In this paper, we develop the Slant Leaf Area Index based Method (SLAIM) to estimate the leaf area of individual trees from single-scan Terrestrial Laser Scanner (TLS) data by introducing the concept of Slant Leaf Area Index (SLAI). SLAI quantifies the amount of leaves along the view direction and can be retrieved at given view zeniths using gap probability. Subsequently, leaf area can be accumulated by SLAI across the whole crown. The innovative SLAIM offers several advantages. Firstly, it operates with single-scan point clouds, which are more accessible than multiple-scan data. Secondly, it effectively corrects the clumping effect resulting from non-uniform leaf distribution. Both simulated and field-measured TLS point clouds of trees are used to test the method. The results show that the error of SLAIM is less than 10% in most cases.

Individual trees are fundamental to urban ecosystems as they play an important role in energy transfer, pollutant removal, and habitat formation. Leaf area (LA) is an important factor to quantify the effect of individual trees on urban ecosystems. Terrestrial laser scanners (TLSs) are widely recognized as the most accurate devices for tree structural measurements. However, they face challenges in estimating LA from LA index (LAI) for individual trees primarily due to arbitrary and confusing horizontal projection areas. Occlusion and clumping effects further hinder the objective and accurate LA measurements of individual trees. Therefore, we developed the slant leaf area index-based method (SLAIM) to estimate the LA of individual trees from single-scan TLS data by introducing the concept of slant leaf area index (SLAI). SLAI quantifies the amount of leaves along the view direction, and it can be retrieved at given view zeniths using gap probability. Subsequently, LA can be accumulated by SLAI across the whole crown. Tests with simulated and field-measured TLS point clouds demonstrate SLAIM’s accuracy, with the relative errors (REs) in LA below 10% in most cases. Stratified LA validation reveals an$R^{2}$exceeding 0.77 across all realistic crowns, along with a root-mean-square error (RMSE) under 2 m2. SLAIM’s advantages include compatibility with single-scan point clouds, effective correction of clumping effects, and consideration of variations in leaf projection coefficients at different zeniths. SLAIM proves more efficient and practical for actual LA measurements, showcasing its potential for advanced urban ecosystem research.

Abstract Hedged public-key encryption (HPKE), introduced by Bellare et al. (ASIACRYPT 2009), provides useful security when the per-message randomness fails to be uniform due to faulty implementations or adversarial actions. The HPKE scheme achieves IND-CPA (chosen plaintext attack) security when the randomness they used is of high quality, but, when the randomness is poor quality, rather than breaking completely, it achieves a weaker but a useful notion of security called IND-CDA (chosen distribution attack) as long as the message and randomness together have sufficient min-entropy. However, little research on HPKE in the presence of key leakage was done. In this paper, we study HPKE featuring key leakage-resilience and formulate appropriate security notion for key leakage-resilient HPKE. We work in the continual key leakage model where the secret key is refreshed periodically and an adversary can learn arbitrary but bounded leakage on the secret key between the updates. We present two generic constructions of continual leakage-resilient HPKE in the standard model by using a continual leakage-resilient all-but-one lossy trapdoor function. Finally, we give an instantiation of leakage-resilient HPKE under the linear assumption in bilinear groups.