Carme Julià

A new methodology for evaluation of edge detectors

This paper defines a new methodology for evaluating edge detectors through measurements on edginess maps instead of on binary edge maps as previous methodologies do. These measurements avoid possible bias introduced by the application-dependent process of generating binary edge maps from edginess maps. The features of completeness, discriminability, precision and robustness, which a general-purpose edge detector must comply with, are introduced. The R, DS, P and FAR-measurements in addition to PSNR applied to the edginess maps are defined to assess the performance of edge detection. The R, DS, P and FAR-measurements can be seen as generalizations of previously proposed measurements on binary edge maps. Well-known and state-of-the-art edge detectors have been compared by means of the new proposed metrics. Results show that it is difficult for an edge detector to comply with all the proposed features.

Robust color edge detection through tensor voting

This paper presents a new method for color edge detection based on the tensor voting framework, a robust perceptual grouping technique used to extract salient information from noisy data. The tensor voting framework is adapted to encode color information via tensors in order to propagate them into a neighborhood through a voting process specifically designed for color edge detection by taking into account perceptual color differences, region uniformity and edginess according to a set of intuitive perceptual criteria. Perceptual color differences are estimated by means of an optimized version of the CIEDE2000 formula, while uniformity and edginess are estimated by means of saliency maps obtained from the tensor voting process. Experiments show that the proposed algorithm is more robust and has a similar performance in precision when compared with the state-of-the-art.

A factorization‐based approach to photometric stereo

This article presents an adaptation of a factorization technique to tackle the photometric stereo problem. That is to recover the surface normals and reflectance of an object from a set of images obtained under different lighting conditions. The main contribution of the proposed approach is to consider pixels in shadow and saturated regions as missing data, in order to reduce their influence to the result. Concretely, an adapted Alternation technique is used to deal with missing data. Experimental results considering both synthetic and real images show the viability of the proposed factorization‐based strategy.

Rank Estimation in Missing Data Matrix Problems

A novel technique for missing data matrix rank estimation is presented. It is focused on matrices of trajectories, where every element of the matrix corresponds to an image coordinate from a feature point of a rigid moving object at a given frame; missing data are represented as empty entries. The objective of the proposed approach is to estimate the rank of a missing data matrix in order to fill in empty entries with some matrix completion method, without using or assuming neither the number of objects contained in the scene nor the kind of their motion. The key point of the proposed technique consists in studying the frequency behaviour of the individual trajectories, which are seen as 1D signals. The main assumption is that due to the rigidity of the moving objects, the frequency content of the trajectories will be similar after filling in their missing entries. The proposed rank estimation approach can be used in different computer vision problems, where the rank of a missing data matrix needs to be estimated. Experimental results with synthetic and real data are provided in order to empirically show the good performance of the proposed approach.

Predicting Missing Ratings in Recommender Systems: Adapted Factorization Approach

The paper presents a factorization-based approach to make predictions in recommender systems. These systems are widely used in electronic commerce to help customers find products according to their preferences. Taking into account the customers ratings of some products available in the system, the recommender system tries to predict the ratings the customer would give to other products in the system. The proposed factorization-based approach uses all the information provided to compute the predicted ratings, in the same way as approaches based on Singular Value Decomposition (SVD). The main advantage of this technique versus SVD-based approaches is that it can deal with missing data. It also has a smaller computational cost. Experimental results with public data sets are provided to show that the proposed adapted factorization approach gives better predicted ratings than a widely used SVD-based approach.

Full Quadrant Approximations for the Arctangent Function [Tips and Tricks]

This article presents two novel full quadrant approximations for the arctangent function that are specially suitable for real-time applications. The key point of the proposed approximations is that they are valid in a full quadrant. As a result, they can be easily extended to two and four quadrants. The approximations we define are rational functions of second and third order, respectively. This article provides a comparison of the precision and performance of the proposed functions with the best state-of-the-art approximations. Results show that the third-order proposed function outperforms the existing ones in terms of both precision and performance. The second-order proposed function, on the other hand, is the most suitable one for real-time applications, since it has the highest performance. Furthermore, it attains an adequate precision for most applications in the computer vision field.

An Iterative Multiresolution Scheme for SFM with Missing Data

Several techniques have been proposed for tackling the Structure from Motion problem through factorization in the case of missing data. However, when the percentage of unknown data is high, most of them may not perform as well as expected. Focussing on this problem, an iterative multiresolution scheme, which aims at recovering missing entries in the originally given input matrix, is proposed. Information recovered following a coarse-to-fine strategy is used for filling in the missing entries. The objective is to recover, as much as possible, missing data in the given matrix. Thus, when a factorization technique is applied to the partially or totally filled in matrix, instead of to the originally given input one, better results will be obtained. An evaluation study about the robustness to missing and noisy data is reported. Experimental results obtained with synthetic and real video sequences are presented to show the viability of the proposed approach.

Photometric stereo through an adapted alternation approach

Photometric stereo aims at finding the surface normal and reflectance at every point of an object from a set of images obtained under different lighting conditions. The obtained intensity image data are stacked into a matrix that can be approximated by a low-dimensional linear subspace, under the Lambertian model. The current paper proposes to use an adaptation of the Alternation technique to tackle this problem when the images contain missing data, which correspond to pixels in shadow and saturated regions. Experimental results considering both synthetic and real images show the good performance of the proposed Alternation-based strategy.

Motion Segmentation from Feature Trajectories with Missing Data

This paper presents a novel approach for motion segmentation from feature trajectories with missing data. It consists of two stages. In the first stage, missing data are filled in by applying a factorization technique to the matrix of trajectories. Since the number of objects in the scene is not given and the rank of this matrix can not be directly computed, a simple technique for matrix rank estimation, based on a frequency spectra representation, is proposed. In the second stage, motion segmentation is obtained by using a clustering approach based on the normalized cuts criterion. Finally, the shape Sand motion Mof each of the obtained clusters (i.e., single objects) are recovered by applying classical SFM techniques. Experiments with synthetic and real data are provided in order to demonstrate the viability of the proposed approach.

Factorization with missing and noisy data

Several factorization techniques have been proposed for tackling the Structure from Motion problem. Most of them provide a good solution, while the amount of missing data is within an acceptable ratio. Focussing on this problem, we propose an incremental multiresolution scheme able to deal with a high rate of missing data, as well as noisy data. It is based on an iterative approach that applies a classical factorization technique in an incrementally reduced space. Information recovered following a coarse-to-fine strategy is used for both, filling in the missing entries of the input matrix and denoising original data. A statistical study of the proposed scheme compared to a classical factorization technique is given. Experimental results obtained with synthetic data and real video sequences are presented to demonstrate the viability of the proposed approach.