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Exercises
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How many types of orientations are possible in calibration Consider some examples and illustrate the difference among them
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Why is photogrammetry concerned with the camera calibration problem Illustrate using an example What is the effect of rectangular pixels on image measurements How can you compensate for the rectangularity of pixels in measuring areas and centroids of regions How will it affect measurements of relative locations and orientations of regions What care would you take to get correct measurements in the real world Define affine transformation Give three examples of objects that will undergo an affine transformation in an image at different time instants and three examples of objects that will not Define Euler angles Where are they used What are their strengths and weaknesses What are quaternions Why are they considered a good representation for rotation in calibration Demonstrate this considering the calibration of absolute orientation Define the coplanarity constraint Where and how is it used in camera calibration Suppose that you are designing a hand-eye system In this system a camera is mounted at a fixed position in the work space The hand, a robot arm, is used to pick and place objects in the work space What kind of calibration scheme will you require In the above problem, if the camera is mounted on the robot arm itself, what kind of calibration scheme will you require to find the location of objects How many fixed known points will you require to solve the problem
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1210 Now let's provide a stereo system on our robot arm so that we can compute the depth of points easily and perform more dexterous manipulations What kind of calibration scheme is required in this case What are the criteria for selecting scene points for calibration What arrangements of points are bad for calibration
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CHAPTER 12 CALIBRATION
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1211 What camera parameters should be determined for calibrating a camera How can you determine these parameters without directly measuring them What parameters are available from the data sheets provided by the camera manufacturer
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Computer Projects
121 You want to develop a camera calibration algorithm for preparing a three-dimensional model of a football field using lane markers Assume that a sufficient number of lane markers, their intersections, and other similar features are visible in the field of view Develop an approach to solve the camera calibration problem and use it to determine the location of each player, their height, and the location of the ball 122 Develop an algorithm for the calibration of stereo cameras Use this algorithm to calibrate a set of cameras mounted on a mobile robot Develop an approach that will use known calibration points in an environment to determine the camera calibration and then use this to get the exact distance to all points
13 Curves and Surfaces
There are two fundamental problems with surfaces in machine vision: reconstruction and segmentation Surfaces must be reconstructed from sparse depth measurements that may contain outliers Once the surfaces are reconstructed onto a uniform grid, the surfaces must be segmented into different surface types for object recognition and refinement of the surface estimates This chapter begins with a discussion of the geometry of surfaces and includes sections on surface reconstruction and segmentation The chapter will cover the following topics on surfaces:
Representations for surfaces such as polynomial surface patches and tensorproduct cubic splines Interpolation methods such as bilinear interpolation Approximation of surfaces using variational methods and regression splines Segmentation of point measurements into surface patches Registration of surfaces with point measurements
Surface approximation is also called surface fitting, since it is like a regression problem where the model is the surface representation and the data are points sampled on the surface The term surface reconstruction means estimating the continuous function for the surface from point samples, which can be implemented by interpolation or approximation
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