A Bayesian Approach Toward Robust Multidimensional Ellipsoid-Specific Fitting.

This work presents a novel and effective method for fitting multidimensional ellipsoids (i.e., ellipsoids embedded in [Formula: see text]) to scattered data in the contamination of noise and outliers. Unlike conventional algebraic or geometric fitting paradigms that assume each measurement point is a noisy version of its nearest point on the ellipsoid, we approach the problem as a Bayesian parameter estimate process and maximize the posterior probability of a certain ellipsoidal solution given the data. We establish a more robust correlation between these points based on the predictive distribution within the Bayesian framework, i.e., considering each model point as a potential source for generating each measurement. Concretely, we incorporate a uniform prior distribution to constrain the search for primitive parameters within an ellipsoidal domain, ensuring ellipsoid-specific results regardless of inputs. We then establish the connection between measurement point and model data via Bayes' rule to enhance the method's robustness against noise. Due to independent of spatial dimensions, the proposed method not only delivers high-quality fittings to challenging elongated ellipsoids but also generalizes well to multidimensional spaces. To address outlier disturbances, often overlooked by previous approaches, we further introduce a uniform distribution on top of the predictive distribution to significantly enhance the algorithm's robustness against outliers. Thanks to the uniform prior, our maximum a posterior probability coincides with a more tractable maximum likelihood estimation problem, which is subsequently solved by a numerically stable Expectation Maximization (EM) framework. Moreover, we introduce an ε-accelerated technique to expedite the convergence of EM considerably. We also investigate the relationship between our algorithm and conventional least-squares-based ones, during which we theoretically prove our method's superior robustness. To the best of our knowledge, this is the first comprehensive method capable of performing multidimensional ellipsoid-specific fitting within the Bayesian optimization paradigm under diverse disturbances. We evaluate it across lower and higher dimensional spaces in the presence of heavy noise, outliers, and substantial variations in axis ratios. Also, we apply it to a wide range of practical applications such as microscopy cell counting, 3D reconstruction, geometric shape approximation, and magnetometer calibration tasks. In all these test contexts, our method consistently delivers flexible, robust, ellipsoid-specific performance, and achieves the state-of-the-art results.

Accurate Registration of Cross-Modality Geometry via Consistent Clustering.

The registration of unitary-modality geometric data has been successfully explored over past decades. However, existing approaches typically struggle to handle cross-modality data due to the intrinsic difference between different models. To address this problem, in this paper, we formulate the cross-modality registration problem as a consistent clustering process. First, we study the structure similarity between different modalities based on an adaptive fuzzy shape clustering, from which a coarse alignment is successfully operated. Then, we optimize the result using fuzzy clustering consistently, in which the source and target models are formulated as clustering memberships and centroids, respectively. This optimization casts new insight into point set registration, and substantially improves the robustness against outliers. Additionally, we investigate the effect of fuzzier in fuzzy clustering on the cross-modality registration problem, from which we theoretically prove that the classical Iterative Closest Point (ICP) algorithm is a special case of our newly defined objective function. Comprehensive experiments and analysis are conducted on both synthetic and real-world cross-modality datasets. Qualitative and quantitative results demonstrate that our method outperforms state-of-the-art approaches with higher accuracy and robustness. Our code is publicly available at https://github.com/zikai1/CrossModReg.

Synergistic effect of vincristine with tacrolimus or sirolimus in prevention of acute heart allograft rejection in the rat.

The application of multiple immunosuppressive therapy for organ transplantation could enhance therapeutic efficacy, while minimizing the toxicity of individual drugs used in the regimen. In this study, the effect of the combined therapy of vincristine (VCR) with tacrolimus (FK506) or sirolimus (rapamycin, RAPA) was tested in prevention of acute heart allograft rejection in the rat. A Brown Norway (BN, RT 1(n)) to Lewis (LEW, RT 1(1)) rat combination was used in a heart allografting model. VCR was administered intraperitoneally once daily, while FK506 and RAPA were given by gavage once daily for 14 days after transplantation. There were dose-related prolongations of mean survival time (MST) to monotherapy of VCR, FK506, or RAPA. The MST in combination therapy indicated that a synergistic interaction was produced when compared with the respective monotherapies: VCR 0.05 mg/kg/day + FK506 0.5 mg/kg/day (16.00 +/- 1.79 days, P = 0.001; combination index (CI) = 0.557); VCR 0.05 mg/kg/day + FK506 1.0 mg/kg/day (29.00 +/- 10.54 days, P = 0.001; CI = 0.598); VCR 0.05 mg/kg/day + RAPA 0.2 mg/kg/day (17.33 +/- 1.97 days, P = 0.001; CI = 0.500); and VCR 0.05 mg/kg/day + RAPA 0.4 mg/kg/day (21.17 +/- 3.19 days, P = 0.001; CI = 0.838). Combination therapy of VCR and FK506 or RAPA produced synergistic effects in prevention of acute heart allograft rejection in the rat.