Isometry Invariant Shape Recognition of Projectively Perturbed Point Clouds by the Mergegram Extending 0D Persistence

Rigid shapes should be naturally compared up to rigid motion or isometry, which preserves all inter-point distances. The same rigid shape can be often represented by noisy point clouds of different sizes. Hence, the isometry shape recognition problem requires methods that are independent of a cloud size. This paper studies stable-under-noise isometry invariants for the recognition problem stated in the harder form when given clouds can be related by affine or projective transformations. The first contribution is the stability proof for the invariant mergegram, which completely determines a single-linkage dendrogram in general position. The second contribution is the experimental demonstration that the mergegram outperforms other invariants in recognizing isometry classes of point clouds extracted from perturbed shapes in images.

Robust Affine Invariant Shape Descriptors

With the increasing number of available digital images, there is an urgent need of image content description to facilitate content based image retrieval (CBIR). Besides colour and texture, shape is an important low level feature in describing image content. An object can be photographed from different distances and angles. However, we often want to classify the images of the same object into one class, despite the change of perspective. So, it is desired to extract shape features that are invariant to the change of perspective. The shape of an object from one viewpoint to another can be linked through an affine transformation, if it is viewed from a much larger distance than its size along the line of sight. Those invariant shape features are known as affine invariant shape representations. Because of the change of perspective, it is more difficult to develop affine invariant shape representations than normal ones. The goal of this work is to develop affine invariant shape descriptors. Through shape retrieval experiments, we find that the performance of the existing affine invariant shape representations are not satisfactory. Especially, when the shape boundary is corrupted by noise, their performance degrades quickly. In this work, two new affine invariant contour-based shape descriptors, the ICA Fourier shape descriptor (ICAFSD) and the whitening Fourier shape descriptor (WFSD) have been developed. They perform better than most of the existing affine invariant shape representations, while having compact feature size and low computational time requirement. Four region-based affine-invariant shape descriptors, the ICA Zernike moment shape descriptor (ICAZMSD), the whitening Zernike moment shape descriptor (WZMSD), the ICA orthogonal Fourier Mellin moment shape descriptor (ICAOFMMSD), and the whitening orthogonal Fourier Mellin moment shape descriptor (WOFMMSD), are also proposed, in this work. They can be applied to both simple and complex shapes, and have close to perfect performance in retrieval experiments. The advantage of those newly proposed shape descriptors is even more apparent in experiments on shapes with added boundary noise: Their performance does not deteriorate as much as the existing ones.

Robust Affine Invariant Shape Descriptors

With the increasing number of available digital images, there is an urgent need of image content description to facilitate content based image retrieval (CBIR). Besides colour and texture, shape is an important low level feature in describing image content. An object can be photographed from different distances and angles. However, we often want to classify the images of the same object into one class, despite the change of perspective. So, it is desired to extract shape features that are invariant to the change of perspective. The shape of an object from one viewpoint to another can be linked through an affine transformation, if it is viewed from a much larger distance than its size along the line of sight. Those invariant shape features are known as affine invariant shape representations. Because of the change of perspective, it is more difficult to develop affine invariant shape representations than normal ones. The goal of this work is to develop affine invariant shape descriptors. Through shape retrieval experiments, we find that the performance of the existing affine invariant shape representations are not satisfactory. Especially, when the shape boundary is corrupted by noise, their performance degrades quickly. In this work, two new affine invariant contour-based shape descriptors, the ICA Fourier shape descriptor (ICAFSD) and the whitening Fourier shape descriptor (WFSD) have been developed. They perform better than most of the existing affine invariant shape representations, while having compact feature size and low computational time requirement. Four region-based affine-invariant shape descriptors, the ICA Zernike moment shape descriptor (ICAZMSD), the whitening Zernike moment shape descriptor (WZMSD), the ICA orthogonal Fourier Mellin moment shape descriptor (ICAOFMMSD), and the whitening orthogonal Fourier Mellin moment shape descriptor (WOFMMSD), are also proposed, in this work. They can be applied to both simple and complex shapes, and have close to perfect performance in retrieval experiments. The advantage of those newly proposed shape descriptors is even more apparent in experiments on shapes with added boundary noise: Their performance does not deteriorate as much as the existing ones.

Fast and adaptive protein structure representations for machine learning

The growing prevalence and popularity of protein structure data, both experimental and computationally modelled, necessitates fast tools and algorithms to enable exploratory and interpretable structure-based machine learning. Alignment-free approaches have been developed for divergent proteins, but proteins sharing functional and structural similarity are often better understood via structural alignment, which has typically been too computationally expensive for larger datasets. Here, we introduce the concept of rotation-invariant shape-mers to multiple structure alignment, creating a structure aligner that scales well with the number of proteins and allows for aligning over a thousand structures in 20 minutes. We demonstrate how alignment-free shape-mer counts and aligned structural features, when used in machine learning tasks, can adapt to different levels of functional hierarchy in protein kinases, pinpointing residues and structural fragments that play a role in catalytic activity.

Deep Predictive Learning in Neocortex and Pulvinar

How do humans learn from raw sensory experience? Throughout life, but most obviously in infancy, we learn without explicit instruction. We propose a detailed biological mechanism for the widely embraced idea that learning is driven by the differences between predictions and actual outcomes (i.e., predictive error-driven learning). Specifically, numerous weak projections into the pulvinar nucleus of the thalamus generate top–down predictions, and sparse driver inputs from lower areas supply the actual outcome, originating in Layer 5 intrinsic bursting neurons. Thus, the outcome representation is only briefly activated, roughly every 100 msec (i.e., 10 Hz, alpha), resulting in a temporal difference error signal, which drives local synaptic changes throughout the neocortex. This results in a biologically plausible form of error backpropagation learning. We implemented these mechanisms in a large-scale model of the visual system and found that the simulated inferotemporal pathway learns to systematically categorize 3-D objects according to invariant shape properties, based solely on predictive learning from raw visual inputs. These categories match human judgments on the same stimuli and are consistent with neural representations in inferotemporal cortex in primates.

Blur-readable two-dimensional barcode based on blur-invariant shape and geometric features

In recent years, the application of two-dimensional (2D) barcode is more and more extensive and has been used as landmarks for robots to detect and peruse the information. However, it is hard to obtain a sharp 2D barcode image because of the moving robot, and the common solution is to deblur the blurry image before decoding the barcode. Image deblurring is an ill-posed problem, where ringing artifacts are commonly presented in the deblurred image, which causes the increase of decoding time and the limited improvement of decoding accuracy. In this article, a novel approach is proposed using blur-invariant shape and geometric features to make a blur-readable (BR) 2D barcode, which can be directly decoded even when seriously blurred. The finder patterns of BR code consist of two concentric rings and five disjoint disks, whose centroids form two triangles. The outer edges of the concentric rings can be regarded as blur-invariant shapes, which enable BR code to be quickly located even in a blurred image. The inner angles of the triangle are of blur-invariant geometric features, which can be used to store the format information of BR code. When suffering from severe defocus blur, the BR code can not only reduce the decoding time by skipping the deblurring process but also improve the decoding accuracy. With the defocus blur described by circular disk point-spread function, simulation results verify the performance of blur-invariant shape and the performance of BR code under blurred image situation.