中文摘要：

认知地图是外界环境在人们头脑中的表征，往往与现实地图不一致，研究认知地图及其变形对城市规划和建设具有重要意义。手绘草图是当前挖掘认知地图的一种主要方法。通过问卷调查，获得北京居民手绘草图样本，分析草图中体现的北京城市意象要素。采用二维回归（BR）与标准偏差椭圆方法定量测度认知地图整体和局部的变形。对于二维回归计算出的变形系数（DI）进一步采用蒙特卡罗模拟计算其变形半径，得出北京居民的认知地图平均变形在2.3km，整体变形以二环为界，内小外大，并呈西南一东北斜向拉伸，东西收缩的趋势，局部变形北部大于南部。个体的变形系数与对地标的熟悉程度负相关，男性小于女性，驾车者小于不驾车者，日常活动范围越广、出行频率越高、居住时间越久、距离锚点越近的被试认知蛮形微小。

英文摘要：

Cognitive map, an internal representation of outside environment, is usually inconsistent with the real map. Cognitive map and its distortions are very significant for urban planning and construction. To date, sketch mapping is a dominant method to externalize cognitive map. In this study, we conduct a questionnaire investigation in Beijing by radom sampling of people to draw a sketch of Beijing city, then analyze major public imaginary of the city. By a bidimensional regression （BR） along with Standard Deviational Ellipse, we quantitatively measure the global and local map distortions, and derive distortion index （DI）. Besides, we use Monte Carlo simulation to calculate the radius of the distortion based on DI. It shows that the average cognitive distortion of Beijing residents is 2 km to 3 km, the global distortion is elongated in the southwest-northeast direction and contracted in the east-west direction, and the northern local distortions are more obvious than the southern ones. Individual DI is negatively correlated with the extent of the familiarity of all landmarks; and remarkably correlated with other factors, such as gender, driving or not, the scope of activity, daily travel frequency, years of residence, and distance to anchor point.