Measuring leaf area is a critical task in plant biology. Meshing techniques, parametric surface modelling and implicit surface modelling allow estimating plant leaf area from acquired 3D point clouds. However, there is currently no consensus on the best approach because of little comparative evaluation. In this paper, we provide evidence about the performance of each approach, through a comparative study of four meshing, three parametric modelling and one implicit modelling methods. All selected methods are freely available and easy to use. We have also performed a parameter sensitivity analysis for each method in order to optimise its results and fully automate its use. We identified nine criteria affecting the robustness of the studied methods. These criteria are related to either the leaf shape (length/width ratio, curviness, concavity) or the acquisition process (e.g. sampling density, noise, misalignment, holes). We used synthetic data to quantitatively evaluate the robustness of the selected approaches with respect to each criterion. In addition we evaluated the results of these approaches on five tree and crop datasets acquired with laser scanners or photogrammetry. This study allows us to highlight the benefits and drawbacks of each method and evaluate its appropriateness in a given scenario. Our main conclusion is that fitting a Bézier surface is the most robust and accurate approach to estimate plant leaf area in most cases.
We propose a ray-triangle intersection algorithm with fast-rejection strategies. We intersect the ray with the triangle plane, then transform the intersection problem into 2D by applying a transformation matrix to the ray-plane intersection point. For 2D transformation, we study two different approaches. The first approach uses a transformation matrix which transforms the triangle into a unit triangle. Then, simple 2D tests are performed. The second approach transforms the triangle into a 2D triangle while preserving similarity. This allows us to prune (i.e., to clip away) areas surrounding the triangle, determining whether the transformed intersection point lies within the triangle. We discuss several optimizations for this pruning approach. We implemented both approaches into the CPU-based ray-tracing framework PBRT, version 3, and we performed a time-based comparison against PBRT’s default intersection algorithm and Baldwin and Weber’s algorithm. The results show that our algorithms are faster than the default algorithm. They are comparable to or slightly slower than Baldwin and Weber’s algorithm, however, the pruning approach produces watertight results and may be further optimized. Moreover, additional CPU/GPU experiments outside of PBRT document promising speedup over the standard Möller–Trumbore algorithm in areas like ray-casting or collision detection.
The design of correct topological modeling operations is known to be a time-consuming and challenging task. However, these operations are intuitively understood via simple drawings of a representative object before and after modification. We propose to infer topological modeling operations from an application example. Our algorithm exploits a compact and expressive graph-based language. In this framework, topological modeling operations on generalized maps are represented as rules from the theory of graph transformations. Most of the time, operations are generic up to a topological cell (vertex, face, volume). Thus, the rules are parameterized with orbit types indicating which kind of cell is involved. Our main idea is to infer a generic rule by folding a graph comprising a copy of the object before modification, a copy after modification, and information about the modification. We fold this graph according to the cell parametrization of the operation under design. We illustrate our approach with some subdivision schemes because their symmetry simplifies the operation inference.
Explainable neural models have gained a lot of attention in recent years. However, conventional encoder–decoder models do not capture information regarding the importance of the involved latent variables and rely on a heuristic a-priori specification of the dimensionality of the latent space or its selection based on multiple trainings. In this paper, we focus on the efficient structuring of the latent space of encoder–decoder approaches for explainable data reconstruction and compression. For this purpose, we leverage the concept of Shapley values to determine the contribution of the latent variables on the model's output and rank them according to decreasing importance. As a result, a truncation of the latent dimensions to those that contribute the most to the overall reconstruction allows a trade-off between model compactness (i.e. dimensionality of the latent space) and representational power (i.e. reconstruction quality). In contrast to other recent autoencoder variants that incorporate a PCA-based ordering of the latent variables, our approach does not require time-consuming training processes and does not introduce additional weights. This makes our approach particularly valuable for compact representation and compression. We validate our approach at the examples of representing and compressing images as well as high-dimensional reflectance data.
Noise-like artifacts are common in measured or fitted data across various domains, e.g. photography, geometric reconstructions in terms of point clouds or meshes, as well as reflectance measurements and the respective fitting of commonly used reflectance models to them. State-of-the-art denoising approaches focus on specific noise characteristics usually observed in photography. However, these approaches do not perform well if data is corrupted with location-dependent noise. A typical example is the acquisition of heterogeneous materials, which leads to different noise levels due to different behavior of the components either during acquisition or during reconstruction. We address this problem by first automatically determining location-dependent noise levels in the input data and demonstrate that state-of-the-art denoising algorithms can usually benefit from this guidance with only minor modifications to their loss function or employed regularization mechanisms. To generate this information for guidance, we analyze patchwise variances and subsequently derive per-pixel importance values. We demonstrate the benefits of such locally-guided denoising at the examples of the Deep Image Prior method and the Self2Self method.
