Forecasting multivariate time series increasingly uses deep learning, including models inspired by Neural Machine Translation (NMT).While Transformers excel at longrange dependencies, their computational overhead may not suit all problems.This study advocates the relevancy of Long Short-Term Memory (LSTM)-based encoder-decoder networks for scenarios with shorter input windows and prediction horizons.We present a comprehensive empirical evaluation of four classical LSTM-based NMT models, including variants with attention mechanisms specifically adapted for multistep time series forecasting.Our assessment focuses on their performance and the impact of varying input window sizes and prediction horizons within these computationally efficient, short-sequence contexts.We empirically compare these LSTM-based models against Transformer baselines operating under the same short input window and prediction horizon constraints.Key findings indicate that: (i) LSTM-based NMT models achieve or exceed existing state-of-the-art results for shortterm predictions; (ii) within smaller input configurations, input window size minimally affects forecasting performance for tested horizons, suggesting efficiency gains are possible; (iii) for attention-based NMT models, attention scoring critically influences accuracy, demanding careful selection; (iv) our comparative analysis demonstrates that for time series problems where immediate historical context is sufficient, LSTM-based encoder-decoders are competitive with, or even outperform, Transformer-based models while offering a more computationally efficient solution.Overall, our findings signify that original LSTM-based NMT models are robust and capable tools, particularly well-suited for short-term time series prediction tasks where local pattern capture and computational efficiency are priorities, even in the era of Transformers.

The ray projection and its application to recovering a projective geometric transformation and an affine lighting change between two objects are mathematically studied. A novel technique, viz., variable contour, is proposed for accurately evaluating the ray projection. Moreover, a novel flexible framework of the ray projection is devised for the joint recovery of the eight parameters for the projective transformation and the two parameters for the lighting change. Finally, the framework is experimentally evaluated by recovering a variety of geometric and photometric transformations between real images of indoor and outdoor scenes. Its robustness to image blur and occlusion is demonstrated. Its versatility is illustrated through matching different objects in different classes.

Airborne LiDAR data can be used to create 3D terrain models useful in augmented or virtual reality in which real-world landscapes are incorporated. Automatic generation of 3D models of man-made structures such as buildings is essential for creating these detailed models. We present a method that builds a 3D mesh, segments the triangles, and forms planar facets that correspond to a roof structure of a target building. We illustrate our method with real-world data sets.

A ray projection in the inverse-polar space is proposed for recovering a projective transformation between two segmented images. The images are converted from their original Cartesian space to the inverse-polar space. Then, the two ray projections—one shift-invariant and the other shift-sensitive—of the inverse-polar images are computed to create two sets of data. Based on the obtained projection data, a two-step strategy is employed to recover the projective transformation. In the first step, the shift-invariant data are used to recover the four affine parameters. In the second step, the shift-sensitive data are used to recover the two projective parameters. The remaining two translation-related parameters are recovered in, e.g., an exhaustive search combined with the two-step recovery strategy. The proposed approach has been tested successfully to recover a variety of projective transformations between real images.

We describe a new algorithm for coding the connectivity information of three-dimensional planar triangle meshes. Vertices of a mesh are placed on a two-dimensional grid. The connectivity pattern of the grid is implicit and hence the only information that needs to be encoded is the diagonal links. We present experimental results that show that the new method has a low connectivity cost of 2.1 bits per vertex on average.