Agisoft Photoscan/Mateshape 相机参数XML解读

Agisoft Photoscan / Mateshape是一款利用照片进行高质量三维建模的软件，只需要数张照片就可以对场景进行稀疏和稠密重建。Photoscan的重建结果能够以点云（.ply）和相机内外参数（.xml）的格式导出；相机参数文件的基本结构如下：

<?xml version="1.0" encoding="UTF-8"?>
<document version="1.5.0">
  <chunk label="Chunk 2" enabled="1">
    <sensors next_id="2">
      <sensor id="0" label="unknown" type="frame">
        <resolution width="2256" height="1504"/>
        <property name="fixed" value="0"/>
        <property name="layer_index" value="0"/>
        <bands>
          <band label="Red"/>
          <band label="Green"/>
          <band label="Blue"/>
        </bands>
        <data_type>uint8</data_type>
        <calibration type="frame" class="adjusted">
          <resolution width="2256" height="1504"/>
          <f>1940.44326476953</f>
          <cx>13.1749075726049</cx>
          <cy>9.90781070951072</cy>
          <k1>-0.105652576294122</k1>
          <k2>0.181325297027899</k2>
          <k3>-0.0592964727618129</k3>
          <p1>0.00206081605079198</p1>
          <p2>0.000470042919918441</p2>
        </calibration>
        <covariance>
          <params>f cx cy k1 k2 k3 p1 p2</params>
          <coeffs>2.0733588750258165e+000 3.3929432732417547e-001 -3.1733835341771577e-001 -5.4658442369333565e-004 3.0370081230896582e-003 -3.1356947110278534e-003 5.2705435197758904e-005 -5.1942928435856751e-005 3.3929432732417547e-001 2.9030120242126229e+000 -4.4783334115597678e-001 -5.4006412558368184e-004 2.7492718459672764e-003 -3.8449923065214616e-003 4.2175020229014983e-004 -2.4276678093922544e-005 -3.1733835341771577e-001 -4.4783334115597678e-001 3.6157751348946210e+000 -7.6302558122755184e-004 2.6559814107009433e-003 -3.2660344589292524e-003 -6.2426016405221110e-005 1.9002231854318343e-004 -5.4658442369333565e-004 -5.4006412558368184e-004 -7.6302558122755184e-004 6.7239409985664287e-006 -2.9151947830055737e-005 3.8848928879691912e-005 -7.3700638646021470e-008 -6.9366476152724520e-008 3.0370081230896582e-003 2.7492718459672764e-003 2.6559814107009433e-003 -2.9151947830055737e-005 1.3648458206350376e-004 -1.8944698692176858e-004 3.5354142426803448e-007 1.5383589402715499e-007 -3.1356947110278534e-003 -3.8449923065214616e-003 -3.2660344589292524e-003 3.8848928879691912e-005 -1.8944698692176858e-004 2.7211205766284002e-004 -4.7559541398024204e-007 -1.7375904955674177e-007 5.2705435197758904e-005 4.2175020229014983e-004 -6.2426016405221110e-005 -7.3700638646021470e-008 3.5354142426803448e-007 -4.7559541398024204e-007 9.3242309621928652e-008 -1.5342544835203691e-009 -5.1942928435856751e-005 -2.4276678093922544e-005 1.9002231854318343e-004 -6.9366476152724520e-008 1.5383589402715499e-007 -1.7375904955674177e-007 -1.5342544835203691e-009 3.4030427227067055e-008</coeffs>
        </covariance>
 <cameras next_id="26" next_group_id="0">
      <camera id="0" sensor_id="0" label="00000000" enabled="1">
        <transform>9.7295244355931876e-001 -2.4137605644869383e-002 -2.2974098146757183e-001 2.3001938083983617e+000 -1.5022238929850992e-002 -9.9903205136995099e-001 4.1343592890339495e-002 -2.9793714733084692e-001 -2.3051653934042321e-001 -3.6774125812593164e-002 -9.7237327645366456e-001 -4.5274423068157277e-001 0.0000000000000000e+000 0.0000000000000000e+000 0.0000000000000000e+000 1.0000000000000000e+000</transform>

此处我们对相机的内外参数做一个简单的约定，采用简单针孔相机模型时，三维点 P_c = (X_c,Y_c,Z_c) 向图像点 p=(μ,ν) 的投影公式为：

其中相机的内参数包括： dx, dy 为像素点的宽和高，f 为相机焦距，cx, cy 为光心位置；
相机的外参数包括：3×3 旋转矩阵 R 和 3×1 平移矩阵 T，表示从世界坐标系向相机坐标系的变换

直接按照点云坐标和 xml 文件中所给出的相机参数进行投影时，会发现结果有较大的偏差；经过数个星期的摸索发现，相机参数的正确使用方式为：

f = 1940.443

c_x = 2256 / 2 + 13.175

c_y = 1504 / 2 + 9.908

Rt = [9.729e-001, -2.414e-002, -2.297e-001, 2.300e+000,
-1.502e-002, -9.990e-001, 4.134e-002, -2.979e-001,
-2.305e-001, -3.677e-002, -9.724e-001 -4.527e-001,
0, 0, 0, 1] ^-1

也即实际的光心位置为图像 0.5×width / 0.5×height + c_x / c_y
实际相机旋转平移矩阵为将 transform 中的十六个元素组成4×4矩阵之后取逆

Refs:
[1] https://www.agisoft.com/forum/index.php?topic=2351.0
[2] https://www.cnblogs.com/wangguchangqing/p/8126333.html