In this paper, we address the problem of automatic three-dimensional cephalometric analysis. Cephalometric analysis performed on lateral radiographs doesn’t fully exploit the structure of 3D objects due to projection onto the lateral plane. With the development of three-dimensional imaging techniques such as CT, several analysis methods have been proposed that extend to the 3D case. The analysis based on these methods is invariant to rotations and translations and can describe difficult skull deformation, where 2D cephalometry has no use. In this paper, we provide a wide overview of existing approaches for cephalometric landmark regression. Moreover, we perform a series of experiments with state of the art 3D convolutional neural network (CNN) based methods for keypoint regression: direct regression with CNN, heatmap regression and Softargmax regression. For the first time, we extensively evaluate the described methods and demonstrate their effectiveness in the estimation of Frankfort Horizontal and cephalometric points locations for patients with severe skull deformations. We demonstrate that Heatmap and Softargmax regression models provide sufficient regression error for medical applications (less than 4 mm). Moreover, the Softargmax model achieves 1.15° inclination error for the Frankfort horizontal. For the fair comparison with the prior art, we also report results projected on the lateral plane.

This article is devoted to searching for high-level explainable features that can remain explainable for a wide class of objects or phenomena and become an integral part of explainable AI (XAI). The present study involved a 25-day experiment on early diagnosis of wheat stress using drought stress as an example. The state of the plants was periodically monitored via thermal infrared (TIR) and hyperspectral image (HSI) cameras. A single-layer perceptron (SLP)-based classifier was used as the main instrument in the XAI study. To provide explainability of the SLP input, the direct HSI was replaced by images of six popular vegetation indices and three HSI channels (R₆₃₀, G₅₅₀, and B₄₈₀; referred to as indices), along with the TIR image. Furthermore, in the explainability analysis, each of the 10 images was replaced by its 6 statistical features: min, max, mean, std, max–min, and the entropy. For the SLP output explainability, seven output neurons corresponding to the key states of the plants were chosen. The inner layer of the SLP was constructed using 15 neurons, including 10 corresponding to the indices and 5 reserved neurons. The classification possibilities of all 60 features and 10 indices of the SLP classifier were studied. Study result: Entropy is the earliest high-level stress feature for all indices; entropy and an entropy-like feature (max–min) paired with one of the other statistical features can provide, for most indices, 100% accuracy (or near 100%), serving as an integral part of XAI.

This work is mostly devoted to the search for effective solutions to the problem of early diagnosis of plant stress (given an example of wheat and its drought stress), which would be based on explainable artificial intelligence (XAI). The main idea is to combine the benefits of two of the most popular agricultural data sources, hyperspectral images (HSI) and thermal infrared images (TIR), in a single XAI model. Our own dataset of a 25-day experiment was used, which was created via both (1) an HSI camera Specim IQ (400–1000 nm, 204, 512 × 512) and (2) a TIR camera Testo 885-2 (320 × 240, res. 0.1 °C). The HSI were a source of the k-dimensional high-level features of plants (k ≤ K, where K is the number of HSI channels) for the learning process. Such combination was implemented as a single-layer perceptron (SLP) regressor, which is the main feature of the XAI model and receives as input an HSI pixel-signature belonging to the plant mask, which then automatically through the mask receives a mark from the TIR. The correlation of HSI channels with the TIR image on the plant’s mask on the days of the experiment was studied. It was established that HSI channel 143 (820 nm) was the most correlated with TIR. The problem of training the HSI signatures of plants with their corresponding temperature value via the XAI model was solved. The RMSE of plant temperature prediction is 0.2–0.3 °C, which is acceptable for early diagnostics. Each HSI pixel was represented in training by a number (k) of channels (k ≤ K = 204 in our case). The number of channels used for training was minimized by a factor of 25–30, from 204 to eight or seven, while maintaining the RMSE value. The model is computationally efficient in training; the average training time was much less than one minute (Intel Core i3-8130U, 2.2 GHz, 4 cores, 4 GB). This XAI model can be considered a research-aimed model (R-XAI), which allows the transfer of knowledge about plants from the TIR domain to the HSI domain, with their contrasting onto only a few from hundreds of HSI channels.