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Carme Julia, Angel Sappa, Felipe Lumbreras, Joan Serrat, & Antonio Lopez. (2009). An iterative multiresolution scheme for SFM with missing data. JMIV - Journal of Mathematical Imaging and Vision, 34(3), 240–258.
Abstract: 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.
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Carme Julia, Angel Sappa, Felipe Lumbreras, Joan Serrat, & Antonio Lopez. (2009). Predicting Missing Ratings in Recommender Systems: Adapted Factorization Approach. International Journal of Electronic Commerce, 14(1), 89–108.
Abstract: 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 customer's 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.
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Carme Julia, Angel Sappa, Felipe Lumbreras, Joan Serrat, & Antonio Lopez. (2010). An Iterative Multiresolution Scheme for SFM with Missing Data: single and multiple object scenes. IMAVIS - Image and Vision Computing, 28(1), 164–176.
Abstract: Most of the techniques proposed for tackling the Structure from Motion problem (SFM) cannot deal with high percentages of missing data in the matrix of trajectories. Furthermore, an additional problem should be faced up when working with multiple object scenes: the rank of the matrix of trajectories should be estimated. This paper presents an iterative multiresolution scheme for SFM with missing data to be used in both the single and multiple object cases. The proposed scheme aims at recovering missing entries in the original input matrix. The objective is to improve the results by applying a factorization technique to the partially or totally filled in matrix instead of to the original input one. Experimental results obtained with synthetic and real data sequences, containing single and multiple objects, are presented to show the viability of the proposed approach.
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Carme Julia, Angel Sappa, Felipe Lumbreras, Joan Serrat, & Antonio Lopez. (2011). Rank Estimation in Missing Data Matrix Problems. JMIV - Journal of Mathematical Imaging and Vision, 39(2), 140–160.
Abstract: 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.
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Carme Julia, Felipe Lumbreras, & Angel Sappa. (2011). A Factorization-based Approach to Photometric Stereo. IJIST - International Journal of Imaging Systems and Technology, 21(1), 115–119.
Abstract: 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. © 2011 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 21, 115–119, 2011.
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