The equivariant method of moving frames provides a systematic, algorithmic procedure for determining and analyzing the structure of algebras of differential invariants for both finite-dimensional Lie groups and infinite-dimensional Lie pseudo-groups. This paper surveys recent developments, including a few surprises and several open questions.

The equivariant method of moving frames is used to specify systems of generating differential invariants for finite-dimensional Lie group actions.

A novel dual-frequency pattern is developed which combines a high-frequency sinusoid component with a unit-frequency sinusoid component, where the high-frequency component is used to generate robust phase information, and the unit-frequency component is used to reduce phase unwrapping ambiguities. With our proposed pattern scheme, phase unwrapping can overcome the major shortcomings of conventi...

New ideas were introduced in [3] to treat the problem of connectivity of Parseval frames. With these ideas it was shown that a large set of Parseval frames is arcwise connected. In this article we exhibit a larger class of Parseval frames for which the arcwise connectivity is true. This larger class fails to include all Parseval frames.

Spatial perspective can be directed by various reference frames, as well as by the direction of motion. In the present study, we explored how ambiguity in spatial tasks can be resolved. Participants were presented with virtual reality environments in order to stimulate a spatialreference frame based on motion. They interacted with an ego-moving spatial system in Experiment 1 and an object-movin...

In the present study, we examined how context of instruction and information in the visual array to be described affect spatial information packaging across a range of levels of spatial description. Participants described complex scenes containing 3-D dollhouse furniture across two different arrays (functional vs. nonfunctional arrangements of objects) and across instructional contexts (living ...

The interpretation of a dynamic visual scene requires integrating information within frames (grouping and completion) and across frames (correspondence matching). Fragmentary views of objects were used in five experiments. These views could not be matched with each other by any similarity transformation on the basis of their explicit visual features, but their completed versions were related by...

Remembering where objects are in space is fundamental to adaptive behavior. Little is known about how intact humans combine information from intrinsic (egocentric) and extrinsic (exocentric, allocentric, or landmark-based) coordinate systems to locate objects. Using a simple location estimation paradigm, this study finds that we mostly remember position in extrinsic coordinates. Intrinsic-coord...

Moving objects of interest (MOOIs) in surveillance videos are detected and encapsulated by bounding boxes. Since moving objects are defined by temporal activities through the consecutive video frames, it is necessary to examine a group of frames (GoF) to detect the moving objects. To do that, the traces of moving objects in the GoF are quantified by forming a spatiotemporal gradient map (STGM) ...

Previous studies have demonstrated large errors (over 30 degrees ) in visually perceived exocentric directions (the direction between two objects that are both displaced from the observer's location; e.g., Philbeck et al. [Philbeck, J. W., Sargent, J., Arthur, J. C., & Dopkins, S. (2008). Large manual pointing errors, but accurate verbal reports, for indications of target azimuth. Perception, 3...