Homography Ranking Based on Multiple Groups of Point Correspondences

Homography mapping is often exploited to remove perspective distortion in images and can be estimated using point correspondences of a known object (marker). We focus on scenarios with multiple markers placed on the same plane if their relative positions in the world are unknown, causing an indeterminate point correspondence. Existing approaches may only estimate an isolated homography for each marker and cannot determine which homography achieves the best reprojection over the entire image. We thus propose a method to rank isolated homographies obtained from multiple distinct markers to select the best homography. This method extends existing approaches in the post-processing stage, provided that the point correspondences are available and that the markers differ only by similarity transformation after rectification. We demonstrate the robustness of our method using a synthetic dataset and show an approximately 60% relative improvement over the random selection strategy based on the homography estimation from the OpenCV library.

The role of semantics in the perceptual organization of shape

Establishing correspondence between objects is fundamental for object constancy, similarity perception and identifying transformations. Previous studies measured point-to-point correspondence between objects before and after rigid and non-rigid shape transformations. However, we can also identify ‘similar parts’ on extremely different objects, such as butterflies and owls or lizards and whales. We measured point-to-point correspondence between such object pairs. In each trial, a dot was placed on the contour of one object, and participants had to place a dot on ‘the corresponding location’ of the other object. Responses show correspondence is established based on similarities between semantic parts (such as head, wings, or legs). We then measured correspondence between ambiguous objects with different labels (e.g., between ‘duck’ and ‘rabbit’ interpretations of the classic ambiguous figure). Despite identical geometries, correspondences were different across the interpretations, based on semantics (e.g., matching ‘Head’ to ‘Head’, ‘Tail’ to ‘Tail’). We present a zero-parameter model based on labeled semantic part data (obtained from a different group of participants) that well explains our data and outperforms an alternative model based on contour curvature. This demonstrates how we establish correspondence between very different objects by evaluating similarity between semantic parts, combining perceptual organization and cognitive processes.

Cascaded Regression-Based Segmentation of Cardiac CT under Probabilistic Correspondences

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.