Minimum-cross-entropy estimation of electron-pair densities from scattering intensities

Antolín, J.; Cuchí, J. C.; Angulo, J. C.

doi:10.1016/s0375-9601(99)00426-0

Cited by 3 publications

(1 citation statement)

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“…They also studied the properties of cross-entropy minimization [21]. In addition to image registration, this measure has been applied to the areas of spectral analysis in Shore [22], image reconstruction in Zhuang et al [23], biochemistry in Yee [24], process control in Alwan et al [25], non-linear programming in Das et al [26], and electron density estimation in Antolin et al [27], among many others.…”

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confidence: 99%

Cross-Entropy, Reversed Cross-Entropy, and Symmetric Divergence Similarity Measures for 3D Image Registration: A Comparative Study

Zhu

Cochoff

Topics in Biomedical Engineering International Book Series

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Image registration is a process that quantitatively relates the information in one image to that in another image by determining a one-to-one transformation between coordinates in the two image spaces. Medical image registration is becoming increasingly useful in research and patient care (see [1, 2, 3]). Different imaging modalities often times provide unique and complementary information. Multimodality image registration makes it possible to combine structural (computed tomography or magnetic resonance images) and functional (positron emission tomography or single photon emission tomography) information to improve diagnostic accuracy and aid surgical and/or radiotherapeutic planning.Registration of the same modality images acquired at different times allows clinicians to assess lesion progression/regression or treatment effectiveness. In an interactive, image-guided surgery environment, registration of preoperative images with the physical space is an overriding requirement.Many algorithms have been employed to register medical images and have recently been reviewed and classified (see [4, 5]). Earlier work prior to 1993 has also been reviewed (see [6, 7] Cross-entropy, also known as Kullback-Leibler divergence, is an informationtheoretic measure that quantifies the difference between two probability density functions (pdf). It can be either maximized or minimized, depending on how a priori pdf is given. Cross-entropy maximization degenerates to mutual information maximization, conditional entropy minimization or joint entropy minimization under certain conditions. Cross-entropy has two close relatives known as reversed cross-entropy and symmetric divergence, which have been applied to spectral analysis (see [28,29] Gemini, respectively, [32]. Given this hardware approach to image registration, the question arises as to the continued need for software registration techniques.It is our opinion however, that software image registration will continue to play a vital role in many instances and that the development of registration algorithms shall remain an important research area for years to come. In many cases, hardware registration is impractical or impossible and one must rely on software-based registration techniques. For example, when monitoring treatment effectiveness over time, software image registration is necessary since the single or multimodality images are acquired at different times. In addition, applications involving intersubject or atlas comparisons require software registration since the images originate from different subjects. Other applications for software registration include the correction of motion that occurs between sequential transmission and emission scans in PET and SPECT as well as the positioning of patients with respect to previously determined treatment plans. The need to offer multiple different combinations of imaging modalities (i.e., PET/MR, SPECT/MR, PET/CT, etc.) would be impractical. As most researchers agree, the hybrid devices will likely play a major role primarily in ra...

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confidence: 99%

Cross-Entropy, Reversed Cross-Entropy, and Symmetric Divergence Similarity Measures for 3D Image Registration: A Comparative Study

Zhu

Cochoff

Topics in Biomedical Engineering International Book Series

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Volume image registration by cross-entropy optimization

Zhu

2002

IEEE Trans. Med. Imaging

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Cross-entropy (CE), an information-theoretic measure, quantifies the difference between two probability density functions. This measure is applied to volume image registration. When a good prior estimation of the joint distribution of the voxel values of two images in registration is available, the CE can be minimized to find an optimal registration. If such a prior estimation is not available, one seeks the registration which gives a joint distribution different from unlikely ones as much as possible, i.e., the CE is maximized to find an optimal registration. When the unlikely distribution is a uniform one, CE maximization reduces to joint entropy minimization; when the unlikely distribution is proportional to one of the marginal distributions, it reduces to conditional entropy minimization; when the unlikely distribution is the product of two marginal distributions, it degenerates to mutual-information maximization. These different CEs are added together and are used as criteria for image registration. The accuracy and robustness of this new approach are tested and compared using a likely joint distribution and various unlikely joint distributions and their combinations.

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