A segmentation editing framework based on shape change statistics

Segmentation is a key task in medical image analysis because its accuracy significantly affects successive steps. Automatic segmentation methods often produce inadequate segmentations, which require the user to manually edit the produced segmentation slice by slice. Because editing is time-consuming, an editing tool that enables the user to produce accurate segmentations by only drawing a sparse set of contours would be needed. This paper describes such a framework as applied to a single object. Constrained by the additional information enabled by the manually segmented contours, the proposed framework utilizes object shape statistics to transform the failed automatic segmentation to a more accurate version. Instead of modeling the object shape, the proposed framework utilizes shape change statistics that were generated to capture the object deformation from the failed automatic segmentation to its corresponding correct segmentation. An optimization procedure was used to minimize an energy function that consists of two terms, an external contour match term and an internal shape change regularity term. The high accuracy of the proposed segmentation editing approach was confirmed by testing it on a simulated data set based on 10 in-vivo infant magnetic resonance brain data sets using four similarity metrics. Segmentation results indicated that our method can provide efficient and adequately accurate segmentations (Dice segmentation accuracy increase of 10%), with very sparse contours (only 10%), which is promising in greatly decreasing the work expected from the user

Non-Euclidean, convolutional learning on cortical brain surfaces

In recent years there have been many studies indicating that multiple cortical features, extracted at each surface vertex, are promising in the detection of various neurodevelopmental and neurodegenerative diseases. However, with limited datasets, it is challenging to train stable classifiers with such high-dimensional surface data. This necessitates a feature reduction that is commonly accomplished via regional volumetric morphometry from standard brain atlases. However, current regional summaries are not specific to the given age or pathology that is studied, which runs the risk of losing relevant information that can be critical in the classification process. To solve this issue, this paper proposes a novel data-driven approach by extending convolutional neural networks (CNN) for use on non-Euclidean manifolds such as cortical surfaces. The proposed network learns the most powerful features and brain regions from the extracted large dimensional feature space; thus creating a new feature space in which the dimensionality is reduced and feature distributions are better separated. We demonstrate the usability of the proposed surface-CNN framework in an example study classifying Alzheimers disease patients versus normal controls. The high performance in the cross-validation diagnostic results shows the potential of our proposed prediction system

Zoom invariant vision of figural shape: The mathematics of cores

Believing that figural zoom invariance and the cross-figural boundary linking implied by medial loci are important aspects of object shape, we present the mathematics of and algorithms for the extraction of medial loci directly from image intensities. The medial loci called cores are defined as generalized maxima in scale space of a form of medial information that is invariant to translation, rotation, and in particular, zoom. These loci are very insensitive to image disturbances, in strong contrast to previously available medial loci, as demonstrated in a companion paper. Core-related geometric properties and image object representations are laid out which, together with the aforementioned insensitivities, allow the core to be used effectively for a variety of image analysis objectives.

Post-operative pediatric cerebellar mutism syndrome and its association with hypertrophic olivary degeneration

Background: The dentato-thalamo-cortical (DTC) pathway is recognized as the anatomical substrate for postoperative pediatric cerebellar mutism (POPCMS), a well-recognized complication affecting up to 31% of children undergoing posterior fossa brain tumour resection. The proximal structures of the DTC pathway also form a segment of the Guillain and Mollaret triangle, a neural network which when disrupted causes hypertrophic olivary degeneration (HOD) of the inferior olivary nucleus (ION). We hypothesize that there is an association between the occurrence of POPCMS and HOD and aim to evaluate this on MR imaging using qualitative and quantitative analysis of the ION in children with and without POPCMS. Methods: In this retrospective study we qualitatively analysed the follow up MR imaging in 48 children who underwent posterior fossa tumour resection for presence of HOD. Quantitative analysis of the ION was possible in 28 children and was performed using semi-automated segmentation followed by feature extraction and feature selection techniques and relevance of the features to POPCMS were evaluated. The diagnosis of POPCMS was made independently based on clinical and nursing assessment notes. Results: There was significant association between POPCMS and bilateral HOD (P=0.002) but not unilateral HOD. Quantitative analysis showed that hyperintensity in the left ION was the most relevant feature in children with POPCMS. Conclusions: Bilateral HOD can serve as a reliable radiological indicator in establishing the diagnosis of POPCMS particularly in equivocal cases. The strong association of signal change due to HOD in the left ION suggests that injury to the right proximal efferent cerebellar pathway plays an important role in the causation of POPCMS. Keywords: Cerebellar mutism syndrome (CMS); hypertrophic olivary degeneration; posterior fossa syndrome (PFS); postoperative pediatric cerebellar mutism syndrom

Linking object boundaries at scale: a common mechanism for size and shape judgments

AbstractThe area over which boundary information contributes to the determination of the center of an extended object was inferred from results of a bisection task. The object to be bisected was a rectangle with two long sinusoidally modulated sides, i.e. a wiggly rectangle. The spatial frequency and amplitude of the edge modulation were varied. Two object widths were tested. The modulation of the perceived center approximately equaled that of the edges at very low edge modulation frequencies and decreased in amplitude with increasing edge modulation frequency. The edge modulation had a greater modulating effect on the perceived center for the narrower object than for the wider object. This scaling with object width didn't follow perfect zoom invariance but was precisely matched by the scaling of the bisection threshold with width, strongly supporting the idea that the same mechanism determines both the location of the perceived center for these stimuli and its variance. We propose that this mechanism is the linking of object boundaries at a scale determined by the object width

Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Let $-d$ be a a negative discriminant and let $T$ vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $-d$. We prove an asymptotic formula for $d \to \infty$ for the average over $T$ of the number of representations of $T$ by an integral positive definite quaternary quadratic form and obtain results on averages of Fourier coefficients of linear combinations of Siegel theta series. We also find an asymptotic bound from below on the number of binary forms of fixed discriminant $-d$ which are represented by a given quaternary form. In particular, we can show that for growing $d$ a positive proportion of the binary quadratic forms of discriminant $-d$ is represented by the given quaternary quadratic form.Comment: v5: Some typos correcte

Immunohistochemical Expression of Human Erythrocyte Glucose Transporter and Fatty Acid Synthase in Infiltrating Breast Carcinomas and Adjacent Typical/Atypical Hyperplastic or Normal Breast Tissue

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Skeletal Shape Correspondence Through Entropy

We present a novel approach for improving the shape statistics of medical image objects by generating correspondence of skeletal points. Each object's interior is modeled by an s-rep, i.e., by a sampled, folded, two-sided skeletal sheet with spoke vectors proceeding from the skeletal sheet to the boundary. The skeleton is divided into three parts: the up side, the down side, and the fold curve. The spokes on each part are treated separately and, using spoke interpolation, are shifted along that skeleton in each training sample so as to tighten the probability distribution on those spokes' geometric properties while sampling the object interior regularly. As with the surface/boundary-based correspondence method of Cates et al., entropy is used to measure both the probability distribution tightness and the sampling regularity, here of the spokes' geometric properties. Evaluation on synthetic and real world lateral ventricle and hippocampus data sets demonstrate improvement in the performance of statistics using the resulting probability distributions. This improvement is greater than that achieved by an entropy-based correspondence method on the boundary points

Analysis of Joint Shape Variation from Multi-Object Complexes

Shape correlation of multi-object complexes in the human body can have significant implications in understanding the development of disease. While there exist geometric and statistical methods that aim for multi-object shape analysis, very little research can effectively extract shape correlation. It is especially difficult to extract the correlation when the involved objects have different variability in separate non-Euclidean spaces. To address these difficulties, this paper proposes geometric and statistical methods to extract the shape correlation from multi-object complexes. In particular, we focus on the shape correlation of the hippocampus and the caudate subject to the development of autism. The proposed methods are designed (1) to capture objects’ shape features (2) to capture shape correlation regardless of different variability between the two objects and (3) to provide interpretable shape correlation in multi-object complexes. In our experiments on synthetic data and autism data, the quantitative results and the qualitative visualization suggest that our methods are effective and robust