MTF曲面构造方法研究

调制传递函数（modulation transfer function, MTF）是定义在二维频率域空间的实函数,可用一个MTF空间曲面描述,是光学成像系统成像性能的一种重要的评价指标。由于成像系统的二维MTF曲面不能直接测量,需要先测量几个特定方向的一维 MTF曲线,再由曲面构造方法间接获得。对于同样的MTF曲线组,用不同方法构造出的MTF曲面各不相同,因此有必要研究MTF曲面构造方法的有效性。文章对现有构造 MTF 曲面的乘积法和插值法进行分析,提出一种新的旋转插补法,并使用（准）高斯函数和4次多项式函数作为二维MTF曲面的模拟标准,对上述3种方法的有效性和误差分布进行定量分析。实验结果显示,旋转插补法具有更好的适用性。     

The conventionality of pictorial representation in interstellar messages

Pictorial messages have previously been advocated for interstellar communication because such messages are presumed to be capable of presenting information in a non-arbitrary and easily intelligible manner. In contrast to this view, pictorial messages actually represent information in a partially conventional way. This point is demonstrated by examining pictorial representations of human beings from a range of cultures. While such representations may be understood quite readily by individuals familiar with the conventions of a particular culture, to the uninitiated outsider, such representations can be unintelligible. In spite of the partially arbitrary nature of pictorial representation, we may be able to construct messages that would teach extraterrestrial intelligence (ETI) some of the conventions by which we view pictures. One such approach is to pair numerical information about geometrical objects with pictorial representations of the same objects. Problems of conventionality can also be addressed in part through use of (1) multiple representations of the same object, (2) contextual cues, (3) three- and four-dimensional representations and (4) non-visual representations.     

A Neuro-Cognitive Theory of Deductive Relational Reasoning with Mental Models and Visual Images

Abstract

Many neuro-imaging studies have provided evidence that the parietal cortex plays a key role in reasoning based on mental models, which are supposed to be of abstract spatial nature. However, these studies have also shown concurrent activation in vision-related cortical areas which have often been interpreted as evidence for the role of visual mental imagery in reasoning. The aim of the paper is to resolve the inconsistencies in the previous literature on reasoning and imagery and to develop a neurally and cognitively plausible theory of human relational reasoning. The main assumption is that visual brain areas are only involved if the problem information is easy to visualize and when this information must be processed and maintained in visual working memory. A regular reasoning process, however, does not involve visual images but more abstract spatial representations—spatial mental models—held in parietal cortices. Only these spatial representations are crucial for the genuine reasoning processes.     

Spatial Thinking in Undergraduate Science Education

Spatial thinking is central to many scientific domains and professions spatial ability predicts success and participation in science. However spatial thinking is not is not emphasized in our educational system. This paper presents a selective review of four types of studies regarding spatial thinking in undergraduate science curricula; (1) correlational studies examining the relations between measures of spatial ability and performance in science disciplines, (2) studies that attempt to train aspects of spatial thinking, (3) studies of how students understand specific spatial representations in sciences (4) studies that use dynamic spatial representations to promote scientific understanding. For each type of study, the evidence is critically evaluated and conclusions are drawn about how to nurture spatial thinking in science.     

Combining Locations from Working Memory and Long-Term Memory into a Common Spatial Image

Abstract

This research uses a novel integration paradigm to investigate whether target locations read in from long-term memory (LTM) differ from perceptually encoded inputs in spatial working-memory (SWM) with respect to systematic spatial error and/or noise, and whether SWM can simultaneously encompass both of these sources. Our results provide evidence for a composite representation of space in SWM derived from both perception and LTM, albeit with a loss in spatial precision of locations retrieved from LTM. More generally, the data support the concept of a spatial image in working memory and extend its potential sources to representations retrieved from LTM.     

Spatial updating and common misinterpretations of spatial reference frames

Spatial memory plays an important role in everyday life, and a large amount of research has been devoted to understanding spatial coding and reference frames across many areas. The popular research paradigms to study spatial reference frames include novel shortcut, perspective change, and landmark control tests. However, the growing research on spatial updating challenges the logical foundation of these classical paradigms, and suggests that the experimental findings using these paradigms have usually been misinterpreted. That is, performance in these tasks is generally unrelated to whether the spatial representations themselves are egocentric or allocentric. This article reviews the traditional paradigms and their logic, summarizes the theories of spatial updating, analyzes the logical flaws in these popular paradigms, and discusses their implications.     

Young Children's Perception of Diagrammatic Representations

Diagrams and pictorial representations are common in children's lives and require abstraction away from visual perception. In three experiments, we investigated 4- to 8-year-olds’ comprehension of such representations. In Experiment 1 (N = 80), children were shown photographs of geometric objects and asked to choose the corresponding line drawing from among sets of four, or vice versa. Results showed considerable developmental progression, especially around age 6. Experiment 2 (N = 16) ruled out that 4-year-olds’ difficulties were due to problems with the visual matching task itself. Experiment 3 (N = 32) showed comparable performance for matching diagrams to 3D objects rather than to photographs. Findings suggest increasing understanding of diagrammatic representations around the time of school entry.     

Categorical Bias in Line Angle Judgments: Sex Differences and the Use of Multiple Categories

According to the Category Adjustment (CA) model, spatial estimates (e.g., of location) involve Bayesian combination across multiple, hierarchical pieces information, each weighted by its relative certainty. Recent work, though, has shown that men and women differ in terms of their certainty regarding fine-grained and categorical information in location memory. Here we demonstrate that this reflects a more general sex difference in visuospatial processing by examining bias patterns in a line angle judgment task (JLAP-15). In addition, the data suggest that multiple, hierarchical levels of categorical information influenced spatial judgments. These results imply that the hierarchical combination outlined by the CA model extends beyond two levels, and that men and women apply differential weighting to these representations.     

'Fine-to-Coarse' Route Planning and Navigation in Regionalized Environments

Environments that are divided into regions lead to hierarchical encoding of space. Such memory structures are known to systematically distort estimates of distance and direction and affect spatial priming and memory recall. Here we present two navigation experiments in virtual environments that reveal an influence of environmental regions on human route planning and navigation behaviour. Following the hierarchical theories of spatial representations, it is argued that environmental regions are explicitly represented in spatial memory and that human route planning takes into account region-connectivity and is not based on place-connectivity alone. We also propose a fine-to-coarse planning heuristic that could account for the empirical data by planning in a representation that uses fine-space information for close locations and coarse-space information for distant locations simultaneously.     

Heading south with a north-up map: A choice processing analysis of map alignment effects

This study employed an information accumulation model of choice reaction times to investigate alignment effects in mental representations of maps. University students studied a map from a single orientation (with north at the top). In a subsequent two-choice reaction time task, the students’ spatial knowledge of the map was assessed employing spatial left/right judgments, which were made from imagined perspectives that were either north-aligned or south-aligned. Data showed a standard alignment effect, favoring north- over south-aligned trials. To examine the locus of this effect, data were fit using the Linear Ballistic Accumulator (LBA) model of speeded decisions (Brown & Heathcote, 2008). Of interest were three model parameters: drift rate, the speed at which evidence accumulates toward a response; response threshold, the amount of evidence demanded from the decision maker before selecting a response; and non-decision time, the time consumed by pre- and postdecisional processes. The best-fitting model suggested that non-decision time accounted for the alignment effect. The difference in non-decision time between north and south-aligned judgments suggests a mental alignment stage on south-aligned trials, accounting for the longer reaction times for judgements misaligned with the presented north orientation of the map.     

The Psychological Validity of Qualitative Spatial Reasoning in One Dimension

One of the central questions of spatial reasoning research is whether the underlying processes are inherently visual, spatial, or logical. We applied the dual task interference paradigm to spatial reasoning problems in one dimension, using Allen's interval calculus, in order to make progress towards resolving this argument. Our results indicate that spatial reasoning with interval relations is largely based on the construction and inspection of qualitative spatial representations, or mental models, while no evidence for logical proofs of derivations or the involvement of visual representations and processes was found.     

Transformations and representations supporting spatial perspective taking

Spatial perspective taking is the ability to reason about spatial relations relative to another’s viewpoint. Here, we propose a mechanistic hypothesis that relates mental representations of one’s viewpoint to the transformations used for spatial perspective taking. We test this hypothesis using a novel behavioral paradigm that assays patterns of response time and variation in those patterns across people. The results support the hypothesis that people maintain a schematic representation of the space around their body, update that representation to take another’s perspective, and thereby to reason about the space around their body. This is a powerful computational mechanism that can support imitation, coordination of behavior, and observational learning.     

Gesture in Spatial Cognition: Expressing,Communicating, and Thinking About Spatial Information

Do hand gestures play a role in spatial cognition? This paper reviews literature addressing the roles of gestures in (1) expressing spatial information, (2) communicating about spatial information, and (3) thinking about spatial information. Speakers tend to produce gestures when they produce linguistic units that contain spatial information, and they gesture more when talking about spatial topics than when talking about abstract or verbal ones. Thus, gestures are commonly used to express spatial information. Speakers use gestures more in situations when those gestures could contribute to communication, suggesting that they intend those gestures to communicate. Further, gestures influence addressees' comprehension of the speech they accompany, and addressees also detect information that is conveyed uniquely in gestures. Thus, gestures contribute to effective communication of spatial information. Gestures also play multiple roles in thinking about spatial information. There is evidence that gestures activate lexical and spatial representations, promote a focus on spatial information, and facilitate the packaging of spatial information in speech. Finally, some of the observed variation across tasks in gesture production is associated with task differences in demands on spatial cognitive processes, and individual differences in gesture production are associated with individual differences in spatial and verbal abilities. In sum, gestures appear to play multiple roles in spatial cognition. Central challenges for future research include: (1) better specification of the mental representations that give rise to gestures, (2) deeper understanding of the mechanisms by which gestures play a role in spatial thinking, and (3) greater knowledge of the sources of task and individual differences in gesture production.     

Virtual to Real Transfer of Spatial Learning in a Complex Environment: The Role of Path Network and Additional Features

The effects of the amount and type of spatial information on the orientation accuracy and metric properties of mental representations of a large-scale built environment were evaluated in a virtual-real transfer study. Four groups of participants explored different virtual versions of a campus before being tested in the real environment. Learning with or without additional features and with or without a network of pathways led to different patterns of data. Although direction measures and straight-line and route distance estimates were least accurate in the absence of either type of information, the combination of both types of information did not produce more accurate knowledge than either did alone. In particular, the presence of additional features had a facilitating effect only on the direction estimates. The results highlight the respective importance of amount and type of spatial information in the acquisition and use of mental spatial representations.     

Expert Algorithmic and Imagistic Problem Solving Strategies in Advanced Chemistry

Abstract

Visualization and imagistic reasoning appear central to expert practice in science; however, expert use of these strategies on authentic tasks has not been examined in detail. This study documents how science experts use both algorithms and imagistic reasoning to solve problems. Using protocol analysis, we report expert chemists' preferential use of algorithms for solving spatial problems and imagistic reasoning for deducing spatial transformations. We observed experts employ algorithms to solve the majority of spatial tasks while reserving imagistic strategies to solve a class of tasks that required translating between representations. Strategy used varied widely among experts and tasks.     

SketchMapia: Qualitative Representations for the Alignment of Sketch and Metric Maps

More and more private citizens collect and publish environmental data via web-based geographic information systems. These systems face two challenges: The user interface must be intuitive and the processing of geographic information must account for cognitive impact. We propose to use sketch maps as the medium for interaction, because they reflect a person's spatial knowledge. Information from sketch maps is distorted, schematized, incomplete, and generalized and metric maps are not. This article employs qualitative representations for the alignment of sketch and metric maps. We suggest a set of cognitively oriented aspects in sketch maps stably computed by people and evaluate qualitative representations to formalize these aspects. This allows us to align and integrate geographic information from sketch maps.     

Reasoning about Depth and Motion from an Observer's Viewpoint

ABSTRACT

The goal of this paper is to present a logic-based formalism for representing knowledge about objects in space and their movements, and show how this knowledge could be built up from the viewpoint of an observer immersed in a dynamic world. In this paper space is represented using functions that extract attributes of depth, size and distance from snapshots of the world. These attributes compose a novel spatial reasoning system named Depth Profile Calculus (DPC). Transitions between qualitative relations involving these attributes are represented by an extension of this calculus called Dynamic Depth Profile Calculus (DDPC). We argue that knowledge about objects in the world could be built up via a process of abduction on DDPC relations.