Guaranteeing Convergence of Iterative Skewed Voting Algorithms for Image Segmentation

In this paper we provide rigorous proof for the convergence of an iterative voting-based image segmentation algorithm called Active Masks. Active Masks (AM) was proposed to solve the challenging task of delineating punctate patterns of cells from fluorescence microscope images. Each iteration of AM consists of a linear convolution composed with a nonlinear thresholding; what makes this process special in our case is the presence of additive terms whose role is to "skew" the voting when prior information is available. In real-world implementation, the AM algorithm always converges to a fixed point. We study the behavior of AM rigorously and present a proof of this convergence. The key idea is to formulate AM as a generalized (parallel) majority cellular automaton, adapting proof techniques from discrete dynamical systems

ADAPTIVE CODING OF IMAGES VIA MULTIRESOLUTION ICA

Multiresolution (MR) representations have been very successful in image encoding, due to both their algorithmic performance and coding efficiency. However these transforms are fixed, suggesting that coding efficiency could be further improved if a multiresolution code could be adapted to a specific signal class. Among adaptive coding methods, independent component analysis (ICA) provides the best linear code by finding a linear transform with maximally independent coefficients, given a specific signal distribution. This technique, however, scales poorly with the dimensionality of the data, and has been ill-suited for large-scale image coding. Here, propose a hybrid method (multi-resolution ICA) which derives an ICA basis for each of the subband spaces produced by a given MR transform over the image class. We find that this method produces a significantly more efficient code compared to the MR transform alone. We provide both quantitative and qualitative assessments of coding performance, and illustrate improvement over standard (i.e., non-adaptive) wavelet-based representations such as that used in JPEG2000

Generalized subgraph preconditioners for large-scale bundle adjustment

We present a generalized subgraph preconditioning (GSP) technique to solve large-scale bundle adjustment problems efficiently. In contrast with previous work which uses either direct or iterative methods as the linear solver, GSP combines their advantages and is significantly faster on large datasets. Similar to [11], the main idea is to identify a sub-problem (subgraph) that can be solved efficiently by sparse factorization methods and use it to build a preconditioner for the conjugate gradient method. The difference is that GSP is more general and leads to much more effective preconditioners. We design a greedy algorithm to build subgraphs which have bounded maximum clique size in the factorization phase, and also result in smaller condition numbers than standard preconditioning techniques. When applying the proposed method to the “bal ” datasets [1], GSP displays promising performance. 1

A theoretical analysis of robust coding over noisy overcomplete channels

Biological sensory systems are faced with the problem of encoding a high-fidelity sensory signal with a population of noisy, low-fidelity neurons. This problem can be expressed in information theoretic terms as coding and transmitting a multi-dimensional, analog signal over a set of noisy channels. Previously, we have shown that robust, overcomplete codes can be learned by minimizing the reconstruction error with a constraint on the channel capacity. Here, we present a theoretical analysis that characterizes the optimal linear coder and decoder for one- and twodimensional data. The analysis allows for an arbitrary number of coding units, thus including both under- and over-complete representations, and provides a number of important insights into optimal coding strategies. In particular, we show how the form of the code adapts to the number of coding units and to different data and noise conditions to achieve robustness. We also report numerical solutions for robust coding of highdimensional image data and show that these codes are substantially more robust compared against other image codes such as ICA and wavelets.

CONVERGENCE BEHAVIOR OF THE ACTIVE MASK SEGMENTATION ALGORITHM

We study the convergence behavior of the Active Mask (AM) framework, originally designed for segmenting punctate image patterns. AM combines the flexibility of traditional active contours, the statistical modeling power of region-growing methods, and the computational efficiency of multiscale and multiresolution methods. Additionally, it achieves experimental convergence to zero-change (fixedpoint) configurations, a desirable property for segmentation algorithms. At its a core lies a voting-based distributing function which behaves as a majority cellular automaton. This paper proposes an empirical measure correlated to the convergence behavior of AM, and provides sufficient theoretical conditions on the smoothing filter operator to enforce convergence. Index Terms — active mask, cellular automata, convergence, segmentation 1

Convergence behavior of the Active Mask segmentation algorithm

We study the convergence behavior of the Active Mask (AM) framework, originally designed for segmenting punctate image patterns. AM combines the flexibility of traditional active contours, the statistical modeling power of region-growing methods, and the computational efficiency of multiscale and multiresolution methods. Additionally, it achieves experimental convergence to zero-change (fixed-point) configurations, a desirable property for segmentation algorithms. At its a core lies a voting-based distributing function which behaves as a majority cellular automaton. This paper proposes an empirical measure correlated to the convergence behavior of AM, and provides sufficient theoretical conditions on the smoothing filter operator to enforce convergence.</p

Guaranteeing Convergence of Iterative Skewed Voting Algorithms for Image Segmentation.

<p>In this paper we provide rigorous proof for the convergence of an iterative voting-based image segmentation algorithm called Active Masks. Active Masks (AM) was proposed to solve the challenging task of delineating punctate patterns of cells from fluorescence microscope images. Each iteration of AM consists of a linear convolution composed with a nonlinear thresholding; what makes this process special in our case is the presence of additive terms whose role is to "skew" the voting when prior information is available. In real-world implementation, the AM algorithm always converges to a fixed point. We study the behavior of AM rigorously and present a proof of this convergence. The key idea is to formulate AM as a generalized (parallel) majority cellular automaton, adapting proof techniques from discrete dynamical systems.</p