Kinect realworld速度坐标处理算法的矢量化

Question

我最近开始使用pylibfreenect2在Linux上使用Kinect V2。在

当我第一次能够在散点图中显示深度帧数据时，我很失望地发现没有一个深度像素位于正确的位置。在

房间的侧视图（注意天花板是弯曲的）。

我做了一些研究，发现有一些简单的三角函数来做转换。在

为了测试，我从pylibfreenect2中预先编写的函数开始，该函数接受列、行和深度像素强度，然后返回该像素的实际位置：

X, Y, Z = registration.getPointXYZ(undistorted, row, col)

这在纠正位置方面做得非常好：

使用getPointXYZ（）或getPointXYZRGB（）的唯一缺点是它们一次只能处理一个像素。在Python中这可能需要一段时间，因为它需要使用嵌套for循环，如下所示：

^{pr2}$

计算点xyi（）是如何更好地理解坐标的。 据我所知，它看起来类似于OpenKinect的处理函数：depthToPointCloudPos()。尽管我怀疑libfreenect2的版本有更多的秘密。

以gitHub源代码为例，我尝试用Python重新编写它，以供我自己的实验使用，并得出以下结论：

#camera information based on the Kinect v2 hardware
CameraParams = {
  "cx":254.878,
  "cy":205.395,
  "fx":365.456,
  "fy":365.456,
  "k1":0.0905474,
  "k2":-0.26819,
  "k3":0.0950862,
  "p1":0.0,
  "p2":0.0,
}

def depthToPointCloudPos(x_d, y_d, z, scale = 1000):
    #calculate the xyz camera position based on the depth data    
    x = (x_d - CameraParams['cx']) * z / CameraParams['fx']
    y = (y_d - CameraParams['cy']) * z / CameraParams['fy']

    return x/scale, y/scale, z/scale

这是传统getPointXYZ和我的自定义函数的比较：

他们看起来很相似。但是有明显的区别。左边的比较显示了更直的边缘，也有一些正弦形状的平顶。我怀疑还需要额外的数学知识。在

如果有人知道我的函数和libfreenect2的getPointXYZ有什么不同，我会非常感兴趣的。在

不过，我在这里发布的主要原因是询问是否尝试将上述函数矢量化，以处理整个数组，而不是循环遍历每个元素。在

应用我从上面学到的知识，我可以编写一个函数，它似乎是depthToPointCloudPos的矢量化替代：

[编辑]

感谢本杰明帮助我们使这个功能更加高效！

def depthMatrixToPointCloudPos(z, scale=1000):
    #bacically this is a vectorized version of depthToPointCloudPos()
    C, R = np.indices(z.shape)

    R = np.subtract(R, CameraParams['cx'])
    R = np.multiply(R, z)
    R = np.divide(R, CameraParams['fx'] * scale)

    C = np.subtract(C, CameraParams['cy'])
    C = np.multiply(C, z)
    C = np.divide(C, CameraParams['fy'] * scale)

    return np.column_stack((z.ravel() / scale, R.ravel(), -C.ravel()))

这与前面的函数depthToPointCloudPos（）的工作原理和生成的点云结果相同。唯一的区别是我的处理速度从~1fps提高到了5-10fps（哇哦！）。我相信这消除了Python进行所有计算所造成的瓶颈。因此，我的散点图现在运行顺利，半现实世界的坐标正在计算。在

现在我有了一个从深度帧检索三维坐标的有效函数，我真的想应用这种方法来将彩色相机数据映射到我的深度像素。然而，我不确定这需要什么数学或变量，而且在Google上也没有提到如何计算它。在

或者，我可以使用libfreenect2使用getPointXYZRGB将颜色映射到深度像素：

#Format undistorted and regisered data to real-world coordinates with mapped colors (dont forget color=out_col in setData)
n_rows = d.shape[0]
n_columns = d.shape[1]
out = np.zeros((n_rows * n_columns, 3), dtype=np.float64)
colors = np.zeros((d.shape[0] * d.shape[1], 3), dtype=np.float64)
for row in range(n_rows):
    for col in range(n_columns):
        X, Y, Z, B, G, R = registration.getPointXYZRGB(undistorted, registered, row, col)
        out[row * n_columns + col] = np.array([X, Y, Z])
        colors[row * n_columns + col] = np.divide([R, G, B], 255)
sp2.setData(pos=np.array(out, dtype=np.float64), color=colors, size=2)

生成点云和彩色顶点（非常慢<；1Fps）：

总之，我的两个问题基本上是：

• 需要哪些额外的步骤才能使我的depthToPointCloudPos（）函数返回的实际三维坐标数据（以及矢量化实现）与getPointXYZ（）从libfreenect2返回的数据更相似？

• 而且，在我自己的应用程序中创建一种（可能是矢量化的）生成深度到颜色注册图的方法会涉及到什么？请查看已解决的更新。

---

[更新]

我设法使用注册的帧将颜色数据映射到每个像素。 它非常简单，只需要在调用setData（）之前添加以下行：

colors = registered.asarray(np.uint8)
colors = np.divide(colors, 255)
colors = colors.reshape(colors.shape[0] * colors.shape[1], 4 )
colors = colors[:, :3:] #BGRA to BGR (slices out the alpha channel)  
colors = colors[...,::-1] #BGR to RGB

这使得Python能够快速处理颜色数据并给出平滑的结果。我已经将它们更新/添加到下面的函数示例中。在

在Python中实时运行颜色注册的真实世界坐标处理！

（GIF图像分辨率大大降低）

---

[更新]

在花了一点时间使用这个应用程序之后，我添加了一些额外的参数，并调整了它们的值，希望能够改善散点图的视觉质量，并可能使这个示例/问题的内容更加直观。在

最重要的是，我已将顶点设置为不透明：

sp2 = gl.GLScatterPlotItem(pos=pos)
sp2.setGLOptions('opaque') # Ensures not to allow vertexes located behinde other vertexes to be seen.

然后我注意到，每当缩放到离曲面很近的地方时，相邻顶点之间的距离似乎会扩大，直到所有可见的都是空白。部分原因是顶点的点大小没有改变。在

为了帮助创建一个充满彩色顶点的“缩放友好”视口，我添加了这些线，这些线根据当前缩放级别计算顶点大小（每次更新）：

# Calculate a dynamic vertex size based on window dimensions and camera's position - To become the "size" input for the scatterplot's setData() function.
v_rate = 8.0 # Rate that vertex sizes will increase as zoom level increases (adjust this to any desired value).
v_scale = np.float32(v_rate) / gl_widget.opts['distance'] # Vertex size increases as the camera is "zoomed" towards center of view.
v_offset = (gl_widget.geometry().width() / 1000)**2 # Vertex size is offset based on actual width of the viewport.
v_size = v_scale + v_offset

你瞧：

（同样，GIF图像分辨率大大降低）

也许还不如点云的蒙皮好，但是当你试图理解你真正在看什么时，它似乎确实帮助事情变得更简单。在

所有提到的修改都包含在功能示例中。

---

[更新]

如前两个动画所示，与栅格轴相比，真实世界坐标的点云的方向是倾斜的。这是因为我并没有真正补偿Kinect的实际方位！在

因此，我实现了一个额外的矢量化trig函数，它为每个顶点计算一个新的（旋转和偏移）坐标。这将使它们相对于Kinect在真实空间中的实际位置正确定向。并且在使用倾斜的三脚架时是必要的（也可用于连接INU或陀螺仪/加速计的输出，以进行实时反馈。在

def applyCameraMatrixOrientation(pt):
    # Kinect Sensor Orientation Compensation
    # bacically this is a vectorized version of applyCameraOrientation()
    # uses same trig to rotate a vertex around a gimbal.
    def rotatePoints(ax1, ax2, deg):
        # math to rotate vertexes around a center point on a plane.
        hyp = np.sqrt(pt[:, ax1] ** 2 + pt[:, ax2] ** 2) # Get the length of the hypotenuse of the real-world coordinate from center of rotation, this is the radius!
        d_tan = np.arctan2(pt[:, ax2], pt[:, ax1]) # Calculate the vertexes current angle (returns radians that go from -180 to 180)

        cur_angle = np.degrees(d_tan) % 360 # Convert radians to degrees and use modulo to adjust range from 0 to 360.
        new_angle = np.radians((cur_angle + deg) % 360) # The new angle (in radians) of the vertexes after being rotated by the value of deg.

        pt[:, ax1] = hyp * np.cos(new_angle) # Calculate the rotated coordinate for this axis.
        pt[:, ax2] = hyp * np.sin(new_angle) # Calculate the rotated coordinate for this axis.

    #rotatePoints(1, 2, CameraPosition['roll']) #rotate on the Y&Z plane # Disabled because most tripods don't roll. If an Inertial Nav Unit is available this could be used)
    rotatePoints(0, 2, CameraPosition['elevation']) #rotate on the X&Z plane
    rotatePoints(0, 1, CameraPosition['azimuth']) #rotate on the X&Y plane

    # Apply offsets for height and linear position of the sensor (from viewport's center)
    pt[:] += np.float_([CameraPosition['x'], CameraPosition['y'], CameraPosition['z']])



    return pt

请注意：rotatePoints（）仅用于“仰角”和“方位角”。这是因为大多数三脚架不支持roll，并且为了节省CPU周期，它在默认情况下被禁用。如果你想做一些花哨的事情，那么你一定可以不加评论！！

请注意，此图像中的网格地板是水平的，但左侧的点云没有与其对齐：

设置Kinect方向的参数：

CameraPosition = {
    "x": 0, # actual position in meters of kinect sensor relative to the viewport's center.
    "y": 0, # actual position in meters of kinect sensor relative to the viewport's center.
    "z": 1.7, # height in meters of actual kinect sensor from the floor.
    "roll": 0, # angle in degrees of sensor's roll (used for INU input - trig function for this is commented out by default).
    "azimuth": 0, # sensor's yaw angle in degrees.
    "elevation": -15, # sensor's pitch angle in degrees.
}

您应该根据传感器的实际位置和方向更新这些信息：

两个最重要的参数是theta（仰角）角和离地面的高度。我只用一个简单的卷尺和一个校准过的眼睛，但是我打算有朝一日输入编码器或INU数据来实时更新这些参数（随着传感器的移动）。在

同样，所有的变化都反映在函数示例中。

---

如果有人成功地对这个例子进行了改进，或者对如何使事情更紧凑提出了建议，我将非常感谢您能留下一条解释细节的评论。

以下是本项目的完整功能示例：

#! /usr/bin/python

#--------------------------------#
# Kinect v2 point cloud visualization using a Numpy based 
# real-world coordinate processing algorithm and OpenGL.
#--------------------------------#

import sys
import numpy as np

from pyqtgraph.Qt import QtCore, QtGui
import pyqtgraph.opengl as gl

from pylibfreenect2 import Freenect2, SyncMultiFrameListener
from pylibfreenect2 import FrameType, Registration, Frame, libfreenect2

fn = Freenect2()
num_devices = fn.enumerateDevices()
if num_devices == 0:
    print("No device connected!")
    sys.exit(1)

serial = fn.getDeviceSerialNumber(0)
device = fn.openDevice(serial)

types = 0
types |= FrameType.Color
types |= (FrameType.Ir | FrameType.Depth)
listener = SyncMultiFrameListener(types)

# Register listeners
device.setColorFrameListener(listener)
device.setIrAndDepthFrameListener(listener)

device.start()

# NOTE: must be called after device.start()
registration = Registration(device.getIrCameraParams(),
                            device.getColorCameraParams())

undistorted = Frame(512, 424, 4)
registered = Frame(512, 424, 4)


#QT app
app = QtGui.QApplication([])
gl_widget = gl.GLViewWidget()
gl_widget.show()
gl_grid = gl.GLGridItem()
gl_widget.addItem(gl_grid)

#initialize some points data
pos = np.zeros((1,3))

sp2 = gl.GLScatterPlotItem(pos=pos)
sp2.setGLOptions('opaque') # Ensures not to allow vertexes located behinde other vertexes to be seen.

gl_widget.addItem(sp2)

# Kinects's intrinsic parameters based on v2 hardware (estimated).
CameraParams = {
  "cx":254.878,
  "cy":205.395,
  "fx":365.456,
  "fy":365.456,
  "k1":0.0905474,
  "k2":-0.26819,
  "k3":0.0950862,
  "p1":0.0,
  "p2":0.0,
}

def depthToPointCloudPos(x_d, y_d, z, scale=1000):
    # This runs in Python slowly as it is required to be called from within a loop, but it is a more intuitive example than it's vertorized alternative (Purly for example)
    # calculate the real-world xyz vertex coordinate from the raw depth data (one vertex at a time).
    x = (x_d - CameraParams['cx']) * z / CameraParams['fx']
    y = (y_d - CameraParams['cy']) * z / CameraParams['fy']

    return x / scale, y / scale, z / scale

def depthMatrixToPointCloudPos(z, scale=1000):
    # bacically this is a vectorized version of depthToPointCloudPos()
    # calculate the real-world xyz vertex coordinates from the raw depth data matrix.
    C, R = np.indices(z.shape)

    R = np.subtract(R, CameraParams['cx'])
    R = np.multiply(R, z)
    R = np.divide(R, CameraParams['fx'] * scale)

    C = np.subtract(C, CameraParams['cy'])
    C = np.multiply(C, z)
    C = np.divide(C, CameraParams['fy'] * scale)

    return np.column_stack((z.ravel() / scale, R.ravel(), -C.ravel()))

# Kinect's physical orientation in the real world.
CameraPosition = {
    "x": 0, # actual position in meters of kinect sensor relative to the viewport's center.
    "y": 0, # actual position in meters of kinect sensor relative to the viewport's center.
    "z": 1.7, # height in meters of actual kinect sensor from the floor.
    "roll": 0, # angle in degrees of sensor's roll (used for INU input - trig function for this is commented out by default).
    "azimuth": 0, # sensor's yaw angle in degrees.
    "elevation": -15, # sensor's pitch angle in degrees.
}

def applyCameraOrientation(pt):
    # Kinect Sensor Orientation Compensation
    # This runs slowly in Python as it is required to be called within a loop, but it is a more intuitive example than it's vertorized alternative (Purly for example)
    # use trig to rotate a vertex around a gimbal.
    def rotatePoints(ax1, ax2, deg):
        # math to rotate vertexes around a center point on a plane.
        hyp = np.sqrt(pt[ax1] ** 2 + pt[ax2] ** 2) # Get the length of the hypotenuse of the real-world coordinate from center of rotation, this is the radius!
        d_tan = np.arctan2(pt[ax2], pt[ax1]) # Calculate the vertexes current angle (returns radians that go from -180 to 180)

        cur_angle = np.degrees(d_tan) % 360 # Convert radians to degrees and use modulo to adjust range from 0 to 360.
        new_angle = np.radians((cur_angle + deg) % 360) # The new angle (in radians) of the vertexes after being rotated by the value of deg.

        pt[ax1] = hyp * np.cos(new_angle) # Calculate the rotated coordinate for this axis.
        pt[ax2] = hyp * np.sin(new_angle) # Calculate the rotated coordinate for this axis.

    #rotatePoints(0, 2, CameraPosition['roll']) #rotate on the Y&Z plane # Disabled because most tripods don't roll. If an Inertial Nav Unit is available this could be used)
    rotatePoints(1, 2, CameraPosition['elevation']) #rotate on the X&Z plane
    rotatePoints(0, 1, CameraPosition['azimuth']) #rotate on the X&Y plane

    # Apply offsets for height and linear position of the sensor (from viewport's center)
    pt[:] += np.float_([CameraPosition['x'], CameraPosition['y'], CameraPosition['z']])



    return pt

def applyCameraMatrixOrientation(pt):
    # Kinect Sensor Orientation Compensation
    # bacically this is a vectorized version of applyCameraOrientation()
    # uses same trig to rotate a vertex around a gimbal.
    def rotatePoints(ax1, ax2, deg):
        # math to rotate vertexes around a center point on a plane.
        hyp = np.sqrt(pt[:, ax1] ** 2 + pt[:, ax2] ** 2) # Get the length of the hypotenuse of the real-world coordinate from center of rotation, this is the radius!
        d_tan = np.arctan2(pt[:, ax2], pt[:, ax1]) # Calculate the vertexes current angle (returns radians that go from -180 to 180)

        cur_angle = np.degrees(d_tan) % 360 # Convert radians to degrees and use modulo to adjust range from 0 to 360.
        new_angle = np.radians((cur_angle + deg) % 360) # The new angle (in radians) of the vertexes after being rotated by the value of deg.

        pt[:, ax1] = hyp * np.cos(new_angle) # Calculate the rotated coordinate for this axis.
        pt[:, ax2] = hyp * np.sin(new_angle) # Calculate the rotated coordinate for this axis.

    #rotatePoints(1, 2, CameraPosition['roll']) #rotate on the Y&Z plane # Disabled because most tripods don't roll. If an Inertial Nav Unit is available this could be used)
    rotatePoints(0, 2, CameraPosition['elevation']) #rotate on the X&Z plane
    rotatePoints(0, 1, CameraPosition['azimuth']) #rotate on the X&Y

    # Apply offsets for height and linear position of the sensor (from viewport's center)
    pt[:] += np.float_([CameraPosition['x'], CameraPosition['y'], CameraPosition['z']])



    return pt


def update():
    colors = ((1.0, 1.0, 1.0, 1.0))

    frames = listener.waitForNewFrame()

    # Get the frames from the Kinect sensor
    ir = frames["ir"]
    color = frames["color"]
    depth = frames["depth"]

    d = depth.asarray() #the depth frame as an array (Needed only with non-vectorized functions)

    registration.apply(color, depth, undistorted, registered)

    # Format the color registration map - To become the "color" input for the scatterplot's setData() function.
    colors = registered.asarray(np.uint8)
    colors = np.divide(colors, 255) # values must be between 0.0 - 1.0
    colors = colors.reshape(colors.shape[0] * colors.shape[1], 4 ) # From: Rows X Cols X RGB -to- [[r,g,b],[r,g,b]...]
    colors = colors[:, :3:]  # remove alpha (fourth index) from BGRA to BGR
    colors = colors[...,::-1] #BGR to RGB

    # Calculate a dynamic vertex size based on window dimensions and camera's position - To become the "size" input for the scatterplot's setData() function.
    v_rate = 5.0 # Rate that vertex sizes will increase as zoom level increases (adjust this to any desired value).
    v_scale = np.float32(v_rate) / gl_widget.opts['distance'] # Vertex size increases as the camera is "zoomed" towards center of view.
    v_offset = (gl_widget.geometry().width() / 1000)**2 # Vertex size is offset based on actual width of the viewport.
    v_size = v_scale + v_offset

    # Calculate 3d coordinates (Note: five optional methods are shown - only one should be un-commented at any given time)

    """
    # Method 1 (No Processing) - Format raw depth data to be displayed
    m, n = d.shape
    R, C = np.mgrid[:m, :n]
    out = np.column_stack((d.ravel() / 4500, C.ravel()/m, (-R.ravel()/n)+1))
    """

    # Method 2 (Fastest) - Format and compute the real-world 3d coordinates using a fast vectorized algorithm - To become the "pos" input for the scatterplot's setData() function.
    out = depthMatrixToPointCloudPos(undistorted.asarray(np.float32))

    """
    # Method 3 - Format undistorted depth data to real-world coordinates
    n_rows, n_columns = d.shape
    out = np.zeros((n_rows * n_columns, 3), dtype=np.float32)
    for row in range(n_rows):
        for col in range(n_columns):
            z = undistorted.asarray(np.float32)[row][col]
            X, Y, Z = depthToPointCloudPos(row, col, z)
            out[row * n_columns + col] = np.array([Z, Y, -X])
    """

    """
    # Method 4 - Format undistorted depth data to real-world coordinates
    n_rows, n_columns = d.shape
    out = np.zeros((n_rows * n_columns, 3), dtype=np.float64)
    for row in range(n_rows):
        for col in range(n_columns):
            X, Y, Z = registration.getPointXYZ(undistorted, row, col)
            out[row * n_columns + col] = np.array([Z, X, -Y])
    """

    """
    # Method 5 - Format undistorted and regisered data to real-world coordinates with mapped colors (dont forget color=colors in setData)
    n_rows, n_columns = d.shape
    out = np.zeros((n_rows * n_columns, 3), dtype=np.float64)
    colors = np.zeros((d.shape[0] * d.shape[1], 3), dtype=np.float64)
    for row in range(n_rows):
        for col in range(n_columns):
            X, Y, Z, B, G, R = registration.getPointXYZRGB(undistorted, registered, row, col)
            out[row * n_columns + col] = np.array([Z, X, -Y])
            colors[row * n_columns + col] = np.divide([R, G, B], 255)
    """


    # Kinect sensor real-world orientation compensation.
    out = applyCameraMatrixOrientation(out)

    """
    # For demonstrating the non-vectorized orientation compensation function (slow)
    for i, pt in enumerate(out):
        out[i] = applyCameraOrientation(pt)
    """


    # Show the data in a scatter plot
    sp2.setData(pos=out, color=colors, size=v_size)

    # Lastly, release frames from memory.
    listener.release(frames)

t = QtCore.QTimer()
t.timeout.connect(update)
t.start(50)


## Start Qt event loop unless running in interactive mode.
if __name__ == '__main__':
    import sys
    if (sys.flags.interactive != 1) or not hasattr(QtCore, 'PYQT_VERSION'):
        QtGui.QApplication.instance().exec_()

device.stop()
device.close()

sys.exit(0)

Answer 1

这不是一个完整的答案。。。我只想指出，您正在创建许多临时阵列，在这些阵列中可以执行更多的操作：

def depthMatrixToPointCloudPos2(z, scale=1000):

    R, C = numpy.indices(z.shape)

    R -= CameraParams['cx'])
    R *= z
    R /= CameraParams['fx'] * scale

    C -= CameraParams['cy']
    C *= z
    C /= CameraParams['fy'] * scale

    return np.column_stack((z.ravel() / scale, R.ravel(), -C.ravel()))

（如果我没看错你的代码。）

另外，请注意数据类型，如果您在64位计算机上，则默认为64位。为了减少需要处理的数据量，是否可以使用较小的类型？在