Key point detection and its uncertainty synchronous prediction method

Abstract

The application discloses a key point detection and uncertainty synchronous prediction method, comprising the following steps: constructing a key point prediction model, outputting a key point category, a key point coordinate and a coordinate uncertainty; describing the key point coordinate as a one-dimensional Gaussian distribution; constructing a coordinate prediction loss function based on the KL divergence of the Gaussian distribution of the key point coordinate true value and the predicted value, and training the key point prediction model; and inputting a to-be-detected monocular image into the key point prediction model to realize synchronous prediction of the key point coordinate and the coordinate uncertainty. The application is applied to the monocular pose estimation field, can give the key point coordinate prediction uncertainty while predicting the key point coordinate, and can set the weight of the weighted monocular pose estimation problem as the reciprocal of the key point coordinate prediction uncertainty in the process of monocular pose estimation, then solve the weighted monocular pose estimation constraint equation to obtain a high-precision pose measurement result, and significantly improve the monocular visual pose estimation precision.

Description

Technical Field

[0001] This invention relates to the technical fields of monocular visual pose estimation, semantic key point detection, uncertainty estimation, and deep learning. Specifically, it is a key point detection and its uncertainty synchronous prediction method, which can be used in monocular pose estimation, 3D measurement, gesture recognition, image registration and other scenarios. Background Technology

[0002] For cooperative targets, manually designed cooperative markers can be placed on the target surface to assist in high-precision detection of key feature points, such as diagonal, circular, or ArUco markers. However, in many cases, targets are non-cooperative, and it is inconvenient or impossible to place cooperative markers on their surfaces. Therefore, it is necessary to utilize the texture or structural features of the target's appearance. Traditional methods mainly employ manually designed features for extraction and matching of target key points, with commonly used features including Harris, SIFT, ORB, and BRISK. In many specific tasks, automatic extraction of target key points faces difficulties such as complex target structures, variations in viewing angle and brightness, strong light interference, and complex backgrounds, highlighting the limitations of traditional manually designed features.

[0003] With the development of deep learning technology, deep neural network methods have demonstrated powerful performance in computer vision tasks such as image classification, object detection, and tracking. Subsequently, a series of monocular vision pose estimation methods based on deep learning have emerged. These methods can be categorized into direct and indirect methods based on whether the PnP problem is explicitly solved. Direct methods use neural networks to directly predict the target's relative pose, while indirect methods first use neural networks to predict the target's keypoint coordinates and then solve the PnP problem to obtain the target's relative pose. When processing image tasks, classic deep convolutional neural networks (CNNs) have limited kernel coverage and weak ability to model long-distance dependencies. To address this problem, an end-to-end object detection framework (DEtection TRansformer, DETR) was developed, employing the Transformer model, which models word sequences in sentences from the field of natural language processing. Building upon this, some researchers have proposed a target monocular pose estimation method based on the Transformer model, which directly predicts the target's keypoint coordinates and then solves the PnP problem to obtain the satellite's relative pose parameters.

[0004] The above indirect method for monocular pose estimation ignores the differences in the prediction accuracy of key point coordinates when using predicted key point coordinates to solve the target pose. When solving the PnP problem, it is impossible to construct a weighted constraint equation for each key point based on the prediction accuracy of key point coordinates, which affects the accuracy of monocular pose estimation. Summary of the Invention

[0005] To address the shortcomings of the existing technologies, this invention provides a key point detection and its uncertainty prediction method. While predicting the image coordinates of key points, it also provides the uncertainty of the key point coordinate prediction, thereby enabling the uncertainty to be applied to construct a weighted PnP constraint equation to solve the relative pose, thus significantly improving the accuracy of monocular vision pose estimation.

[0006] To achieve the above objectives, this invention provides a method for key point detection and simultaneous prediction of its uncertainty, comprising the following steps:

[0007] A key point prediction model is constructed. The input of the key point prediction model is a monocular image, and the output includes key point category, key point coordinates, and coordinate uncertainty.

[0008] The keypoint coordinates are described as two independent one-dimensional Gaussian distributions in the x and y directions, respectively. The keypoint coordinates are taken as the mean of the Gaussian distribution, and the coordinate uncertainty is the standard deviation of the Gaussian distribution.

[0009] A coordinate prediction loss function is constructed based on the KL divergence of the Gaussian distribution of the ground and predicted values ​​of keypoint coordinates, and the keypoint prediction model is trained based on the coordinate prediction loss function.

[0010] The monocular image to be tested is input into the trained key point prediction model to achieve simultaneous prediction of key point coordinates and coordinate uncertainty.

[0011] In one embodiment, the keypoint prediction model is a Transformer model, including:

[0012] The backbone network is used to extract and overlay the two-dimensional convolutional features and spatial location codes of monocular images, and unfold them into one-dimensional features;

[0013] An encoder is used to obtain an encoded feature vector based on the one-dimensional features;

[0014] A decoder is used to obtain a decoded feature vector based on a preset target query vector and the encoded feature vector;

[0015] A prediction network is used to obtain prediction results of key point categories, key point coordinates, and coordinate uncertainties in a monocular image based on the decoded feature vector.

[0016] In one embodiment, the coordinate prediction loss function is specifically:

[0017] L = L x-loc +L y-loc

[0018] Where L is the loss function, L x-locLet L be the KL divergence between the true and predicted Gaussian distributions of the keypoint coordinates in the x-direction. y-loc The KL divergence of the Gaussian distribution of the true and predicted values ​​of the keypoint coordinates in the y-direction is given.

[0019] In one embodiment, the KL divergence of the Gaussian distribution of the true and predicted values ​​of the keypoint coordinates in the x-direction is specifically as follows:

[0020]

[0021] α x =log(σ x 2 )

[0022] Where, x g Let x be the true coordinates of the keypoint in the x-direction. e α represents the predicted coordinates of the keypoints in the x-direction. x σ is the coordinate uncertainty term of the key point coordinates in the x-direction. x The coordinate uncertainty of the key point in the x-direction;

[0023] The KL divergence of the Gaussian distribution between the true and predicted values ​​of the keypoint coordinates in the y-direction is specifically as follows:

[0024]

[0025] α y =log(σ y 2 )

[0026] Among them, y g Let y be the true coordinates of the keypoint in the y-direction. e α represents the predicted coordinates of the keypoints in the y-direction. y σ is the coordinate uncertainty term of the key point coordinates in the y-direction. y The coordinate uncertainty of the key point in the y-direction is given.

[0027] In one embodiment, the KL divergence of the Gaussian distribution of the true and predicted values ​​of the keypoint coordinates in the x-direction is specifically as follows:

[0028]

[0029] α x =log(σ x 2 )

[0030] Where, x g Let x be the true coordinates of the keypoint in the x-direction. e α represents the predicted coordinates of the keypoints in the x-direction.x σ is the coordinate uncertainty term of the key point coordinates in the x-direction. x Let β be the coordinate uncertainty of the keypoint in the x-direction. x For the threshold;

[0031] The KL divergence of the Gaussian distribution between the true and predicted values ​​of the keypoint coordinates in the y-direction is specifically as follows:

[0032]

[0033] α y =log(σ y 2 )

[0034] Among them, y g Let y be the true coordinates of the keypoint in the y-direction. e α represents the predicted coordinates of the keypoints in the y-direction. y σ is the coordinate uncertainty term of the key point coordinates in the y-direction. y Let β be the coordinate uncertainty of the key point in the y-direction. y The threshold value is used.

[0035] In one embodiment, the keypoint prediction model outputs a correlation term α. x α y Output coordinate uncertainty σ in the form of x σ y This is to avoid gradient explosion.

[0036] In one embodiment, after obtaining the coordinates and coordinate uncertainty of key points in the monocular image to be tested, when performing monocular pose estimation based on the monocular image to be tested, the reciprocal of the coordinate uncertainty is used as the weight of the corresponding key point coordinates.

[0037] Compared with the prior art, the present invention has the following beneficial technical effects:

[0038] This invention constructs a keypoint prediction model that can provide the keypoint coordinate prediction uncertainty while predicting the keypoint coordinates. Thus, in the process of monocular pose estimation, the weights of the weighted monocular pose estimation problem can be set as the reciprocal of the keypoint coordinate prediction uncertainty. Then, the weighted monocular pose estimation constraint equation is solved to obtain high-precision pose measurement results, thereby significantly improving the accuracy of monocular vision pose estimation. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0040] Figure 1 This is a flowchart of the key point detection and its uncertainty synchronous prediction method in an embodiment of the present invention;

[0041] Figure 2 This is a schematic diagram of the overall framework of the target key point prediction model in an embodiment of the present invention.

[0042] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0044] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0045] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0046] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection, an electrical connection, a physical connection, or a wireless communication connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two elements or the interaction between two elements, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0047] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0048] like Figure 1 The above describes a key point detection and its uncertainty synchronous prediction method disclosed in this embodiment, which mainly includes the following steps:

[0049] Construct a keypoint prediction model. The input of the keypoint prediction model is a monocular image, and the output includes keypoint category, keypoint coordinates, and coordinate uncertainty.

[0050] The keypoint coordinates are described as two independent one-dimensional Gaussian distributions in the x and y directions, respectively. The keypoint coordinates are taken as the mean of the Gaussian distribution, and the coordinate uncertainty is the standard deviation of the Gaussian distribution.

[0051] A coordinate prediction loss function is constructed based on the KL divergence of the Gaussian distribution of the ground and predicted values ​​of keypoint coordinates, and a keypoint prediction model is trained based on the coordinate prediction loss function.

[0052] The monocular image to be tested is input into the trained key point prediction model to achieve simultaneous prediction of key point coordinates and coordinate uncertainty.

[0053] In this embodiment, the keypoint prediction model is a Transformer model, and the model framework mainly consists of four parts: a backbone network, a Transformer encoder, a decoder, and a prediction network. (Reference) Figure 2First, the backbone network extracts and overlays the two-dimensional convolutional features and spatial location codes of the monocular image, unfolds them into one-dimensional features, and inputs them into the Transformer encoder. Then, the Transformer encoder obtains the encoded feature vector based on the one-dimensional features and inputs it into the Transformer decoder. The Transformer decoder obtains the decoded feature vector based on the predefined target query vector and the input encoded feature vector, and then inputs the decoded feature vector into the prediction network. Finally, the prediction network obtains the prediction results of the keypoint category, keypoint coordinates, and coordinate uncertainty in the monocular image based on the decoded feature vector. Assuming the number of target query vectors in the keypoint detection model is Q, and the number of target keypoints in the monocular image is N, then the feature dimensions output by the category prediction branch, coordinate prediction branch, and coordinate uncertainty prediction branch are Q×(N+1), Q×2, and Q×2, respectively. Here, the target query vector is a predefined set of vectors in the Transformer model, and its dimension determines the number of semantic keypoints output by the model.

[0054] In practical applications, the representation of key points of a target mainly includes a category, coordinates, and coordinate uncertainty. The category refers to the object category to which the key point belongs, the coordinates are the image coordinates of the key point, and the coordinate uncertainty is the coordinate uncertainty.

[0055] The keypoint prediction model outputs keypoint categories in one-hot encoded form. Suppose there are N keypoints in a monocular image, and let i be the category index. Adding the background category, the value of i ranges from 1 to N+1. Let the one-hot encoding of the i-th keypoint be... As shown in the following formula:

[0056]

[0057] Where k represents the one-hot encoded index.

[0058] The keypoint coordinates output by the keypoint prediction model are the two-dimensional image coordinates of the keypoints. The keypoint coordinates of the i-th keypoint in the monocular image are denoted as p. i =[x i ,y i The coordinate uncertainty output by the keypoint prediction model is the standard deviation of the keypoint predictions, denoted as . in, Let be the coordinate uncertainty of the i-th keypoint in the monocular image in the x-direction. Let represent the coordinate uncertainty of the i-th keypoint in the monocular image in the y-direction.

[0059] In this embodiment, during the training process of the keypoint prediction model, the training data is a set of keypoints with N elements, each element consisting of a category and coordinates. This set of truth values ​​is denoted as... Specifically:

[0060]

[0061] Among them, t i This represents the i-th keypoint element; the value of i ranges from 1 to N; c i p is the one-hot encoding of the i-th keypoint, representing the probability that it belongs to every keypoint of the target (including the background category); i Represents the two-dimensional image coordinates of the i-th key point.

[0062] The keypoint prediction model outputs a set of keypoints containing Q elements, each element consisting of a category term, a coordinate term, and a coordinate uncertainty term. This prediction set is denoted as . Specifically:

[0063]

[0064] Among them, h j This represents the set of predicted keypoints for the j-th key point; the value of j ranges from 1 to Q; c j p represents the probability (including background category) that the j-th prediction belongs to each keypoint; j and d j Let represent the image coordinates and coordinate uncertainty of the j-th predicted keypoint, respectively.

[0065] When calculating the loss function for training the keypoint prediction model, first, the set of ground truth keypoints is... and prediction set Each element is matched and mapped using the conventional DETR target detection method, which will not be elaborated further here. To describe the uncertainty of keypoint coordinate prediction, this embodiment describes the two-dimensional image coordinate prediction results of keypoints as two independent one-dimensional Gaussian distributions in the x and y directions. Taking the x-component of keypoint coordinates as an example, the Gaussian distribution function N(x... e ,σ 2 The definition is as follows:

[0066]

[0067] Wherein, the mean of the Gaussian distribution is x e Let be the predicted value of the x-component of the keypoint coordinates, and let σ be the standard deviation representing the prediction uncertainty of the x-component. A smaller standard deviation indicates more accurate coordinate prediction. The true values ​​of the keypoint coordinates in the training data can be described by a Gaussian distribution as σ approaches 0, which is the Dirac delta function, as follows:

[0068] P D (x)=δ(xx g )

[0069] Where, x g The x-component of the keypoint coordinates is positive.

[0070] Therefore, the coordinate prediction loss function in this embodiment is specifically as follows:

[0071] L = L x-loc +L y-loc

[0072] Where L is the loss function, L x-loc Let L be the KL divergence between the true and predicted Gaussian distributions of the keypoint coordinates in the x-direction. x-loc The KL divergence of the Gaussian distribution of the true and predicted values ​​of the keypoint coordinates in the y-direction;

[0073] The KL divergence of the Gaussian distribution of the true and predicted values ​​of the keypoint coordinates in the x-direction is:

[0074]

[0075] α x =log(σ x 2 )

[0076] Where, α x σ is the coordinate uncertainty term of the key point coordinates in the x-direction. x The coordinate uncertainty of the key point in the x-direction;

[0077] The KL divergence of the Gaussian distribution between the true and predicted values ​​of the keypoint coordinates in the y-direction is as follows:

[0078]

[0079] α y =log(σ y 2 )

[0080] Among them, y g Let y be the true coordinates of the keypoint in the y-direction. e α represents the predicted coordinates of the keypoints in the y-direction. y σ is the coordinate uncertainty term of the key point coordinates in the y-direction. y The coordinate uncertainty of the key point in the y-direction is given.

[0081] The KL divergence of the Gaussian distributions of the true and predicted values ​​in the x and y directions of the keypoint coordinates consists of two terms, with the second term controlling the overall prediction standard deviation σ.x σ y To keep it as small as possible, the first term adaptively adjusts the predicted value and the prediction standard deviation. When the predicted value x... e y e With truth value x g y g When the difference is large, the prediction standard deviation σ x σ y The tendency is to choose a larger value to minimize the loss function when the predicted value x e y e With truth value x g y g When the difference is small, the prediction standard deviation σ x σ y It tends to take a smaller value. Especially when σ x σ y When the value is equal to 1, the loss function will degenerate into the Euclidean distance loss function.

[0082] As a preferred embodiment, during the actual training of the key point prediction model, the correlation term α is selected. x α y As the output of the coordinate uncertainty term in the keypoint prediction model, it replaces σ. x σ y The output of σ is used to avoid gradient explosion. It is worth noting that σ is output only after the keypoint prediction model has been trained. x σ y The output is the coordinate uncertainty term of the key point prediction model.

[0083] In a preferred embodiment, the loss function can also be changed from the 2-norm loss to the 1-norm loss by setting a threshold, specifically:

[0084]

[0085] αx=log(σ x 2 )

[0086]

[0087] Where, β x β y The threshold value is used.

[0088] By setting the threshold β x β y Changing the loss function from the 2-norm loss to the 1-norm loss combines the advantages of both, avoiding excessively large gradients in the early stages of model training and the unsmoothness near the zero point in the later stages of model training.

[0089] The key point detection and uncertainty prediction method in this embodiment can provide the key point coordinate prediction uncertainty while predicting the key point coordinates. Thus, in the process of monocular pose estimation, the weight of the weighted monocular pose estimation problem can be set as the reciprocal of the key point coordinate prediction uncertainty. Then, the weighted monocular pose estimation constraint equation is solved to obtain high-precision pose measurement results, thereby significantly improving the accuracy of monocular vision pose estimation.

[0090] The attitude rotation matrix from the target body coordinate system to the camera coordinate system is: The position vector (i.e., translation vector) of the origin of the target body coordinate system in the camera coordinate system is: ), respectively:

[0091]

[0092] T = [t] x t y t z ] T

[0093] Let P be the three-dimensional spatial coordinates of the i-th key point of the target in its body coordinate system. i =[X i Y i Z i ] T The key point corresponds to the two-dimensional coordinates p in the image. i =[x i y i ] T The imaging model of the target key points can be represented by the collinearity equation, as follows:

[0094]

[0095] Among them, C x and C y For the principal point of the camera image, F x and F y f is the equivalent focal length of the camera. x (·) and f y (·) represent the imaging functions in the x and y directions, respectively.

[0096] Conventional keypoint detection methods cannot obtain the uncertainty of keypoint image coordinate prediction, and all keypoints have the same weight when solving monocular pose problems. The high-precision target keypoint detection method proposed in this embodiment can provide the uncertainty of keypoint coordinate prediction while simultaneously predicting the coordinates, expressed as the standard deviation of the coordinate prediction. When solving the monocular pose estimation problem, the optimization weights for pose estimation can be determined based on the coordinate prediction uncertainty. Then, solving the weighted monocular pose estimation constraint equations yields more accurate pose measurement results. The weighted monocular pose estimation optimization problem is expressed as follows:

[0097]

[0098] in, and Let x and y represent the optimal weights for the i-th key point in the x and y directions, respectively.

[0099] In this embodiment, based on the weighted least squares theory, the weights of the weighted monocular pose estimation in the above formula can be adjusted to the reciprocal of the uncertainty of the key point coordinate prediction. After normalizing the weights, the weights of the weighted monocular pose estimation problem are obtained as follows:

[0100]

[0101] This allows for real-time adjustment of the weights of monocular pose estimation based on the coordinate uncertainty of each key point, thereby significantly improving the accuracy of monocular visual pose estimation.

[0102] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A method for keypoint detection and its uncertainty synchronous prediction, characterized in that, Includes the following steps: A key point prediction model is constructed. The input of the key point prediction model is a monocular image, and the output includes key point category, key point coordinates, and coordinate uncertainty. The keypoint coordinates are described as two independent one-dimensional Gaussian distributions in the x and y directions, respectively. The keypoint coordinates are taken as the mean of the Gaussian distribution, and the coordinate uncertainty is the standard deviation of the Gaussian distribution. A coordinate prediction loss function is constructed based on the KL divergence of the Gaussian distribution of the ground truth and predicted values ​​of keypoint coordinates. The keypoint prediction model is then trained based on this coordinate prediction loss function. Specifically, the coordinate prediction loss function is as follows: wherein, is a loss function, is a KL divergence of ground truth and predicted value Gaussian distribution of key point coordinate in x direction, is a KL divergence of ground truth and predicted value Gaussian distribution of key point coordinate in y direction; The monocular image to be tested is input into the trained key point prediction model to achieve simultaneous prediction of key point coordinates and coordinate uncertainty.

2. The key point detection and its uncertainty synchronous prediction method according to claim 1, characterized in that, The keypoint prediction model is a Transformer model, including: The backbone network is used to extract and overlay the two-dimensional convolutional features and spatial location codes of monocular images, and unfold them into one-dimensional features; An encoder is used to obtain an encoded feature vector based on the one-dimensional features; A decoder is used to obtain a decoded feature vector based on a preset target query vector and the encoded feature vector; A prediction network is used to obtain prediction results of key point categories, key point coordinates, and coordinate uncertainties in a monocular image based on the decoded feature vector.

3. The key point detection and its uncertainty synchronous prediction method according to claim 1, characterized in that, The KL divergence of the Gaussian distribution of the true and predicted values ​​of the keypoint coordinates in the x-direction is specifically as follows: in, This represents the true coordinates of the keypoints in the x-direction. These are the predicted coordinates of the key points in the x-direction. This refers to the coordinate uncertainty term of the key point coordinates in the x-direction. The coordinate uncertainty of the key point in the x-direction; The KL divergence of the Gaussian distribution between the true and predicted values ​​of the keypoint coordinates in the y-direction is specifically as follows: in, This represents the true coordinates of the keypoints in the y-direction. These are the predicted coordinates of the key points in the y-direction. This refers to the coordinate uncertainty term of the key point coordinates in the y-direction. The coordinate uncertainty of the key point in the y-direction is given.

4. The key point detection and its uncertainty synchronous prediction method according to claim 1, characterized in that, The KL divergence of the Gaussian distribution of the true and predicted values ​​of the keypoint coordinates in the x-direction is specifically as follows: in, This represents the true coordinates of the keypoints in the x-direction. These are the predicted coordinates of the key points in the x-direction. This refers to the coordinate uncertainty term of the key point coordinates in the x-direction. Let x be the coordinate uncertainty of the key point in the x-direction. For the threshold; The KL divergence of the Gaussian distribution between the true and predicted values ​​of the keypoint coordinates in the y-direction is specifically as follows: in, This represents the true coordinates of the keypoints in the y-direction. These are the predicted coordinates of the key points in the y-direction. This refers to the coordinate uncertainty term of the key point coordinates in the y-direction. Let represent the coordinate uncertainty of the key point in the y-direction. The threshold value is used.

5. The key point detection and its uncertainty synchronous prediction method according to claim 3 or 4, characterized in that, The key point prediction model outputs correlation terms. , Output coordinate uncertainty in the form of , This is to avoid gradient explosion.

6. The key point detection and its uncertainty synchronous prediction method according to any one of claims 1 to 4, characterized in that, After obtaining the coordinates and coordinate uncertainty of the key points in the monocular image to be tested, when performing monocular pose estimation based on the monocular image to be tested, the reciprocal of the coordinate uncertainty is used as the weight of the corresponding key point coordinates.

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