Do I have to rectify/crop images before process them with viso2_ros mono_odometry?

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Yes, it is mandatory to rectify the images before feeding them to viso2_ros. And no, the library does not compute odometry using unrectified images. To produce rectified images you can use the package image_proc. Your camera driver should publish sensor_msgs/Image together with sensor_msgs/CameraInfo containing the calibration. image_proc then creates the rectified image for you which you can feed into viso2_ros.

A sample launch file would look like this:

<!-- example launch file for mono_odometer -->
<launch>
  <arg name="camera"/> <!-- camera must be set at launch -->
  <node name="image_proc" pkg="image_proc" type="image_proc" ns="$(arg camera)"/>
  <node name="mono_odometer" pkg="viso2_ros" type="mono_odometer" output="screen">
    <remap from="image" to="$(arg camera)/image_rect" />
    <param name="camera_height" value="0.5" /> <!-- cam is 0.5m above ground -->
    <param name="camera_pitch" value="0.0" /> <!-- cam is looking straight forward -->
  </node>
</launch>