Tracking Objects as Points

Tracking has traditionally been the art of following interest points through space and time. This changed with the rise of powerful deep networks. Nowadays, tracking is dominated by pipelines that perform object detection followed by temporal association, also known as tracking-by-detection. In this paper, we present a simultaneous detection and tracking algorithm that is simpler, faster, and more accurate than the state of the art. Our tracker, CenterTrack, applies a detection model to a pair of images and detections from the prior frame. Given this minimal input, CenterTrack localizes objects and predicts their associations with the previous frame. That's it. CenterTrack is simple, online (no peeking into the future), and real-time. It achieves 67.3% MOTA on the MOT17 challenge at 22 FPS and 89.4% MOTA on the KITTI tracking benchmark at 15 FPS, setting a new state of the art on both datasets. CenterTrack is easily extended to monocular 3D tracking by regressing additional 3D attributes. Using monocular video input, it achieves 28.3% [email protected] on the newly released nuScenes 3D tracking benchmark, substantially outperforming the monocular baseline on this benchmark while running at 28 FPS.Comment: ECCV 2020 Camera-ready version. Updated track rebirth results. Code available at https://github.com/xingyizhou/CenterTrac

Topological correction of hypertextured implicit surfaces for ray casting

Hypertextures are a useful modelling tool in that they can add three-dimensional detail to the surface of otherwise smooth objects. Hypertextures can be rendered as implicit surfaces, resulting in objects with a complex but well defined boundary. However, representing a hypertexture as an implicit surface often results in many small parts being detached from the main surface, turning an object into a disconnected set. Depending on the context, this can detract from the realism in a scene where one usually does not expect a solid object to have clouds of smaller objects floating around it. We present a topology correction technique, integrated in a ray casting algorithm for hypertextured implicit surfaces, that detects and removes all the surface components that have become disconnected from the main surface. Our method works with implicit surfaces that are C2 continuous and uses Morse theory to find the critical points of the surface. The method follows the separatrix lines joining the critical points to isolate disconnected components

The Topology of Probability Distributions on Manifolds

Let $P$ be a set of $n$ random points in $R^d$, generated from a probability measure on a $m$-dimensional manifold $M \subset R^d$. In this paper we study the homology of $U(P,r)$ -- the union of $d$-dimensional balls of radius $r$ around $P$, as $n \to \infty$, and $r \to 0$. In addition we study the critical points of $d_P$ -- the distance function from the set $P$. These two objects are known to be related via Morse theory. We present limit theorems for the Betti numbers of $U(P,r)$, as well as for number of critical points of index $k$ for $d_P$. Depending on how fast $r$ decays to zero as $n$ grows, these two objects exhibit different types of limiting behavior. In one particular case ($n r^m > C \log n$), we show that the Betti numbers of $U(P,r)$ perfectly recover the Betti numbers of the original manifold $M$, a result which is of significant interest in topological manifold learning

A novel approach to recognition of the detected moving objects in non-stationary background using heuristics and colour measurements : a thesis presented in partial fulfilment of the requirement for the degree of Master of Engineering at Massey University, Albany, New Zealand

Computer vision has become a growing area of research which involves two fundamental steps, object detection and object recognition. These two steps have been implemented in real world scenarios such as video surveillance systems, traffic cameras for counting cars, or more explicit detection such as detecting faces and recognizing facial expressions. Humans have a vision system that provides sophisticated ways to detect and recognize objects. Colour detection, depth of view and our past experience helps us determine the class of objects with respect to object’s size, shape and the context of the environment. Detection of moving objects on a non-stationary background and recognizing the class of these detected objects, are tasks that have been approached in many different ways. However, the accuracy and efficiency of current methods for object detection are still quite low, due to high computation time and memory intensive approaches. Similarly, object recognition has been approached in many ways but lacks the perceptive methodology to recognise objects. This thesis presents an improved algorithm for detection of moving objects on a non-stationary background. It also proposes a new method for object recognition. Detection of moving objects is initiated by detecting SURF features to identify unique keypoints in the first frame. These keypoints are then searched through individually in another frame using cross correlation, resulting in a process called optical flow. Rejection of outliers is performed by using keypoints to compute global shift of pixels due to camera motion, which helps isolate the points that belong to the moving objects. These points are grouped into clusters using the proposed improved clustering algorithm. The clustering function is capable of adapting to the search radius around a feature point by taking the average Euclidean distance between all the feature points into account. The detected object is then processed through colour measurement and heuristics. Heuristics provide context of the surroundings to recognize the class of the object based upon the object’s size, shape and the environment it is in. This gives object recognition a perceptive approach. Results from the proposed method have shown successful detection of moving objects in various scenes with dynamic backgrounds achieving an efficiency for object detection of over 95% for both indoor and outdoor scenes. The average processing time was computed to be around 16.5 seconds which includes the time taken to detect objects, as well as recognize them. On the other hand, Heuristic and colour based object recognition methodology achieved an efficiency of over 97%

Cyclonic spectra, cyclotomic spectra, and a conjecture of Kaledin

With an explicit, algebraic indexing $(2,1)$-category, we develop an efficient homotopy theory of cyclonic objects: circle-equivariant objects relative to the family of finite subgroups. We construct an $\infty$-category of cyclotomic spectra as the homotopy fixed points of an action of the multiplicative monoid of the natural numbers on the category of cyclonic spectra. Finally, we elucidate and prove a conjecture of Kaledin on cyclotomic complexes.Comment: 28 pages. Comments very welcom