A Novel Similarity Measure for Image Sequences

Abstract

Quantification of image similarity is a common problem in image processing. For pairs of two images, a variety of options is available and well-understood. However, some applications such as dynamic imaging or serial sectioning involve the analysis of image sequences and thus require a simultaneous and unbiased comparison of many images. This paper proposes a new similarity measure, that takes a global perspective and involves all images at the same time. The key idea is to look at Schatten-q-norms of a matrix assembled from normalized gradient fields of the image sequence. In particular, for q = 0, the measure is minimized if the gradient information from the image sequence has a low rank. This global perspective of the novel SqN-measure does not only allow to register sequences from dynamic imaging, e.g. DCE-MRI, but is also a new opportunity to simultaneously register serial sections, e.g. in histology. In this way, an accumulation of small, local registration errors may be avoided. First numerical experiments show very promising results for a DCE-MRI sequence of a human kidney as well as for a set of serial sections. The global structure of the data used for registration with SqN is preserved in all cases.

A Bronchoscope Localization Method Using an Augmented Reality Co-Display of Real Bronchoscopy Images with a Virtual 3D Bronchial Tree Model

“…Furthermore, the preliminary studies on the HMM model-based path planner showed that it is promising, but further research is required before its effectiveness in aiding surgeons can be reported. Other similarity measures and matching methods proposed in the literature [34,35] as well as other path planners mentioned in the literature, such as the Rapidly Exploring Random Trees (RRT) [36] and Probability Roadmap Planner (PRP) [37], may be investigated in future research. A comparison test with ORB-SLAM based methods may also be performed.…”

Functional Liftings of Vectorial Variational Problems with Laplacian Regularization

“…The second experiment ( Figure 2) consists of two coronal slices from a DCE-MRI dataset of a human kidney (data courtesy of Jarle Rørvik, Haukeland University Hospital Bergen, Norway; taken from [3]). The deformation computed using our proposed model is able to significantly reduce the misfit in liver and kidney in the left half while accurately fixing the spinal cord at the right edge.…”

Variational Registration of Multiple Images with the SVD Based $$\mathrm {S}q\mathrm {N}$$ Distance Measure

“…The above considerations suggest to choose rank F as a distance measure. In [2,3], Brehmer et al proposed to reformulate the rank minimization problem in terms of a relaxation of the rank function based on a so-called Schatten q-norm.…”

“…Recently, Guyader [8] and Brehmer [2,3] proposed groupwise registration methods for a sequence of images. The underlying assumption is that images are linearly dependent if they are aligned.…”

“…Both of these methods construct an image matrix where each column is corresponding to an image from the sequence. Brehmer [2,3] estimates transformation fields by minimizing the rank of the matrix and implicitly forcing columns of the matrix to become linear dependent to each other. Guyader [8] utilizes the multivariate version of mutual information, called total correlation, to define a groupwise registration model.…”