Framed slant helices in Euclidean 3-space

In this paper, we define framed slant helices and give a necessary and sufficient condition for them in three-dimensional Euclidean space. Then, we introduce the spherical images of a framed curve. Also, we examine the relations between a framed slant helix and its spherical images. Moreover, we give an example of a framed slant helix and its spherical images with figures.

Sampling with probability proportional to prediction (3P sampling) using covariates derived from spherical images

Using a two-phase sampling approach with systematic selection of large samples of covariates followed by a sampling with probability proportional to prediction (3P sampling) process to subsample field measures of the parameters of interest can be an efficient design to sample larger forest areas. To assist in obtaining predictions for each sample plot consistently and rapidly, we propose using a 360° spherical camera. In this study, three covariates derived from spherical images were evaluated: (i) basal area (P[BA]); (ii) sum of squared heights per hectare (P[SHT]); and (iii) stem fraction (P[SF]). These covariates were used to estimate volume. Sample simulations showed no biases in volume estimates for any of the three covariates. Overall, P[SF] had the lowest standard error percentages across different simulated sample sizes (10% for five subsamples to 2.5% for 50 subsamples), even though it had the lowest correlations with field volume (correlation = 0.30–0.31). This may be a result of the relatively consistent stand conditions within the study site. Based on our results, standard errors of 5% were obtainable with measurement fractions of about 25% of the number of image-based predictions when using P[SF] or P[BA] and 75% when using P[SHT].

THE RELIABILITY ASSESSMENT OF THE TLS REGISTRATION METHODS – THE CASE STUDY OF THE ROYAL CASTLE IN WARSAW

Modern measurement technologies are commonly applied to monitor and preserve the cultural heritage as it is an integral part of modern societies. The Terrestrial Laser Scanning (TLS) method is one of the common technologies investigated by the researchers for accurate data acquisition and processing required for architectural documentation. In recent years, many methods were developed for TLS data registration to improve the processing time and accuracy of the bundle adjustment. The aim of this research is to compare the existing TLS target-based registration methods and compare them with the proposed novel method based on the reliability assessment- the robustness analysis. The novel feature-based approach also includes 2D detectors, which were applied to the TLS data converted into spherical images. Measurements were carried out at the Royal Castle in Warsaw using TLS Z+F 5006H and total station Leica TCRP1202. The collected data was analysed using existing software Z+F LaserControl, LupoScan and developed the application to perform 2D + 1H / 3D registration. The main results demonstrated that the proposed method for TLS registration removed the outliers that could not be eliminated by the deviation analysis on control and check points. The accuracy of TLS registration increased with a RMSE difference between 0.1 mm and 3.7 mm in comparison to existing methods. Furthermore, the accuracy of the results from 2D detectors was improved with relative orientation RMSE ≤ 2.1 mm and equivalent for control and check points for X, Y, and Z coordinates in comparison to target-based registration.

Underwater Depth Estimation for Spherical Images

This paper proposes a method for monocular underwater depth estimation, which is an open problem in robotics and computer vision. To this end, we leverage publicly available in-air RGB-D image pairs for underwater depth estimation in the spherical domain with an unsupervised approach. For this, the in-air images are style-transferred to the underwater style as the first step. Given those synthetic underwater images and their ground truth depth, we then train a network to estimate the depth. This way, our learning model is designed to obtain the depth up to scale, without the need of corresponding ground truth underwater depth data, which is typically not available. We test our approach on style-transferred in-air images as well as on our own real underwater dataset, for which we computed sparse ground truth depths data via stereopsis. This dataset is provided for download. Experiments with this data against a state-of-the-art in-air network as well as different artificial inputs show that the style transfer as well as the depth estimation exhibit promising performance.

Biomass estimates derived from sector subsampling of 360° spherical images

Efficient subsampling designs reduce forest inventory costs by focusing sampling efforts on more variable forest attributes. Sector subsampling is an efficient and accurate alternative to big basal area factor (big BAF) sampling to estimate the mean basal area to biomass ratio. In this study, we apply sector subsampling of spherical images to estimate aboveground biomass and compare our image-based estimates with field data collected from three early spacing trials on western Newfoundland Island in eastern Canada. The results show that sector subsampling of spherical images produced increased sampling errors of 0.3–3.4 per cent with only about 60 trees measured across 30 spherical images compared with about 4000 trees measured in the field. Photo-derived basal area was underestimated because of occluded trees; however, we implemented an additional level of subsampling, collecting field-based basal area counts, to correct for bias due to occluded trees. We applied Bruce’s formula for standard error estimation to our three-level hierarchical subsampling scheme and showed that Bruce’s formula is generalizable to any dimension of hierarchical subsampling. Spherical images are easily and quickly captured in the field using a consumer-grade 360° camera and sector subsampling, including all individual tree measurements, were obtained using a custom-developed python software package. The system is an efficient and accurate photo-based alternative to field-based big BAF subsampling.

Panoramic Visual SLAM Technology for Spherical Images

Simultaneous Localization and Mapping (SLAM) technology is one of the best methods for fast 3D reconstruction and mapping. However, the accuracy of SLAM is not always high enough, which is currently the subject of much research interest. Panoramic vision can provide us with a wide range of angles of view, many feature points, and rich information. The panoramic multi-view cross-imaging feature can be used to realize instantaneous omnidirectional spatial information acquisition and improve the positioning accuracy of SLAM. In this study, we investigated panoramic visual SLAM positioning technology, including three core research points: (1) the spherical imaging model; (2) spherical image feature extraction and matching methods, including the Spherical Oriented FAST and Rotated BRIEF (SPHORB) and ternary scale-invariant feature transform (SIFT) algorithms; and (3) the panoramic visual SLAM algorithm. The experimental results show that the method of panoramic visual SLAM can improve the robustness and accuracy of a SLAM system.