The field of computer graphics was revolutionized by models such as NeRF and 3D Gaussian Splatting, displacing triangles as the dominant representation for photogrammetry. In this paper, we argue for a triangle comeback. We develop a differentiable renderer that directly optimizes triangles via end-to-end gradients. We achieve this by rendering each triangle as differentiable splats, combining the efficiency of triangles with the adaptive density of representations based on independent primitives. Compared to popular 2D and 3D Gaussian Splatting methods, our approach achieves competitive rendering and convergence speed, and demonstrates high visual quality. On the Mip-NeRF360 dataset, our method outperforms concurrent nonvolumetric primitives in visual fidelity and achieves higher perceptual quality than the state-of-the-art Zip-NeRF on indoor scenes. Triangles are simple, compatible with standard graphics stacks and GPU hardware, and highly efficient. Our results highlight the efficiency and effectiveness of triangle-based representations for high-quality novel view synthesis. Triangles bring us closer to mesh-based optimization by combining classical computer graphics with modern differentiable rendering frameworks. The project page is https://trianglesplatting.github.io/

Recent advances in radiance field reconstruction, such as 3D Gaussian Splatting (3DGS), have achieved high-quality novel view synthesis and fast rendering by representing scenes with compositions of Gaussian primitives. However, 3D Gaussians present several limitations for scene reconstruction. Accurately capturing hard edges is challenging without significantly increasing the number of Gaussians, creating a large memory footprint. Moreover, they struggle to represent flat surfaces, as they are diffused in space. Without hand-crafted regularizers, they tend to disperse irregularly around the actual surface. To circumvent these issues, we introduce a novel method, named 3D Convex Splatting (3DCS), which leverages 3D smooth convexes as primitives for modeling geometrically-meaningful radiance fields from multi-view images. Smooth convex shapes offer greater flexibility than Gaussians, allowing for a better representation of 3D scenes with hard edges and dense volumes using fewer primitives. Powered by our efficient CUDA-based rasterizer, 3DCS achieves superior performance over 3DGS on benchmarks such as MipNeRF360, Tanks and Temples, and Deep Blending. Specifically, our method attains an improvement of up to 0.81 in PSNR and 0.026 in LPIPS compared to 3DGS while maintaining high rendering speeds and reducing the number of required primitives. Our results highlight the potential of 3D Convex Splatting to become the new standard for high-quality scene reconstruction and novel view synthesis. The project page is https://convexsplatting.github.io

Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal theory for performance-based ranking. First, we introduce a rigorous framework built on top of both the probability and order theories. Our new framework encompasses the elements necessary to (1) manipulate performances as mathematical objects, (2) express which performances are worse than or equivalent to others, (3) model tasks through a variable called satisfaction, (4) consider properties of the evaluation, (5) define scores, and (6) specify application-specific preferences through a variable called importance. On top of this framework, we propose the first axiomatic definition of performance orderings and performance-based rankings. Then, we introduce a universal parametric family of scores, called ranking scores, that can be used to establish rankings satisfying our axioms, while considering application-specific preferences. Finally, we show, in the case of two-class classification, that the family of ranking scores encompasses well-known performance scores, including the accuracy, the true positive rate (recall, sensitivity), the true negative rate (specificity), the positive predictive value (precision), and F1. However, we also show that some other scores commonly used to compare classifiers are unsuitable to derive performance orderings satisfying the axioms.

In video understanding, action spotting consists in temporally localizing human-induced events annotated with single timestamps. In this paper, we propose a novel loss function that specifically considers the temporal context naturally present around each action, rather than focusing on the single annotated frame to spot. We benchmark our loss on a large dataset of soccer videos, SoccerNet, and achieve an improvement of 12.8% over the baseline. We show the generalization capability of our loss for generic activity proposals and detection on ActivityNet, by spotting the beginning and the end of each activity. Furthermore, we provide an extended ablation study and display challenging cases for action spotting in soccer videos. Finally, we qualitatively illustrate how our loss induces a precise temporal understanding of actions and show how such semantic knowledge can be used for automatic highlights generation.