Deformable 2-D template matching using orthogonal curves

A new formulation of the two-dimensional (2-D) deformable template matching problem is proposed. It uses a lower-dimensional search space than conventional methods by precomputing extensions of the deformable template along orthogonal curves. The reduction in search space allows the use of dynamic programming to obtain globally optimal solutions and reduces the sensitivity of the algorithm to initial placement of the template. Further, the technique guarantees that the result is a curve which does not collapse to a point in the absence of strong image gradients and is always nonself intersecting. Examples of the use of the technique on real-world images and in simulations at low signal-to-noise ratios (SNRs) are also provided     

Evaluation of four probability distribution models for speckle in clinical cardiac ultrasound images

Segmenting cardiac ultrasound images requires a model for the statistics of speckle in the images. Although the statistics of speckle are well understood for the raw transducer signal, the statistics of speckle in the image are not. This paper evaluates simple empirical models for first-order statistics for the distribution of gray levels in speckle. The models are created by analyzing over 100 images obtained from commercial ultrasound machines in clinical settings. The data in the images suggests a unimodal scalable family of distributions as a plausible model. Four families of distributions (Gamma, Weibull, Normal, and Log-normal) are compared with the data using goodness-of-fit and misclassification tests. Attention is devoted to the analysis of artifacts in images and to the choice of goodness-of-fit and misclassification tests. The distribution of parameters of one of the models is investigated and priors for the distribution are suggested.     

A maximum-likelihood strategy for directing attention during visualsearch

A precise analysis of an entire image is computationally wasteful if one is interested in finding a target object located in a subregion of the image. A useful “attention strategy” can reduce the overall computation by carrying out fast but approximate image measurements and using their results to suggest a promising subregion. The paper proposes a maximum-likelihood attention mechanism that does this. The attention mechanism recognizes that objects are made of parts and that parts have different features. It works by proposing object part and image feature pairings which have the highest likelihood of coming from the target. The exact calculation of the likelihood as well as approximations are provided. The attention mechanism is adaptive, that is, its behavior adapts to the statistics of the image features. Experimental results suggest that, on average, the attention mechanism evaluates less than 2 percent of all part-feature pairs before selecting the actual object, showing a significant reduction in the complexity of visual search     

On the Topology and Geometry of Spaces of Affine Shapes

We define the space of affine shapes of k points in R ⁿ to be the topological quotient of (R ⁿ ) ^k modulo the natural action of the affine group of R ⁿ . These spaces arise naturally in many image-processing applications, and despite having poor separation properties, have some topological and geometric properties reminiscent of the more familiar Procrustes shape spaces Σ _n ^k in which one identifies configurations related by an orientation-preserving Euclidean similarity transformation. We examine the topology of the connected, non-Hausdorff spaces Sh _n ^k in detail. Each Sh _n ^k is a disjoint union of naturally ordered strata, each of which is homeomorphic in the relative topology to a Grassmannian, and we show how the strata are attached to each other. The top stratum carries a natural Riemannian metric, which we compute explicitly for k>n, expressing the metric purely in terms of “pre-shape” data, i.e. configurations of k points in R ⁿ .     

Symmetric Non-rigid Registration: A Geometric Theory and Some Numerical Techniques

This paper proposes ℒ₂- and information-theory-based (IT) non-rigid registration algorithms that are exactly symmetric. Such algorithms pair the same points of two images after the images are swapped. Many commonly-used ℒ₂ and IT non-rigid registration algorithms are only approximately symmetric. The asymmetry is due to the objective function as well as due to the numerical techniques used in discretizing and minimizing the objective function. This paper analyzes and provides techniques to eliminate both sources of asymmetry. This paper has five parts. The first part shows that objective function asymmetry is due to the use of standard differential volume forms on the domain of the images. The second part proposes alternate volume forms that completely eliminate objective function asymmetry. These forms, called graph-based volume forms, are naturally defined on the graph of the registration diffeomorphism f, rather than on the domain of f. When pulled back to the domain of f they involve the Jacobian J _f and therefore appear “non-standard”. In the third part of the paper, graph-based volume forms are analyzed in terms of four key objective-function properties: symmetry, positive-definiteness, invariance, and lack of bias. Graph-based volume forms whose associated ℒ₂ objective functions have the first three properties are completely classified. There is an infinite-dimensional space of such graph-based forms. But within this space, up to scalar multiple, there is a unique volume form whose associated ℒ₂ objective function is unbiased. This volume form, which when pulled back to the domain of f is (1+det(J _f )) times the standard volume form on Euclidean space, is exactly the differential-geometrically natural volume form on the graph of f. The fourth part of the paper shows how the same volume form also makes the IT objective functions symmetric, positive semi-definite, invariant, and unbiased. The fifth part of the paper introduces a method for removing asymmetry in numerical computations and presents results of numerical experiments. The new objective functions and numerical method are tested on a coronal slice of a 3-D MRI brain image. Numerical experiments show that, even in the presence of noise, the new volume form and numerical techniques reduces asymmetry practically down to machine precision without compromising registration accuracy.

Non-Rigid Shape Comparison of Plane Curves in Images

A mathematical theory for establishing correspondences between curves and for non-rigid shape comparison is developed in this paper. The proposed correspondences, called bimorphisms, are more general than those obtained from one-to-one functions. Their topology is investigated in detail.A new criterion for non-rigid shape comparison using bimorphisms is also proposed. The criterion avoids many of the mathematical problems of previous approaches by comparing shapes non-rigidly from the bimorphism.Geometric invariants are calculated for curves whose shapes can be exactly matched with a bimorphism. The invariants are related to the concave and convex segments of a curve and provide justification for parsing the curve into such segments.     

On the localization performance measure and optimal edge detection

The localization performance measure of edge detectors is addressed. A one-dimensional formulation of the problem is considered. A linear space-invariant filter is used for the detection. The locations of local maxima in the thresholded output of the filter are declared to be the edges. The limitations of conventional performance measures are shown, and a localization performance measure for edge detection is suggested. This performance measure is based on the theory of zero-crossings of stochastic processes. It is shown that the derivative of a Gaussian is the optimal edge detector for the measure     

Instabilities of horizontal magnetoconvection with rotating fluid in a sparsely packed porous media

We studied linear and nonlinear instabilities of horizontal magnetoconvection with rotating fluid in a sparsely packed porous media. We studied the critical Rayleigh number and traced marginal stability curves at different parameters , , , and . We obtained Takens‐Bogdanov and co‐dimension two bifurcation points. The Newell‐Whitehead multiple scheme was employed to derive amplitude equations at Pitchfork and Hopf bifurcation. At the onset of Pitchfork bifurcation we identified Eckhaus and Zigzag instability regions and studied Nusselt number. The system of coupled Landau Ginzburg equations were derived at the onset of Hopf bifurcation and identified secondary instability regions for fixed parameters, steady state mode shifted to standing and traveling waves as increases.     

A Family of Regularizing Kernels for Averaging in the Presence of Template Jitter

While computing the regularized mean in medical image analysis, compensation for anatomical variation between different subjects is achieved by registering data with a standard template. In practice, template registration is never perfect and registration error (called jitter) can influence any statistic that is calculated using the template. This paper considers the design of regularizing filters which makes the effect of jitter harmless on the computed mean. The design is based on a new notion called jitter-resistant filtering. A regularizing kernel is jitter resistant if the effect of jitter on the regularized data is similar to a slight change in the scale of the kernel in the absence of jitter. Based on this notion, it is shown that the family of Gaussian filters is a jitter-resistant family of regularizing filters. Simulations in support of the theory are also presented.