm Through 3D Features

The state of the algorithms in order to achieve the task 3D matching is heavily based on [drost2010], which is one of the first and main practical methods presented in this area. The approach is composed of extracting 3D feature points randomly from depth images or generic point clouds, indexing them and later in runtime querying them efficiently. Only the 3D structure is considered, and a trivial hash table is used for feature queries.

While being fully aware that utilization of the nice CAD model structure in order to achieve a smart point sampling, I will be leaving that aside now in order to respect the generalizability of the methods (Typically for such algorithms training on a CAD model is not needed, and a point cloud would be sufficient). Below is the outline of the entire algorithm:

Outline of the Algorithm

As explained, the algorithm relies on the extraction and indexing of point pair features, which are defined as follows:

$\bf{{F}}(\bf{{m1}}, \bf{{m2}}) = (||\bf{{d}}||_2, <(\bf{{n1}},\bf{{d}}), <(\bf{{n2}},\bf{{d}}), <(\bf{{n1}},\bf{{n2}}))$

where $\bf{{m1}}$ and $\bf{{m2}}$ are feature two selected points on the model (or scene), $\bf{{d}}$ is the difference vector, $\bf{{n1}}$ and $\bf{{n2}}$ are the normals at $\bf{{m1}}$ and $\bf{m2}$ . During the training stage, this vector is quantized, indexed. In the test stage, same features are extracted from the scene and compared to the database. With a few tricks like separation of the rotational components, the pose estimation part can also be made efficient (check the reference for more details). A Hough-like voting and clustering is employed to estimate the object pose. To cluster the poses, the raw pose hypotheses are sorted in decreasing order of the number of votes. From the highest vote, a new cluster is created. If the next pose hypothesis is close to one of the existing clusters, the hypothesis is added to the cluster and the cluster center is updated as the average of the pose hypotheses within the cluster. If the next hypothesis is not close to any of the clusters, it creates a new cluster. The proximity testing is done with fixed thresholds in translation and rotation. Distance computation and averaging for translation are performed in the 3D Euclidean space, while those for rotation are performed using quaternion representation. After clustering, the clusters are sorted in decreasing order of the total number of votes which determines confidence of the estimated poses.

This pose is further refined using $ICP$ in order to obtain the final pose.

PPF presented above depends largely on robust computation of angles between 3D vectors. Even though not reported in the paper, the naive way of doing this ( $\theta = cos^{-1}({\bf{a}}\cdot{\bf{b}})$ remains numerically unstable. A better way to do this is then use inverse tangents, like:

$<(\bf{n1},\bf{n2})=tan^{-1}(||{\bf{n1} \wedge \bf{n2}}||_2, \bf{n1} \cdot \bf{n2})$

Rough Computation of Object Pose Given PPF

Let me summarize the following notation:

: $i^{th}$ point of the model ( accordingly)
: Normal of the $i^{th}$ point of the model ( accordingly)
: $i^{th}$ point of the scene ( accordingly)
: Normal of the $i^{th}$ point of the scene ( accordingly)
$T_{m\rightarrow g}$ : The transformation required to translate to the origin and rotate its normal onto the -axis.
$R_{m\rightarrow g}$ : Rotational component of $T_{m\rightarrow g}$ .
$t_{m\rightarrow g}$ : Translational component of $T_{m\rightarrow g}$ .
$(p^i_m)^{'}$ : $i^{th}$ point of the model transformed by $T_{m\rightarrow g}$ . ( $(p^j_m)^{'}$ accordingly).
${\bf{R_{m\rightarrow g}}}$ : Axis angle representation of rotation $R_{m\rightarrow g}$ .
$\theta_{m\rightarrow g}$ : The angular component of the axis angle representation ${\bf{R_{m\rightarrow g}}}$ .

The transformation in a point pair feature is computed by first finding the transformation $T_{m\rightarrow g}$ from the first point, and applying the same transformation to the second one. Transforming each point, together with the normal, to the ground plane leaves us with an angle to find out, during a comparison with a new point pair.

We could now simply start writing

$(p^i_m)^{'} = T_{m\rightarrow g} p^i_m$

where

$T_{m\rightarrow g} = -t_{m\rightarrow g}R_{m\rightarrow g}$

Note that this is nothing but a stacked transformation. The translational component $t_{m\rightarrow g}$ reads

$t_{m\rightarrow g} = -R_{m\rightarrow g}p^i_m$

and the rotational being

$\theta_{m\rightarrow g} = \cos^{-1}(n^i_m \cdot {\bf{x}})\\ {\bf{R_{m\rightarrow g}}} = n^i_m \wedge {\bf{x}}$

in axis angle format. Note that bold refers to the vector form. After this transformation, the feature vectors of the model are registered onto the ground plane X and the angle with respect to $x=0$ is called $\alpha_m$ . Similarly, for the scene, it is called $\alpha_s$ .

Hough-like Voting Scheme

As shown in the outline, PPF (point pair features) are extracted from the model, quantized, stored in the hashtable and indexed, during the training stage. During the runtime however, the similar operation is perfomed on the input scene with the exception that this time a similarity lookup over the hashtable is performed, instead of an insertion. This lookup also allows us to compute a transformation to the ground plane for the scene pairs. After this point, computing the rotational component of the pose reduces to computation of the difference $\alpha=\alpha_m-\alpha_s$ . This component carries the cue about the object pose. A Hough-like voting scheme is performed over the local model coordinate vector and $\alpha$ . The highest poses achieved for every scene point lets us recover the object pose.

Source Code for PPF Matching

// pc is the loaded point cloud of the model

// (Nx6) and pcTest is a loaded point cloud of

// the scene (Mx6)

ppf_match_3d::PPF3DDetector
detector(0.03, 0.05);
detector.trainModel(pc);
vector<Pose3DPtr> results;
detector.match(pcTest, results, 1.0/10.0, 0.05);
cout <<
"Poses: "
<< endl;

// print the poses

for
(size_t
i=0; i<results.size(); i++)
{

Pose3DPtr
pose = results[i];

cout <<
"Pose Result "
<< i << endl;

pose->printPose();
}

Pose Registration via ICP

The matching process terminates with the attainment of the pose. However, due to the multiple matching points, erroneous hypothesis, pose averaging and etc. such pose is very open to noise and many times is far from being perfect. Although the visual results obtained in that stage are pleasing, the quantitative evaluation shows $~10$ degrees variation (error), which is an acceptable level of matching. Many times, the requirement might be set well beyond this margin and it is desired to refine the computed pose.

Furthermore, in typical RGBD scenes and point clouds, 3D structure can capture only less than half of the model due to the visibility in the scene. Therefore, a robust pose refinement algorithm, which can register occluded and partially visible shapes quickly and correctly is not an unrealistic wish.

At this point, a trivial option would be to use the well known iterative closest point algorithm . However, utilization of the basic ICP leads to slow convergence, bad registration, outlier sensitivity and failure to register partial shapes. Thus, it is definitely not suited to the problem. For this reason, many variants have been proposed . Different variants contribute to different stages of the pose estimation process.

ICP is composed of $6$ stages and the improvements I propose for each stage is summarized below.

Sampling

To improve convergence speed and computation time, it is common to use less points than the model actually has. However, sampling the correct points to register is an issue in itself. The naive way would be to sample uniformly and hope to get a reasonable subset. More smarter ways try to identify the critical points, which are found to highly contribute to the registration process. Gelfand et. al. exploit the covariance matrix in order to constrain the eigenspace, so that a set of points which affect both translation and rotation are used. This is a clever way of subsampling, which I will optionally be using in the implementation.

Correspondence Search

As the name implies, this step is actually the assignment of the points in the data and the model in a closest point fashion. Correct assignments will lead to a correct pose, where wrong assignments strongly degrade the result. In general, KD-trees are used in the search of nearest neighbors, to increase the speed. However this is not an optimality guarantee and many times causes wrong points to be matched. Luckily the assignments are corrected over iterations.

To overcome some of the limitations, Picky ICP [pickyicp] and BC-ICP (ICP using bi-unique correspondences) are two well-known methods. Picky ICP first finds the correspondences in the old-fashioned way and then among the resulting corresponding pairs, if more than one scene point $p_i$ is assigned to the same model point $m_j$ , it selects $p_i$ that corresponds to the minimum distance. BC-ICP on the other hand, allows multiple correspondences first and then resolves the assignments by establishing bi-unique correspondences. It also defines a novel no-correspondence outlier, which intrinsically eases the process of identifying outliers.

For reference, both methods are used. Because P-ICP is a bit faster, with not-so-significant performance drawback, it will be the method of choice in refinment of correspondences.

Weighting of Pairs

In my implementation, I currently do not use a weighting scheme. But the common approaches involve normal compatibility* ( $w_i=n^1_i\cdot n^2_j$ ) or assigning lower weights to point pairs with greater distances ( $w=1-\frac{||dist(m_i,s_i)||_2}{dist_{max}}$ ).

Rejection of Pairs

The rejections are done using a dynamic thresholding based on a robust estimate of the standard deviation. In other words, in each iteration, I find the MAD estimate of the Std. Dev. I denote this as $mad_i$ . I reject the pairs with distances $d_i>\tau mad_i$ . Here $\tau$ is the threshold of rejection and by default set to $3$ . The weighting is applied prior to Picky refinement, explained in the previous stage.

Error Metric

As described in , a linearization of point to plane as in [koklimlow] error metric is used. This both speeds up the registration process and improves convergence.

Minimization

Even though many non-linear optimizers (such as Levenberg Mardquardt) are proposed, due to the linearization in the previous step, pose estimation reduces to solving a linear system of equations. This is what I do exactly using cv::solve with DECOMP_SVD option.

ICP Algorithm

Having described the steps above, here I summarize the layout of the ICP algorithm.

Efficient ICP Through Point Cloud Pyramids

While the up-to-now-proposed variants deal well with some outliers and bad initializations, they require significant number of iterations. Yet, multi-resolution scheme can help reducing the number of iterations by allowing the registration to start from a coarse level and propagate to the lower and finer levels. Such approach both improves the performances and enhances the runtime.

The search is done through multiple levels, in a hierarchical fashion. The registration starts with a very coarse set of samples of the model. Iteratively, the points are densified and sought. After each iteration the previously estimated pose is used as an initial pose and refined with the ICP.

Visual Results

Results on Synthetic Data

In all of the results, the pose is initiated by PPF and the rest is left as: $[\theta_x, \theta_y, \theta_z, t_x, t_y, t_z]=[0]$

Source Code for Pose Refinement Using ICP

ICP
icp(200, 0.001f, 2.5f, 8);

// Using the previously declared pc and pcTest

// This will perform registration for every pose

// contained in results
icp.registerModelToScene(pc, pcTest, results);

// results now contain the refined poses

Results

This section is dedicated to the results of surface matching (point-pair-feature matching and a following ICP refinement):

Several matches of a single frog model using ppf + icp

Matches of different models for Mian dataset is presented below:

Matches of different models for Mian dataset

You might checkout the video on youTube here.

A Complete Sample

Parameter Tuning

Surface matching module treats its parameters relative to the model diameter (diameter of the axis parallel bounding box), whenever it can. This makes the parameters independent from the model size. This is why, both model and scene cloud were subsampled such that all points have a minimum distance of $RelativeSamplingStep*DimensionRange$ , where $DimensionRange$ is the distance along a given dimension. All three dimensions are sampled in similar manner. For example, if $RelativeSamplingStep$ is set to 0.05 and the diameter of model is 1m (1000mm), the points sampled from the object's surface will be approximately 50 mm apart. From another point of view, if the sampling RelativeSamplingStep is set to 0.05, at most $20x20x20 = 8000$ model points are generated (depending on how the model fills in the volume). Consequently this results in at most 8000x8000 pairs. In practice, because the models are not uniformly distributed over a rectangular prism, much less points are to be expected. Decreasing this value, results in more model points and thus a more accurate representation. However, note that number of point pair features to be computed is now quadratically increased as the complexity is O(N\^2). This is especially a concern for 32 bit systems, where large models can easily overshoot the available memory. Typically, values in the range of 0.025 - 0.05 seem adequate for most of the applications, where the default value is 0.03. (Note that there is a difference in this paremeter with the one presented in [drost2010] . In [drost2010] a uniform cuboid is used for quantization and model diameter is used for reference of sampling. In my implementation, the cuboid is a rectangular prism, and each dimension is quantized independently. I do not take reference from the diameter but along the individual dimensions.

It would very wise to remove the outliers from the model and prepare an ideal model initially. This is because, the outliers directly affect the relative computations and degrade the matching accuracy.

During runtime stage, the scene is again sampled by $RelativeSamplingStep$ , as described above. However this time, only a portion of the scene points are used as reference. This portion is controlled by the parameter $RelativeSceneSampleStep$ , where $SceneSampleStep = (int)(1.0/RelativeSceneSampleStep)$ . In other words, if the $RelativeSceneSampleStep = 1.0/5.0$ , the subsampled scene will once again be uniformly sampled to 1/5 of the number of points. Maximum value of this parameter is 1 and increasing this parameter also increases the stability, but decreases the speed. Again, because of the initial scene-independent relative sampling, fine tuning this parameter is not a big concern. This would only be an issue when the model shape occupies a volume uniformly, or when the model shape is condensed in a tiny place within the quantization volume (e.g. The octree representation would have too much empty cells).

$RelativeDistanceStep$ acts as a step of discretization over the hash table. The point pair features are quantized to be mapped to the buckets of the hashtable. This discretization involves a multiplication and a casting to the integer. Adjusting RelativeDistanceStep in theory controls the collision rate. Note that, more collisions on the hashtable results in less accurate estimations. Reducing this parameter increases the affect of quantization but starts to assign non-similar point pairs to the same bins. Increasing it however, wanes the ability to group the similar pairs. Generally, because during the sampling stage, the training model points are selected uniformly with a distance controlled by RelativeSamplingStep, RelativeDistanceStep is expected to equate to this value. Yet again, values in the range of 0.025-0.05 are sensible. This time however, when the model is dense, it is not advised to decrease this value. For noisy scenes, the value can be increased to improve the robustness of the matching against noisy points.

関数詳解

◆ addNoisePC()

CV_EXPORTS_W Mat cv::ppf_match_3d::addNoisePC	(	Mat	pc,
		double	scale
	)

入力点群に，与えられたスケールの一様なノイズを追加します．

引数

[in].	pc	入力点群（CV_32F family）．
[in].	scale	ノイズの入力スケール．スケールが大きくなるほど，出力はノイズだらけになります．

◆ computeNormalsPC3d()

CV_EXPORTS_W int cv::ppf_match_3d::computeNormalsPC3d	(	const Mat &	PC,
		CV_OUT Mat &	PCNormals,
		const int	NumNeighbors,
		const bool	FlipViewpoint,
		const Vec3f &	viewpoint
	)

任意の点群の法線を計算する computeNormalsPC3d は，平面フィットの手法を用いて，局所的な法線をスムーズに計算します．法線は、最小の固有値に対応する共分散行列の固有ベクトルによって得られます。PCNormalsにNx6の行列が指定された場合、新たな割り当ては行われず、既存のメモリが上書きされます。

引数

[in].	PC	法線を計算するための入力点群．
[out].	PCNormals	出力点群．
[in].	NumNeighbors	局所領域で考慮すべき隣人の数。
[in].	FlipViewpoint	法線を見る方向に反転させるか？
[in].	viewpoint

戻り値: 成功したら0を返す

◆ getRandomPose()

CV_EXPORTS_W void cv::ppf_match_3d::getRandomPose ( Matx44d & Pose )

4x4 のランダムなポーズ行列を生成します。

引数

[out]. Pose ポーズのランダム化

◆ loadPLYSimple()

CV_EXPORTS_W Mat cv::ppf_match_3d::loadPLYSimple	(	const char *	fileName,
		int	withNormals = `0`
	)

PLYファイルの読み込み

引数

[in].	fileName	読み込むPLYモデル
[in].	withNormals	入力PLYに通常の情報が含まれているかどうか，そしてそれを読み込むべきかどうかのフラグ

戻り値: 読み込みに成功したら，行列を返す

◆ next_power_of_two()

static uint cv::ppf_match_3d::next_power_of_two ( uint value )

inline static

2の次のべき乗に切り上げる

から最大でhttp://www-graphics.stanford.edu/~seander/bithacks.html

◆ samplePCByQuantization()

CV_EXPORTS_W Mat cv::ppf_match_3d::samplePCByQuantization	(	Mat	pc,
		Vec2f &	xrange,
		Vec2f &	yrange,
		Vec2f &	zrange,
		float	sample_step_relative,
		int	weightByCenter = `0`
	)

一様な手順での点群のサンプリング

引数

[in].	pc	入力点群
[in].	xrange	モデルのバウンディングボックスのX成分（最小値と最大値
[in].	yrange	モデルのバウンディング・ボックスのY成分（最小値と最大値
[in].	zrange	モデルのバウンディングボックスのZ成分（最小値と最大値
[in].	sample_step_relative	点群は，すべての点が一定の最小距離を持つようにサンプリングされる．この最小距離は，パラメータ sample_step_relative を用いて相対的に決定されます．
[in].	weightByCenter	量子化されたデータポイントの寄与は、原点からの距離によって重み付けすることができます。このパラメータは、重み付けの使用を有効/無効にします。

戻り値: サンプリングされた点群

◆ transformPCPose()

CV_EXPORTS_W Mat cv::ppf_match_3d::transformPCPose	(	Mat	pc,
		const Matx44d &	Pose
	)

点群を，与えられた4×4の均質な姿勢行列（倍精度）で変換します．

引数

[in].	pc	入力点群（CV_32F 形式）．1行あたり3要素または6要素の点群が想定されます．法線が与えられている場合は，変換全体に対応するように法線も回転されます．
[in].	Pose	4x4 のポーズ行列を，行ごとに線形化したもの．

戻り値: 変換された点群

◆ writePLY()

CV_EXPORTS_W void cv::ppf_match_3d::writePLY	(	Mat	PC,
		const char *	fileName
	)

PLYファイルへの点群の書き込み

引数

[in].	PC	入力点群
[in].	fileName	書き込むPLYモデルファイル

◆ writePLYVisibleNormals()

CV_EXPORTS_W void cv::ppf_match_3d::writePLYVisibleNormals	(	Mat	PC,
		const char *	fileName
	)

デバッグ用に使用され、法線ベクトルの先端を赤い点で表示して点群をPLYファイルに書き込む

引数

[in].	PC	入力点群
[in].	fileName	書き込むPLYモデルファイル

クラス

型定義

関数

詳解

Note about the License and Patents

Introduction to Surface Matching

Surface Matching Algorithm Through 3D Features

Rough Computation of Object Pose Given PPF

Hough-like Voting Scheme

Source Code for PPF Matching

Pose Registration via ICP

Sampling

Correspondence Search

Weighting of Pairs

Rejection of Pairs

Error Metric

Minimization

ICP Algorithm

Efficient ICP Through Point Cloud Pyramids

Visual Results

Results on Synthetic Data

Source Code for Pose Refinement Using ICP

Results

A Complete Sample

Parameter Tuning

関数詳解

◆ addNoisePC()

◆ computeNormalsPC3d()

◆ getRandomPose()

◆ loadPLYSimple()

◆ next_power_of_two()

◆ samplePCByQuantization()

◆ transformPCPose()

◆ writePLY()

◆ writePLYVisibleNormals()