Course 9 Texture
Definition: Texture is repeating patterns of local variations in image intensity, which is too fine to be distinguished. Texture evokes the image of large number of structural primitive of (statistically) identical shape and size placed (statistically) uniformly. To perceive a homogeneous texture, What features should be homogeneous? What features are unimportant?
The answer may lie in what signifies the constant of changing scene geometry. The texture image includes two homogeneous regions
The answer may lie in what signifies the constant of changing scene geometry. The texture image includes two homogeneous regions
1. Gray-level co-occurrence Matrix Characterized to capture spatial dependence of image gray- level value, which contribute to the perception of texture. Gray-level co-occurrence matrix P is defined by first specifying a displacement vector, and counting all pairs of pixels separated by having gray level values i and j. Specifically, for a given image of size and with L gray levels. For a defined displacement vector
a) Systemically scan image from top to the row of,from left-most to the column of For, count the number of occurrence, say being. b) Set matrix element c) Repeat operations b) and c) until all combinations of i and j are completed. d) Normalize matrix P by.
For example: Note: for the same image with different displacement vector, it will yield different gray-level co-occurrence matrix, which characterizes the texture homogeneity of different special distribution and orientations.
From co-occurrence matrix, some useful measurements can be derived. Energy : Contrast: Homogeneity: Entropy :
2. Structural analysis of texture Assumptions: － Texture is ordered. － Texture primitives are large enough. － Texture primitives can be separated.
After primitive regions are identified, homogeneity properties can be measured. － Centroid distances of different directions. － Size. － Elongation. － Orientation. Then, co-occurrence based measurements of the primitives are used to characterize the texture.
3. Model-based Texture Analysis Concept: － Establish an analytical model of the given textured image. － Then, analysis the model. Difficulty: too many parameters in the model to be determined. Example: Gauss-Markove random field model: where: is weight, is an additive noise.
In this model, any pixel is modeled as a linear combination of gray level of its neighbors to pixel. The parameters are the weight, which can be estimated by least-square from the given textured image. 4. Shape From Texture － Recover 3D information from 2D image clues. － Image clues: variations of size, shape, and density of texture primitives. － Yield: surface shape and orientation.
An simple example for analysis Assumptions: 1)3D surface is slanted with angel. 2)Till angel being zero, i.e. points along horizontal line on the surface have the same depth from the camera. 3)Texture primitive is disk. 4)Perspective projection imaging model.
Observations from image: 1)3D disks appear to be ellipses in image plane. 2)The size of ellipses decrease as a function of, the y- coordinate of image plane, causing “density gradients”. 3)The ratio of minor to major diameters of ellipses does not remain constant along -axis. Def. aspect ratio =
At image center: let the diameter of 3D disk be d, then Thus, aspect ration is
At point of So, Thus,
(AC parallel to image plane) (Assume ) Thus, aspect ration =
Note : is known from image plane, the 3D surface orientation can be computed from aspect ratio.
5. Surface Orientation from statistic Texture Assumptions: 1) 3D texture primitives are small line segments, called needles. 2) Needles are distributed uniformly on 3D surface, their directions are independent. 3) Surface is approximately planar. 4) Orthographic image projection Given: image of N needles with needle angle from x-axis. Find: surface orientation
Method (omitting detail deriving): For a give image needle direction, define an auxiliary vector The average of the vector is: From orthographic projection
Thus, one can solve for: where