nearest neighbor interpolation

bilinear interpolation

Contrary to what the name suggests, bilinear interpolation is not a linear operation because it involves multiplication of coordinates (which is not a linear operation).

bicubic interpolation 商业软件常用，可以退化为上面的bilinear interpolation。

 

 像素之间的一些基本关系

　　adjacency

　　　　8-adjacency包括了m-adjacency和4-adjacency，m-adjacency包括了4-adjacency。

　　　　m-adjacency和4-adjacency都是8-adjacency的子集。

　　　　符合m-adjacency的两个像素是8-adjacency里没有两条通路的那一部分。no ambiguity

Mixed adjacency is a modification of 8-adjacency, and is introduced to eliminate the ambiguities that may result from using 8-adjacency.

　　之所以要分清这个概念，我猜想是在处理的时候需要进行分区，那么是否邻接也需要明确的规则进行判断。

　　connectivity

Let S represent a subset of pixels in an image. Two pixels p and q are said to be
connected in S if there exists a path between them consisting entirely of pixels in S.
For any pixel p in S, the set of pixels that are connected to it in S is called a connected
component of S. If it only has one component, and that component is connected,
then S is called a connected set.

　　regions

Let R represent a subset of pixels in an image. We call R a region of the image if R is a connected set. Two regions, Ri and Rj are said to be adjacent if their union forms a connected set. Regions that are not adjacent are said to be disjoint. We consider 4-
and 8-adjacency when referring to regions. For our definition to make sense, the type of adjacency used must be specified.

　　boundaries

The boundary (also called the border or contour) of a region R is the set of pixels in R that are adjacent to pixels in the complement of R. Stated another way, the border of a region is the set of pixels in the region that have at least one background neighbor. Here again, we must specify the connectivity being used to define adjacency.

 

The preceding definition sometimes is referred to as the inner border of the region to distinguish it from its outer border, which is the corresponding border in the background. This distinction is important in the development of border-following algorithms. Such algorithms usually are formulated to follow the outer boundary in order to guarantee that the result will form a closed path.

If R happens to be an entire image, then its boundary (or border) is defined as the set of pixels in the first and last rows and columns of the image. This extra definition is required because an image has no neighbors beyond its border. Normally, when
we refer to a region, we are referring to a subset of an image, and any pixels in the boundary of the region that happen to coincide with the border of the image are
included implicitly as part of the region boundary

　　Distance measures

 

     

Euclidean distance

 

 

 

 

 Dm disitance 与pixel的intensity有关。