Christophe Avenel

Tracking Closed Curves with Non-linear Stochastic Filters

The joint analysis of motions and deformations is crucial in a number of computer vision applications. In this paper, we introduce a non-linear stochastic filtering technique to track the state of a free curve. The approach we propose is implemented through a particle filter which includes color measurements characterizing the target and the background respectively. We design a continuous-time dynamics that allows us to infer inter-frame deformations. The curve is defined by an implicit level-set representation and the stochastic dynamics is expressed on the level-set function. It takes the form of a stochastic differential equation with Brownian motion of low dimension. Specific noise models lead to traditional evolution laws based on mean curvature motions, while other forms lead to new evolution laws with different smoothing behaviors. In these evolution models, we propose to combine local motion information extracted from the images and an incertitude modeling of the dynamics. The associated filter we propose for curve tracking thus belongs to the family of conditional particle filters. Its capabilities are demonstrated on various sequences with highly deformable objects.

Stochastic Level Set Dynamics to Track Closed Curves Through Image Data

We introduce a stochastic filtering technique for the tracking of closed curves from image sequence. For that purpose, we design a continuous-time dynamics that allows us to infer inter-frame deformations. The curve is defined by an implicit level-set representation and the stochastic dynamics is expressed on the level-set function. It takes the form of a stochastic partial differential equation with a Brownian motion of low dimension. The evolution model we propose combines local photometric information, deformations induced by the curve displacement and an uncertainty modeling of the dynamics. Specific choices of noise models and drift terms lead to an evolution law based on mean curvature as in classic level set methods, while other choices yield new evolution laws. The approach we propose is implemented through a particle filter, which includes color measurements characterizing the target and the background photometric probability densities respectively. The merit of this filter is demonstrated on various satellite image sequences depicting the evolution of complex geophysical flows.

Tracking level set representation driven by a stochastic dynamics

We introduce a non-linear stochastic filtering technique to track the state of a free curve from image data. The approach we propose is implemented through a particle filter, which includes color measurements characterizing the target and the background respectively. We design a continuous-time dynamics that allows us to infer inter-frame deformations. The curve is defined by an implicit level-set representation and the stochastic dynamics is expressed on the level-set function. It takes the form of a stochastic partial differential equation with a Brownian motion of low dimension. Specific noise models lead to the traditional level set evolution law based on mean curvature motions, while other forms lead to new evolution laws with different smoothing behaviors. In these evolution models, we propose to combine local photometric information, some velocity induced by the curve displacement and an uncertainty modeling of the dynamics. The associated filter capabilities are demonstrated on various sequences with highly deformable objects.

Stochastic Filtering of Level Sets for Curve Tracking

This paper focuses on the tracking of free curves using non-linear stochastic filtering techniques. It relies on a particle filter which includes color measurements. The curve and its velocity are defined through two coupled implicit level set representations. The stochastic dynamics of the curve is expressed directly on the level set function associated to the curve representation and combines a velocity field captured from the additional second level set attached to the past curves points location. The curves dynamics combines a low-dimensional noise model and a data-driven local force. We demonstrate how this approach allows the tracking of highly and rapidly deforming objects, such as convective cells in infra-red satellite images, while providing a location-dependent assessment of the estimation confidence.

Solving the Table Maker's Dilemma on Current SIMD Architectures

Correctly-rounded implementations of some elementary functions are recommended by the IEEE 754-2008 standard, which aims at ensuring portable and predictable floating-point computations. Such implementations require the solving of the Table Makers Dilemma which implies a huge amount of computation time. These computations are embarrassingly and massively parallel, but present control flow divergence which limits performance at the SIMD parallelism level, whose share in the overall performance of current and forthcoming HPC architectures is increasing. In this paper, we show that efficiently solving the Table Makers Dilemma on various multi-core and many-core SIMD architectures (CPUs, GPUs, Intel Xeon Phi) requires to jointly handle divergence at the algorithmic, programming and hardware levels in order to scale with the number of SIMD lanes. Depending on the architecture, the performance gains can reach 10.5x over divergent code, or be constrained by different limits that we detail.