Measuring linearity of curves in 2D and 3D

In this paper we define a new linearity measure for open curve segments in 2D and 3D . The measure considers the distance of the curve end points to the curve centroid. It is simple to compute and has the basic properties that should be satisfied by any linearity measure. The new measure ranges over the interval (0,1], and produces the value 1 if and only if the measured curve is a perfect straight line segment. Also, the new linearity measure is invariant with respect to translations, rotations and scaling transformations. The new measure is theoretically well founded and, because of this, its behaviour can be well understood and predicted to some extent. This is always beneficial because it indicates the suitability of the new measure to the desired application. Several experiments are provided to illustrate the behaviour and to demonstrate the efficiency and applicability of the new linearity measure

Semantic Evaluation and Deformation of Curves Based on Aesthetic Criteria

To better simulate the way designers work, specific tools are needed to handle directly specific shape features meaningful for the design intent, without focusing on the underlying mathematic representation. For this purpose it is fundamental to identify proper higher-level shape descriptors as well as the corresponding manipulation techniques. The paper presents the definition and implementation of semantic operators for curve deformation based on a shape characterization that is specific to the industrial design context. The work grounds on the innovative approach suggested by the FIORES-II project for the intent-driven modeling tools for direct shape modification and on the multi-layered architecture proposed by the Network of Excellence AIM@SHAPE for the definition of semantic-oriented 3D models. In particular the paper proposes the use of meaningful aesthetic features for the evaluation of planar curve signature and for their intent-driven direct modification

Mapping polygons to the grid with small Hausdorff and Fréchet distance

We show how to represent a simple polygon P by a grid (pixel-based) polygon Q that is simple and whose Hausdorff or Fréchet distance to P is small. For any simple polygon P, a grid polygon exists with constant Hausdorff distance between their boundaries and their interiors. Moreover, we show that with a realistic input assumption we can also realize constant Fréchet distance between the boundaries. We present algorithms accompanying these constructions, heuristics to improve their output while keeping the distance bounds, and experiments to assess the output

Full interpretation of minimal images

The goal in this work is to model the process of ‘full interpretation’ of object images, which is the ability to identify and localize all semantic features and parts that are recognized by human observers. The task is approached by dividing the interpretation of the complete object to the interpretation of multiple reduced but interpretable local regions. In such reduced regions, interpretation is simpler, since the number of semantic components is small, and the variability of possible configurations is low. We model the interpretation process by identifying primitive components and relations that play a useful role in local interpretation by humans. To identify useful components and relations used in the interpretation process, we consider the interpretation of ‘minimal configurations’: these are reduced local regions, which are minimal in the sense that further reduction renders them unrecognizable and uninterpretable. We show that such minimal interpretable images have useful properties, which we use to identify informative features and relations used for full interpretation. We describe our interpretation model, and show results of detailed interpretations of minimal configurations, produced automatically by the model. Finally, we discuss implications of full interpretation to difficult visual tasks, such as recognizing human activities or interactions, which are beyond the scope of current models of visual recognition.This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF-1231216

Monocular Pose Estimation Based on Global and Local Features

The presented thesis work deals with several mathematical and practical aspects of the monocular pose estimation problem. Pose estimation means to estimate the position and orientation of a model object with respect to a camera used as a sensor element. Three main aspects of the pose estimation problem are considered. These are the model representations, correspondence search and pose computation. Free-form contours and surfaces are considered for the approaches presented in this work. The pose estimation problem and the global representation of free-form contours and surfaces are defined in the mathematical framework of the conformal geometric algebra (CGA), which allows a compact and linear modeling of the monocular pose estimation scenario. Additionally, a new local representation of these entities is presented which is also defined in CGA. Furthermore, it allows the extraction of local feature information of these models in 3D space and in the image plane. This local information is combined with the global contour information obtained from the global representations in order to improve the pose estimation algorithms. The main contribution of this work is the introduction of new variants of the iterative closest point (ICP) algorithm based on the combination of local and global features. Sets of compatible model and image features are obtained from the proposed local model representation of free-form contours. This allows to translate the correspondence search problem onto the image plane and to use the feature information to develop new correspondence search criteria. The structural ICP algorithm is defined as a variant of the classical ICP algorithm with additional model and image structural constraints. Initially, this new variant is applied to planar 3D free-form contours. Then, the feature extraction process is adapted to the case of free-form surfaces. This allows to define the correlation ICP algorithm for free-form surfaces. In this case, the minimal Euclidean distance criterion is replaced by a feature correlation measure. The addition of structural information in the search process results in better conditioned correspondences and therefore in a better computed pose. Furthermore, global information (position and orientation) is used in combination with the correlation ICP to simplify and improve the pre-alignment approaches for the monocular pose estimation. Finally, all the presented approaches are combined to handle the pose estimation of surfaces when partial occlusions are present in the image. Experiments made on synthetic and real data are presented to demonstrate the robustness and behavior of the new ICP variants in comparison with standard approaches