内插是三维重建中的一个重要步骤.一般传统的插值算法大体可分为灰度插值和基于对象形状的插值两种.其中直接的灰度插值对二值及灰度图象均适用，但结果在多数情况下并不准确 ;而基于形状的插值，早期仅适用于二值图象.近来，人们将两者较好地结合起来，使得基于形状的插值同样适用于灰度图象.为了克服直接灰度插值易造成较严重的轮廓模糊问题及为克服 Chuang等人提出用基于形状的插值方法求得的对应点易产生偏差的问题，提出了一种新的基于形状的二维灰度图象插值算法.该算法首先采用数学形态学的方法分别对两幅源图象进行膨胀和腐蚀，用于确定插值图象的轮廓 ;然后对轮廓内的点，分别找出其在两幅源图象上的对应点，再通过灰度的线性插值来求得此点的灰度，进而得到最终的插值图象.实验结果表明，此算法得到的插值结果是令人满意的.

Typically,the image data we get are anisotropic, that is, the distance between adjacent image elements within a slice is different from the spacing between adjacent image elements in two neighboring slices. Interpolation is the key to convert such anisotropic data into isotropic one. The traditional interpolation methods include grey-level interpolation and shape-based interpolation. But both of them have their own shortcomings. Grey-level interpolation is easy to blur the object's boundary and shape-based interpolation is nearly limited to binary images only. In this paper, in order to solve these questions, we present a new way to interpolate grey-level images, which is based on the shape of these images. First, we use mathematical morphology to acquire the contour of the interpolated image. To each point in this contour, we find the corresponding points in both original images. According to the acquired grey value of the two corresponding points, we use linear interpolation to calculate the grey value of the interpolated point. Once we acquire each point's gray value, we obtain the final interpolated image. The experimental results show that the new method is effective.