The creation of 3D models for cardiac mapping systems is time-consuming, and the models suffer from issues with repeatability among operators. The present study aimed to construct a double-shaped model composed of the left ventricle and left atrium. We developed cascaded-regression-based segmentation software with probabilistic point and appearance correspondence. Group-wise registration of point sets constructs the point correspondence from probabilistic matches, and the proposed method also calculates appearance correspondence from these probabilistic matches. Final point correspondence of group-wise registration constructed independently for three surfaces of the double-shaped model. Stochastic appearance selection of cascaded regression enables the effective construction in the aspect of memory usage and computation time. The two correspondence construction methods of active appearance models were compared in terms of the paired segmentation of the left atrium (LA) and left ventricle (LV). The proposed method segmented 35 cardiac CTs in six-fold cross-validation, and the symmetric surface distance (SSD), Hausdorff distance (HD), and Dice coefficient (DC), were used for evaluation. The proposed method produced 1.88 ± 0.37 mm of LV SSD, 2.25 ± 0.51 mm* of LA SSD, and 2.06 ± 0.34 mm* of the left heart (LH) SSD. Additionally, DC was 80.45% ± 4.27%***, where * $p<$ 0.05, ** $p<$ 0.01, and *** $p<$ 0.001. All p values derive from paired t-tests comparing iterative closest registration with the proposed method. In conclusion, the authors developed a cascaded regression framework for 3D cardiac CT segmentation.

Sparse autoencoders (SAEs) decompose transformer activations into sparse feature dictionaries, but one-shot support selection can leave many features unused and become difficult to optimize at very small active budgets. We study an SAE-like dictionary-learning procedure that combines a learned TopK encoder with a few unrolled Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) steps for coefficient refinement. On GPT-2 Small layer-11 residual streams, a 12,288-feature TopK256 model with five FISTA steps achieves ΔCE = 0.0745 and a 3.09% dead-feature ratio, compared with 0.0859 and 50.76% for a matched TopK SAE. Ablations show that initialization and learned TopK feature selection explain most of the reduction in dead features, while FISTA further improves fidelity. In a 32,768-feature regime, direct exact-TopK32 training is unstable. Training becomes feasible by retaining a TopK128 candidate support while reducing the final active budget from TopK128 to TopK64 and then TopK32. Five refinement steps reach ΔCE = 0.2442 and 17.84% dead features after 264 million token presentations. A residual-gain-ranked loss over candidates at ranks 33–48 improves near-boundary feature recruitment with a modest fidelity cost. These results show that lightweight iterative correction can improve fixed-budget sparse decomposition without replacing one-shot SAE inference with a full optimization solver.