足球视频AI(一)——位置与平面坐标的转换

依赖： C# OpenCVSharp WPF Numpy

目的：解决足球场上，人物投影到二维平面的位置坐标

图A / B/ C

一、基础概念

1.1标准球场的定义：

参考：https://zh.m.wikipedia.org/zh/%E8%B6%B3%E7%90%83%E5%A0%B4

图 D

1.2 配准思路

图A->图B，建立坐标关系对；

图B->图D，建立真实坐标系的配准基准点对（需要4个以上）

图D->图C，建立显示坐标系的配准基准点对（图C尺寸已知，所有关键位置A-J均已知）

对于全局，利用OpenCV FindHomography，求得D-C坐标转换矩阵T；

对于每帧图片，利用OpenCV FindHomography，求得B-D坐标转换矩阵T1；

将对象检测的球员投影到图3

二、代码实现

2.1 标画关键点

WPF界面

    <Grid><Grid.ColumnDefinitions><ColumnDefinition Width="0.4*"/><ColumnDefinition Width="0.6*"/></Grid.ColumnDefinitions><Grid x:Name="gridPointSelector" Width="350" Height="234" VerticalAlignment="Center" HorizontalAlignment="Center" ><Grid.ColumnDefinitions><ColumnDefinition Width="0.15619*"/><ColumnDefinition Width="0.34762*"/><ColumnDefinition Width="0.34762*"/><ColumnDefinition Width="0.15619*"/></Grid.ColumnDefinitions><Grid.RowDefinitions><RowDefinition Height="0.20441*" /><RowDefinition Height="0.59118*"/><RowDefinition Height="0.20441*"/></Grid.RowDefinitions><Image Source="{StaticResource 2D_field}" Grid.ColumnSpan="4" Grid.RowSpan="3" /><ToggleButton Content="A" Grid.Row="0" Grid.Column="0"  HorizontalAlignment="Left" VerticalAlignment="Top"  Margin="-15,-15,0,0" Click="ToggleButton_Click"/><ToggleButton Content="B" Grid.Row="0" Grid.Column="1" HorizontalAlignment="Right" VerticalAlignment="Top" Margin="0,-15,-15,0"  Click="ToggleButton_Click"/><ToggleButton Content="C" Grid.Row="0" Grid.Column="3" HorizontalAlignment="Right" VerticalAlignment="Top" Margin="0,-15,-15,0"  Click="ToggleButton_Click"/><ToggleButton Content="D" Grid.Row="1" Grid.Column="0" HorizontalAlignment="Right" VerticalAlignment="Top" Margin="0,-15,-15,0"  Click="ToggleButton_Click"/><ToggleButton Content="E" Grid.Row="1" Grid.Column="2" HorizontalAlignment="Right" VerticalAlignment="Top" Margin="0,-15,-15,0"  Click="ToggleButton_Click"/><ToggleButton Content="F" Grid.Row="2" Grid.Column="0" HorizontalAlignment="Right" VerticalAlignment="Top" Margin="0,-15,-15,0"  Click="ToggleButton_Click"/><ToggleButton Content="G" Grid.Row="2" Grid.Column="2" HorizontalAlignment="Right" VerticalAlignment="Top"   Click="ToggleButton_Click"/><ToggleButton Content="H" Grid.Row="2" Grid.Column="0"HorizontalAlignment="Left" VerticalAlignment="Bottom"    Click="ToggleButton_Click" /><ToggleButton Content="I" Grid.Row="2" Grid.Column="1" HorizontalAlignment="Right" VerticalAlignment="Bottom"  Click="ToggleButton_Click"/><ToggleButton Content="J" Grid.Row="2" Grid.Column="3" HorizontalAlignment="Right" VerticalAlignment="Bottom"  Click="ToggleButton_Click"/></Grid><Grid Grid.Column="1" x:Name="gridMain" ClipToBounds="True"><Image x:Name="imgMain" Source="{Binding OriginalImage }" Stretch="Uniform"/><Canvas x:Name="canvas" Height="{Binding ElementName=imgMain,Path=ActualHeight}"Width="{Binding ElementName=imgMain,Path=ActualWidth}" Background="Transparent"IsEnabled="{Binding IsSelectting}" MouseLeftButtonUp="canvas_MouseLeftButtonUp"></Canvas></Grid></Grid>

数据结构

public class VedioPointMark
{public string? Name { get; set; }/// <summary>/// 球场坐标/// </summary>public Point2d FiledPoint { get; set; }/// <summary>/// 视频像素坐标/// </summary>public Point2d VideoPixelPoint { get; set; }}

WPF后端代码

 public partial class UCPointMark : UserControl{MPointMark model;private readonly int ellipseSize = 16;ToggleButton? selectButton;public UCPointMark(){InitializeComponent();model = new MPointMark();this.DataContext = model;}private Border? DrawPoint(){if (selectButton == null)return null;Border myBorder = new Border();myBorder.CornerRadius = new CornerRadius(ellipseSize);myBorder.Width = ellipseSize;myBorder.BorderBrush = new SolidColorBrush(Colors.Blue);myBorder.Background = new SolidColorBrush(Colors.Red);myBorder.Child = new TextBlock() { Text = selectButton.Content.ToString(),Foreground = new SolidColorBrush(Colors.White),TextAlignment = TextAlignment.Center};selectButton.Tag = myBorder;return myBorder;}public List<VedioPointMark> CalculateTransform() {var markPoints = new List<VedioPointMark>();//必须选择4各以上if (canvas.Children.Count < 4)return markPoints;var allPoints = VideoFieldTransform.CreatePointMarks();var axisX = (double)model.OriginalImageSize.Width / this.imgMain.ActualWidth;var axisY = (double)model.OriginalImageSize.Height / this.imgMain.ActualHeight;foreach (var element in this.gridPointSelector.Children){if (element is ToggleButton toggle && toggle.Tag is Border pixcelBorder&& pixcelBorder.Tag is Point pixcelPoint && toggle.IsChecked == true){var mark = allPoints.Where(p => p.Name?.Equals(toggle.Content.ToString()) == true).FirstOrDefault();if (mark == null)continue;mark.VideoPixelPoint = new OpenCvSharp.Point2d( pixcelPoint.X * axisX, pixcelPoint.Y * axisY -40 );markPoints.Add(mark);}}return markPoints;}private void canvas_MouseLeftButtonUp(object sender, MouseButtonEventArgs e){try{var clickPoint = e.GetPosition(this.canvas);var ellipse = DrawPoint();if (null == ellipse) return;this.canvas.Children.Add(ellipse);Canvas.SetLeft(ellipse, clickPoint.X - ellipseSize / 2);Canvas.SetTop(ellipse, clickPoint.Y - ellipseSize / 2);ellipse.Tag = new Point(clickPoint.X, clickPoint.Y);model.IsSelectting = false;}catch (Exception ex){this.Log(ex);}}

2.2 配准转换类

    public class VideoFieldTransform{private readonly Point2d[] point1;  //视频可视范围内的关键点坐标（4个以上）private readonly Point2d[] point2;  //真实球场坐标系 或 平面坐标系private readonly Mat H; //变换矩阵public VideoFieldTransform(List<VedioPointMark> pointMarks,bool haspoint2 = false){if (!haspoint2){//视频坐标投影到物理坐标pointMarks = pointMarks.OrderBy(p => p.Name).ToList();point1 = pointMarks.Select(p => p.FiledPoint).ToArray();point2 = pointMarks.Select(p => p.VideoPixelPoint).ToArray();}else{//物理坐标投影到图片point1 = new Point2d[] {new Point2d(0, 0),new Point2d(16.4f, 13.9f),new Point2d(52.5f, 0.0f),new Point2d(88.6f, 13.9f ),new Point2d(105f, 0.0f),new Point2d(105f, 68.0f),new Point2d(52.5f, 68f),new Point2d(0, 68f)};point2 = new Point2d[] {new Point2d(0.0f, 0.0f ),new Point2d(164f, 152f ),new Point2d( 525f, 0.0f),new Point2d(886f, 152f),new Point2d(1050f, 0f),new Point2d(1050f, 699f),new Point2d(525f, 699f),new Point2d(0f, 699f),};}H = CalculateHomoGraphy(haspoint2);}public static List<VedioPointMark> CreatePointMarks(){return new List<VedioPointMark>(){new VedioPointMark() {  Name = "A", FiledPoint = new Point2d(0, 0)},new VedioPointMark() {  Name = "D", FiledPoint = new Point2d(16.4f, 13.9f)},new VedioPointMark() {  Name = "B", FiledPoint = new Point2d(52.5f, 0.0f)},new VedioPointMark() {  Name = "E", FiledPoint = new Point2d(88.6f, 13.9f)},new VedioPointMark() {  Name = "C", FiledPoint = new Point2d(105f, 0.0f)},new VedioPointMark() {  Name = "J", FiledPoint = new Point2d(105f, 68.0f)},new VedioPointMark() {  Name = "I", FiledPoint = new Point2d(52.5f, 68f)},new VedioPointMark() {  Name = "H", FiledPoint = new Point2d(0, 68f)},new VedioPointMark() {  Name = "F", FiledPoint = new Point2d(16.4f, 40.2f)},new VedioPointMark() {  Name = "G", FiledPoint = new Point2d(88.6, 40.2f)},};}/// <summary>///     视频帧(假定摄像头位置不变)与 平面模式的球场位置的坐标系换算，求得矩阵/// </summary>/// <param name="make_rotate"></param>/// <returns>返回H 为变换矩阵</returns>private Mat CalculateHomoGraphy(bool make_rotate = false){//var k = InputArray.Create(point2.GetData<float[]>());if (!make_rotate)return Cv2.FindHomography(point2, point1, HomographyMethods.Ransac);return Cv2.FindHomography(point1,point2, HomographyMethods.Ransac);}/// <summary>/// 根据坐标点(X,Y) 与 坐标系变换矩阵乘积，换算帧图像的位置到平面球场坐标的位置/// </summary>public Point Transform(Point p){var img2Bounds = new[]{new Point2d(p.X, p.Y)};var img2BoundsTransformed = Cv2.PerspectiveTransform(img2Bounds, H);var drawingPoints = img2BoundsTransformed.Select(p => (Point)p).FirstOrDefault();return drawingPoints;}}

2.3 初始化

图D->图C，建立显示坐标系的配准基准点对（图C尺寸已知，所有关键位置A-J均已知）

其中，pointMarks为WPF标记的点集

if (pointMarks?.Count > 3)proj_field_to_top = new VideoFieldTransform(pointMarks);  //真实球场坐标

从绝对球场尺寸到显示尺寸的变换，参见1.2 D-C变换

 proj_field_2d = new VideoFieldTransform(true);  //平面显示坐标

加载底图

//加载球场真实坐标系底图
D_field_photo = LoadImages.Load("2D_field.png");

初始化目标检测

//对象检测,此处略...参见AI机器学习（五）相关的内容
detector = new DetectorYolov7();

2.4 逐帧变换

假设某个球员的Mat 区域，在视频中的像素位置标记为rect

//获取帧图片
foreach(var frame in LoadImages.LoadVideo("你的视频路径"))
{Mat imagedetect = new Mat();//投影所有的球员foreach(var prediction =detector.Detect(imagedetect)){var rect = prediction.Rectangle;//拷贝真实球场坐标底图  var J = D_field_photo.Clone();//转换坐标系var pfield = proj_field_to_top.Transform(new OpenCvSharp.Point(rect.X , rect.Y));//用于显示的图像var pshow = proj_field_2d.Transform(new OpenCvSharp.Point(pfield.X, pfield.Y));Cv2.Circle(J, pshow.X, pshow.Y, 10, Scalar.LightCyan, -1);//发送给前端WPF，这里没给出用于显示的页面，大家自己实现一个即可，只需要一个Image控件OnDisplay?.Invoke(null, J.Resize(new OpenCvSharp.Size(300, 200)).ToBytes());}
}

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