Sinisa Todorovic

ICLR Conference 2020 Conference Paper

Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform

• Jun Li 0098
• Fuxin Li
• Sinisa Todorovic

Strictly enforcing orthonormality constraints on parameter matrices has been shown advantageous in deep learning. This amounts to Riemannian optimization on the Stiefel manifold, which, however, is computationally expensive. To address this challenge, we present two main contributions: (1) A new efficient retraction map based on an iterative Cayley transform for optimization updates, and (2) An implicit vector transport mechanism based on the combination of a projection of the momentum and the Cayley transform on the Stiefel manifold. We specify two new optimization algorithms: Cayley SGD with momentum, and Cayley ADAM on the Stiefel manifold. Convergence of Cayley SGD is theoretically analyzed. Our experiments for CNN training demonstrate that both algorithms: (a) Use less running time per iteration relative to existing approaches that enforce orthonormality of CNN parameters; and (b) Achieve faster convergence rates than the baseline SGD and ADAM algorithms without compromising the performance of the CNN. Cayley SGD and Cayley ADAM are also shown to reduce the training time for optimizing the unitary transition matrices in RNNs.

NeurIPS Conference 2010 Conference Paper

(RF)^2 -- Random Forest Random Field

• Nadia Payet
• Sinisa Todorovic

We combine random forest (RF) and conditional random field (CRF) into a new computational framework, called random forest random field (RF)^2. Inference of (RF)^2 uses the Swendsen-Wang cut algorithm, characterized by Metropolis-Hastings jumps. A jump from one state to another depends on the ratio of the proposal distributions, and on the ratio of the posterior distributions of the two states. Prior work typically resorts to a parametric estimation of these four distributions, and then computes their ratio. Our key idea is to instead directly estimate these ratios using RF. RF collects in leaf nodes of each decision tree the class histograms of training examples. We use these class histograms for a non-parametric estimation of the distribution ratios. We derive the theoretical error bounds of a two-class (RF)^2. (RF)^2 is applied to a challenging task of multiclass object recognition and segmentation over a random field of input image regions. In our empirical evaluation, we use only the visual information provided by image regions (e. g. , color, texture, spatial layout), whereas the competing methods additionally use higher-level cues about the horizon location and 3D layout of surfaces in the scene. Nevertheless, (RF)^2 outperforms the state of the art on benchmark datasets, in terms of accuracy and computation time.

NeurIPS Conference 2010 Conference Paper

Segmentation as Maximum-Weight Independent Set

• William Brendel
• Sinisa Todorovic

Given an ensemble of distinct, low-level segmentations of an image, our goal is to identify visually meaningful" segments in the ensemble. Knowledge about any specific objects and surfaces present in the image is not available. The selection of image regions occupied by objects is formalized as the maximum-weight independent set (MWIS) problem. MWIS is the heaviest subset of mutually non-adjacent nodes of an attributed graph. We construct such a graph from all segments in the ensemble. Then, MWIS selects maximally distinctive segments that together partition the image. A new MWIS algorithm is presented. The algorithm seeks a solution directly in the discrete domain, instead of relaxing MWIS to a continuous problem, as common in previous work. It iteratively finds a candidate discrete solution of the Taylor series expansion of the original MWIS objective function around the previous solution. The algorithm is shown to converge to a maximum. Our empirical evaluation on the benchmark Berkeley segmentation dataset shows that the new algorithm eliminates the need for hand-picking optimal input parameters of the state-of-the-art segmenters, and outperforms their best, manually optimized results. "

ICML Conference 2005 Conference Paper

Unifying the error-correcting and output-code AdaBoost within the margin framework

• Yijun Sun
• Sinisa Todorovic
• Jian Li
• Dapeng Wu 0001

ICRA Conference 2004 Conference Paper

Intelligent Missions for MAVs: Visual Contexts for Control, Tracking and Recognition

• Sinisa Todorovic
• Michael C. Nechyba

In this paper, we develop a unified vision system for small-scale aircraft that not only addresses basic flight stability and control, but also enables more intelligent missions, such as ground object recognition and moving-object tracking. The proposed system defines a framework for real-time image feature extraction, horizon detection and sky/ground segmentation, and contextual ground object detection. Multiscale Linear Discriminant Analysis (MLDA) defines the first stage of the vision system, and generates a multiscale description of images, incorporating both color and texture through a dynamic representation of image details. This representation is ideally suited for horizon detection and sky/ground segmentation of images, which we accomplish through the probabilistic representation of tree-structured belief networks (TSBN). Specifically, we propose incomplete meta TSBNs (IMTSBN) to accommodate the properties of our MLDA representation and to enhance the descriptive component of these statistical models. In the last stage of the vision processing, we seamlessly extend this probabilistic framework to perform computationally efficient detection and recognition of objects in the segmented ground region, through the idea of visual contexts. By exploiting visual contexts, we can quickly focus on candidate regions where objects of interest may be found, and then perform additional analysis for those regions only. Throughout, our approach is heavily influenced by real-time constraints and robustness to transient video noise.

ICRA Conference 2003 Conference Paper

Sky/ground modeling for autonomous MAV flight

• Sinisa Todorovic
• Michael C. Nechyba
• Peter G. Ifju

Recently, we have implemented a computer-vision based horizon-tracking algorithm for flight stability and autonomy in micro air vehicles (MAVs) [S. M. Ettinger et al. , 2002]. Occasionally, this algorithm fails in scenarios where the underlying Gaussian assumption for the sky and ground appearances is not appropriate. Therefore, in this paper, we present a general statistical image modeling framework which we have use to build prior models of the sky and ground. Once trained, these models can be incorporated into our existing horizon-tracking algorithm. Since the appearances of the sky and ground vary enormously, no single feature is sufficient for accurate modeling: as such, we rely both on color and texture as critical features in our modeling framework. Specifically, we choose hue and intensity for our color representation, and the complex wavelet transform (CWT) for our texture representation. We then use hidden Markov tree (HMT) models, which are particularly well suited for the CWT's inherent tree structure, as our underlying statistical models over our feature space. With this approach, we have achieved reliable and robust image segmentation of flight images from on-board our MAVs as well as on more difficult-to-classify sky/ground images.