MOSES: A Streaming Algorithm for Linear Dimensionality Reduction.

This paper introduces Memory-limited Online Subspace Estimation Scheme (MOSES) for both estimating the principal components of streaming data and reducing its dimension. More specifically, in various applications such as sensor networks, the data vectors are presented sequentially to a user who has limited storage and processing time available. Applied to such problems, MOSES can provide a running estimate of leading principal components of the data that has arrived so far and also reduce its dimension. MOSES generalises the popular incremental Singular Vale Decomposition (iSVD) to handle thin blocks of data, rather than just vectors. This minor generalisation in part allows us to complement MOSES with a comprehensive statistical analysis, thus providing the first theoretically-sound variant of iSVD, which has been lacking despite the empirical success of this method. This generalisation also enables us to concretely interpret MOSES as an approximate solver for the underlying non-convex optimisation program. We find that MOSES consistently surpasses the state of the art in our numerical experiments with both synthetic and real-world datasets, while being computationally inexpensive.

Stabilizing embedology: Geometry-preserving delay-coordinate maps.

Delay-coordinate mapping is an effective and widely used technique for reconstructing and analyzing the dynamics of a nonlinear system based on time-series outputs. The efficacy of delay-coordinate mapping has long been supported by Takens' embedding theorem, which guarantees that delay-coordinate maps use the time-series output to provide a reconstruction of the hidden state space that is a one-to-one embedding of the system's attractor. While this topological guarantee ensures that distinct points in the reconstruction correspond to distinct points in the original state space, it does not characterize the quality of this embedding or illuminate how the specific parameters affect the reconstruction. In this paper, we extend Takens' result by establishing conditions under which delay-coordinate mapping is guaranteed to provide a stable embedding of a system's attractor. Beyond only preserving the attractor topology, a stable embedding preserves the attractor geometry by ensuring that distances between points in the state space are approximately preserved. In particular, we find that delay-coordinate mapping stably embeds an attractor of a dynamical system if the stable rank of the system is large enough to be proportional to the dimension of the attractor. The stable rank reflects the relation between the sampling interval and the number of delays in delay-coordinate mapping. Our theoretical findings give guidance to choosing system parameters, echoing the tradeoff between irrelevancy and redundancy that has been heuristically investigated in the literature. Our initial result is stated for attractors that are smooth submanifolds of Euclidean space, with extensions provided for the case of strange attractors.

Changes of the Mandible after Orthodontic Treatment with and without Extraction of Four Premolars.

OBJECTIVES: This study was designed to assess the changes of the mandible of patients who underwent orthodontic treatment with or without extraction of four premolars. MATERIALS AND METHODS: Eighteen Class I bimaxillary protrusion patients treated with extraction of four first premolars and retraction of anterior teeth and 18 Class I non-extraction patients with a mean age of 16.38±0.4 years were selected. Cephalometric analysis was performed before and after treatment. Twenty-four variables for analyzing the hard and soft tissues of the mandible were compared between the two groups. Repeated measures ANOVA was used for the comparison of the two groups fallowed by paired t-test. The relationship between the soft and hard tissue variables was studied using the Pearson's correlation coefficient. RESULTS: In both groups, the mean value of angular measurements related to B point and Pogonion (Pog) decreased with treatment (P<0.05). Similarly, the symphysis depth of soft tissue decreased (P=0.008). The mean angular value of Y-axis increased in both groups after treatment (P=0.007). The mean changes in hard tissue symphysis depth after treatment were different in the two groups (P=0.021). Vertical, horizontal and rotational changes in soft tissue B point (B') and Pogonion (pog') followed their underlying hard tissue changes (P<0.05). CONCLUSIONS: Points B and Pog showed backward movement after orthodontic treatments in both extraction and non-extraction patients. Changes in B' and Pog' were directly influenced by the changes in the corresponding points of the underlying hard tissue. Orthodontic treatments with and without extraction of premolars produced insignificant changes in vertical facial dimension.

Endocardial boundary extraction in left ventricular echocardiographic images using fast and adaptive B-spline snake algorithm.

PURPOSE: A fast and robust algorithm was developed for automatic segmentation of the left ventricular endocardial boundary in echocardiographic images. The method was applied to calculate left ventricular volume and ejection fraction estimation. METHODS: A fast adaptive B-spline snake algorithm that resolves the computational concerns of conventional active contours and avoids computationally expensive optimizations was developed. A combination of external forces, adaptive node insertion, and multiresolution strategy was incorporated in the proposed algorithm. Boundary extraction with area and volume estimation in left ventricular echocardiographic images was implemented using the B-spline snake algorithm. The method was implemented in MATLAB and 50 medical images were used to evaluate the algorithm performance. Experimental validation was done using a database of echocardiographic images that had been manually evaluated by experts. RESULTS: Comparison of methods demonstrates significant improvement over conventional algorithms using the adaptive B-spline technique. Moreover, our method reached a reasonable agreement with the results obtained manually by experts. The accuracy of boundary detection was calculated with Dice's coefficient equation (91.13%), and the average computational time was 1.24 s in a PC implementation. CONCLUSION: In sum, the proposed method achieves satisfactory results with low computational complexity. This algorithm provides a robust and feasible technique for echocardiographic image segmentation. Suggestions for future improvements of the method are provided.

Fast and automatic LV mass calculation from echocardiographic images via B-spline snake model and Markov random fields.

Left ventricular (LV) mass has several important diagnostic and indicative implications. In this paper, a fast and accurate technique for detection of inner and outer boundaries of LV and, consequently, calculation of LV mass from apical 4-chamber echocardiographic images is presented. For detection of the inner boundary, a modified B-spline snake is proposed, which relies merely on image intensity and obviates the need for computationally-demanding image forces. The outer boundary is then obtained using a Markov random fields model in the neighborhood of the estimated inner border. Experimental validation of the proposed technique demonstrates remarkable improvement over conventional algorithms.

Object contour extraction in medical images by fast adaptive B-Snake.

Detection of edge contours to define the object class and segmenting it from the background(s) class is a major challenge in medical image processing. In this paper, we introduce a fast adaptive B-Spline Snake algorithm that overcomes the limitations of previous B-Snakes by avoiding computationally expensive optimization stages. Furthermore, we present novel strategies for adaptive knot insertion to fulfill the specific requirements of the medical application accordingly. Experimental results on pulmonary CT images and brain MR images demonstrated that our method is superior both in accuracy and convergence speed over previous B-Spline Snake algorithms. The proposed algorithm is also robust to missing the boundaries.