As a popular research direction in computer vision

the development of local invariant feature algorithms has become more and more mature and stable. But now

almost all the feature point extraction algorithms cannot give the accuracy index of feature points. In fact

the precision of feature points'position is requested in many areas

such as device calibration and visual inspection. To solve this problem

this paper proposed a feature point precision index-feature point's range. Since there are always disturbances in the process of acquiring images

it is difficult to obtain absolutely perfect images and feature points. This paper defines the feature point's range as the range of a feature point's fluctuation in different conditions which is stable in different disturbances. This paper choses the most popular algorithms of local invariant feature named SIFT(Scale-invariant feature transform)as an example. To make the result more intuitive and clear

the experiment selects those pictures whose backgrounds are simple and objectives are clear. This paper analyses the fluctuation of feature points in noise conditions

fuzzy conditions

light transform conditions and all those disturbances which are the common interferences in actual operations to achieve the fluctuation range of different feature points. First

this paper establishes the experimental galleries. We make not only a noise gallery

light treatment gallery and fuzzy diagram gallery but also a gallery which contains the three disturbances. It is worth noting that considering the randomness of noise

we generate 100 pictures for one noise intensity. Secondly

the stable feature points which can be detected in all disturbances are found by matching. We get 16 points in this experiment which has its own point cloud. Once more

because different points fluctuate differently in different situations

we use a circle to fit every point's fluctuation in different conditions. It means we use a circle to fit every point's cloud. The radius of those circles can characterize those feature points' ranges. Last but not least

this paper uses histograms which is very intuitive to describe every point's fluctuation. In addition

those points' coordinates are provided. In this experiment we gain 16 stable points. This experiment shows that the fluctuation ranges of different feature points are different

but there are still a part of feature points whose precisions are higher. The points whose fluctuations are smaller in the case of the presence of interference can be considered as better and more accurate points. Selection of feature points is based on the following work. If the requirement of precision is higher

a lower threshold should be designated. Therefore

fluctuation range can characterize the precision of different points very well. This can underpin the related work. Although this paper choses SIFT feature point as an example

other local invariant feature points' have similar properties. This paper provides an idea and method to study feature points' properties to be helpful to the related work.