Predicting Signed Distance Functions for Visual Instance Segmentation

Visual instance segmentation is a challenging problem and becomes even more difficult if objects of interest varies unconstrained in shape. Some objects are well described by a rectangle, however, this is hardly always the case. Consider for instance long, slender objects such as ropes. Anchor-based approaches classify predefined bounding boxes as either negative or positive and thus provide a limited set of shapes that can be handled. Defining anchor-boxes that fit well to all possible shapes leads to an infeasible number of prior boxes. We explore a different approach and propose to train a neural network to compute distance maps along different directions. The network is trained at each pixel to predict the distance to the closest object contour in a given direction. By pooling the distance maps we obtain an approximation to the signed distance function (SDF). The SDF may then be thresholded in order to obtain a foreground-background segmentation. We compare this segmentation to foreground segmentations obtained from the state-of-the-art instance segmentation method YOLACT. On the COCO dataset, our segmentation yields a higher performance in terms of foreground intersection over union (IoU). However, while the distance maps contain information on the individual instances, it is not straightforward to map them to the full instance segmentation. We still believe that this idea is a promising research direction for instance segmentation, as it better captures the different shapes found in the real world.

The Push-Forward Transform for Continuous and Robust Comparison of Dynamic Shapes

We introduce a mathematical framework for shape comparison based on mapping functions from the shape domain to a common reference domain. This Push-Forward Transform enables invariant and robust comparison of shapes, preserving intrinsic geometric information. Quantitatively comparing shapes and their temporal evolution is a fundamental challenge in image analysis. Meaningful shape comparison requires representations that are invariant to transformations that do not alter shape itself, such as translation, rotation, reflection, re-parametrization, and uniform scaling, while remaining sensitive to intrinsic geometric variation. Existing approaches often rely on sensitive parameterizations, landmark correspondence, or learned representations that are difficult to interpret and reproduce. We show that the Push-Forward Transform (PF-T) applied to Signed Distance Functions (SDFs) yields a continuous representation that captures both boundary and interior geometry. We derive an interpretable morphometric that quantifies shape similarity and reveals features such as skeletal topology and rotational symmetries. The push-forward transform applies consistently to two- and three-dimensional shapes, extends to time-evolving geometries, and supports the joint analysis of shape and additional scalar fields defined over shapes, such as intensity or molecular signals. We present the mathematical formulation, describe an efficient algorithm, and benchmark the approach on 2D, 3D, and temporal data sets.

PEPS: Positional Encoding Projected Sampling -- Extended

Implicit neural representations (INRs) are increasingly being used as tools to map coordinates to signals, encompassing applications from neural fields to texture compression, shape representations, and beyond. Most INR methods are based on using high-dimensional projections of the initial coordinates through encoders such as grid or positional encoding. Nevertheless, positional encoding is often insufficient and grids, as we show in this paper, require high resolution for being able to learn. In this paper, we demonstrate that positional encoding can be used not only as a high-dimensional embedding but also decomposed as a series of meaningful points. We propose the Positional Encoding Projected Sampling, where we treat the projection of the original coordinate at each frequency as a point of interest. We describe the motion of each point with respect to the frequencies and show that it follows a unique pattern. Finally, we use the unique motion of each point as a basis decomposition for doing learned positional encoding using grids. We prove, using three competitive applications; image representation, texture compression, and signed distance function; that the proposed approach outperforms the current state of the art methods, and often requires 25\% less parameters for equivalent reconstruction error or rendering.