As 3D point clouds become a cornerstone of modern technology, the need for sophisticated generative models and reliable evaluation metrics has grown exponentially. In this work, we first expose that some commonly used metrics for evaluating generated point clouds, particularly those based on Chamfer Distance (CD), lack robustness against defects and fail to capture geometric fidelity and local shape consistency when used as quality indicators. We further show that introducing samples alignment prior to distance calculation and replacing CD with Density-Aware Chamfer Distance (DCD) are simple yet essential steps to ensure the consistency and robustness of point cloud generative model evaluation metrics. While existing metrics primarily focus on directly comparing 3D Euclidean coordinates, we present a novel metric, named Surface Normal Concordance (SNC), which approximates surface similarity by comparing estimated point normals. This new metric, when combined with traditional ones, provides a more comprehensive evaluation of the quality of generated samples. Finally, leveraging recent advancements in transformer-based models for point cloud analysis, such as serialized patch attention, we propose a new architecture for generating high-fidelity 3D structures, the Diffusion Point Transformer (DiPT). We perform extensive experiments and comparisons on the ShapeNet dataset, showing that our model outperforms previous solutions, particularly in terms of quality of generated point clouds, achieving new state-of-the-art. Code available at https://github.com/matteobastico/DiffusionPointTransformer.

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In this paper, we present a method that allows the conditioning of Neural Fields using Regularization by Denoising (RED). As opposed to learning a joint convolutional neural network to condition the output of a neural field, the RED framework is memory-efficient. It allows us to decouple the conditioning network and neural field optimization entirely. We focus our work on applications for 3D sparse-view X-ray Computed Tomography (CT) and propose a flexible procedure that does not assume coordinate-friendly partitioning of the forward operator. Indeed, our method applies to any CT geometry, particularly Cone-Beam CT, which is the most common setup in industrial inspection. We quantitatively evaluate our approach and show that our method is either better or on par with the state-of-the-art regarding reconstruction quality while being the most memory-efficient. Code is available at https://github.com/romainvo/nef-red.

Point cloud matching, a crucial technique in computer vision, medical and robotics fields, is primarily concerned with finding correspondences between pairs of point clouds or voxels. In some practical scenarios, emphasizing lo-cal differences is crucial for accurately identifying a cor-rect match, thereby enhancing the overall robustness and reliability of the matching process. Commonly used shape descriptors have several limitations and often fail to provide meaningful local insights about the paired geome-tries. In this work, we propose a new technique, based on graph Laplacian eigenmaps, to match point clouds by taking into account fine local structures. To deal with the order and sign ambiguity of Laplacian eigenmaps, we in-troduce a new operator, called Coupled Laplacian11Code: https://github.com/matteo-bastico/CoupLap, that allows to easily generate aligned eigenspaces for multiple registered geometries. We show that the similarity between those aligned high-dimensional spaces provides a locally meaningful score to match shapes. We firstly evaluate the performance of the proposed technique in a point-wise man-ner, focusing on the task of object anomaly localization on the MVTec 3D-AD dataset. Additionally, we define a new medical task, called automatic Bone Side Estimation (BSE), which we address through a global similarity score derived from coupled eigenspaces. In order to test it, we propose a benchmark collecting bone surface structures from various public datasets. Our matching technique, based on Cou-pled Laplacian, outperforms other methods by reaching an impressive accuracy on both tasks.

Many approaches for image segmentation rely on a first low-level segmentation step, where an image is partitioned into homogeneous regions with enforced regularity and adherence to object boundaries. Methods to generate these superpixels have gained substantial interest in the last few years, but only a few have made it into applications in practice, in particular because the requirements on the processing time are essential but are not met by most of them. Here, we propose waterpixels as a general strategy for generating superpixels which relies on the marker controlled watershed transformation. We introduce a spatially regularized gradient to achieve a tunable tradeoff between the superpixel regularity and the adherence to object boundaries. The complexity of the resulting methods is linear with respect to the number of image pixels. We quantitatively evaluate our approach on the Berkeley segmentation database and compare it against the state-of-the-art.

Many sophisticated segmentation algorithms rely on a first low-level segmentation step where an image is partitioned into homogeneous regions with enforced compactness and adherence to object boundaries. These regions are called “superpixels”. While the marker controlled watershed transformation should in principle be well suited for this type of application, it has never been seriously tested in this setup, and comparisons to other methods were not made with the best possible settings. Here, we provide a scheme for applying the watershed transform for superpixel generation, where we use a spatially regularized gradient to achieve a tunable trade-off between superpixel regularity and adherence to object boundaries. We quantitatively evaluate our method on the Berkeley segmentation database and show that we achieve comparable results to a previously published state-of-the art algorithm, while avoiding some of the arbitrary postprocessing steps the latter requires.

Path openings and closings are morphological tools used to preserve long, thin, and tortuous structures in gray level images. They explore all paths from a defined class, and filter them with a length criterion. However, most paths are redundant, making the process generally slow. Parsimonious path openings and closings are introduced in this paper to solve this problem. These operators only consider a subset of the paths considered by classical path openings, thus achieving a substantial speed-up, while obtaining similar results. In addition, a recently introduced 1D opening algorithm is applied along each selected path. Its complexity is linear with respect to the number of pixels, independent of the size of the opening. Furthermore, it is fast for any input data accuracy (integer or floating point) and works in stream. Parsimonious path openings are also extended to incomplete paths, i.e., paths containing gaps. Noise-corrupted paths can thus be processed with the same approach and complexity. These parsimonious operators achieve a several orders of magnitude speed-up. Examples are shown for incomplete path openings, where computing times are brought from minutes to tens of milliseconds, while obtaining similar results.

A weakly supervised image classification framework is presented in this paper. Given reference images marked by clinicians as relevant or irrelevant, we learn to automatically detect relevant patterns, i.e. patterns that only appear in relevant images. After training, relevant patterns are sought in unseen images in order to classify each image as relevant or irrelevant. No manual segmentations are required. Because manual segmentation of medical images is extremely time-consuming, existing classification algorithms are usually trained on limited reference datasets. With the proposed framework, much larger medical datasets are now available for training. The proposed approach has been successfully applied to diabetic retinopathy detection in the Messidor dataset (Az=0.855). Moreover, we observed, in a new dataset of 473 manually segmented images, that all eight types of diabetic retinopathy lesions are detected.

Openings constitute one of the fundamental operators in mathematical morphology. They can be applied to a wide range of applications, including noise reduction and feature extraction and enhancement. In this paper, we introduce a new, efficient and adaptable algorithm to compute one dimensional openings along discrete lines, in arbitrary orientation. The complexity of this algorithm is linear with respect to the number of pixels of the image. More interestingly, the average complexity per pixel is constant, with respect to the size of the opening.

Film restoration using digital image processing has been an active research field. However, the restoration of the soundtrack has been mainly performed in the sound domain, using signal processing methods, in spite of the fact that it is recorded as a continuous image between the film images and the perforations. In this paper, we present a complete system for variable area optical soundtrack restoration at the image level. The scanned soundtrack is treated using morphological operators, including a novel quasi-distance function. Working with the image representation of the soundtrack allows to take advantage of its redundancy. Moreover, with this approach only those defects that have been caused by ageing are corrected. The first results, concerning variable area soundtracks, are reported.

This article presents the use of morphological amoebas for the enhancement of 3D medical images. Morphological amoebas are kernels adapting their shape in such a way that they do not cross the contours of the image. They can be used in morphological operations in quite a similar way as classical kernel and are well-fitted for noise-reduction in 3D medical images.

A nonlinear interpolator using a rational function filter is applied to the restoration of image sequence frames of digitized old movies. Samples to be interpolated are due to stationary and random defects. The interpolator is preceded by a defect localization algorithm. The performance of the proposed interpolator has been assessed on several sequences and compared with a classical morphological operator. The hardware implementation of the proposed rational interpolator is also considered. Simulations show that the interpolated frames with the proposed operator are free from blockiness and jaggedness which are very difficult to avoid when using linear operators.