Abstract
Abstract. The paper deals with estimation of 3-D object deformation from multiple images initially in fixed positions with weak or strong imaging geometry. A new method is proposed to detect automatically if the exterior or interior orientations (rotations, translations, focal length, principal point) of one or several images have changed and which image or images contain the error, when the object deforms at the same time. The method is based on comparing novel feature vectors computed for each image from changes in the image coordinates of the object points and from residuals derived from the collinearity equations. Bundle adjustment is performed to simultaneously estimate the deformation of the object and to correct the changed orientations of the images. The rigidity needed in the weak case is obtained by approximating the deformation by a novel shape function containing parameters the values of which are estimated during adjustment. Test results with synthetic data show that even rather small changes in one orientation parameter of one image can be detected with high confidence. Weak imaging geometry allows to detect smaller changes than the strong one. The closer an initial approximation of deformation is available, the higher is the probability of correct detection. Subsequent correction of changed orientations and estimation of deformation may provide a high accuracy of 1:140000 of the object dimensions for both weak and strong imaging geometries, when the noise level in the image measurements is 0.1 pixel. Experiments with real data illustrate the good performance of the methods.
Highlights
We consider the case where multiple cameras mounted in fixed positions and having a weak or strong imaging geometry monitor an object with special target points attached on the surface of the object
Hundred randomized trials were performed by having for each trial, different true values of parameters a, different initial values of parameters a given by perturbing the true values by plus or minus five percent, one randomly selected image, the orientation parameters of which were changed by a given partly randomized amount, and different randomized noise added to the image observations of the target points
Bundle adjustment was performed for correction of the changed orientations and estimation of object deformation using a novel idea of a shape function
Summary
We consider the case where multiple cameras mounted in fixed positions and having a weak or strong imaging geometry monitor an object with special target points attached on the surface of the object. Long-term monitoring aims to detect changes in the image coordinates of the target points and to interpret the changes observed. Possible reasons for changes in the image coordinates include that the object has experienced a deformation or something has changed in the measurement system such as the exterior or interior orientation of one or several images has changed. The objective is to correct the changed orientations simultaneously with estimation of the object deformation when the imaging geometry may be either weak or strong. Weak imaging geometry (cameras close to each others with respect to depth to the object) may be the only choice when, e.g., restrictions set by the measurement environment hinder obtaining strong imaging geometry
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