International Workshop on Computer Vision Computer Vision at IPM Mehrdad Shahshahani Institute for Studies in Theoretical Physics and Mathematics International Workshop on Computer Vision April 26-30, Tehran,Iran
Computer Vision Group Masoud Alipour Somayeh Danafar Ali Farhadi Hanif Mohammadi Nima Razavi Azad Shadman Lila Taghavi Ali-Reza Tavakoli
Scope of Effort Limited to the Analysis of A Single Image Object Differentiation Segmentation Conspicuously Absent: Use of a Data Bank
Methodologies Emphasis on Experimental Methods Statistical Analysis Higher Order Statistics SVD Transforms Application of Methods of Computational Geometry Memory/Priors
Variation of Correlations (cont.)
Variation of Correlations (cont.)
Variation of Correlations (cont.)
Rough Classification of Images
Rough Classification of Images (cont.)
Detection
Detection (cont.)
Detection (cont.) General Conclusion Analysis of local correlations in a single image allows the detection of an extraneous object in a texture environment.
Segmentation Application of analysis of correlations to segmentation of images Requires more elaborate analysis Roughly Speaking, two step process: 1. Identification of regions (windows) containing object. 2. Determination of the boundary of the object.
Segmentation (cont.)
Segmentation (cont.)
Segmentation (cont.)
Segmentation (cont.) General Conclusion By analysis of local correlations segmentation can be achieved on the basis of local structure of textures. Not necessary to make use of memory. Analysis is based on a single image. Complexity of algorithm is O(N).
A Test Case How can one tell the difference between a cat and a dog? The question can be viewed from a neurophysiologic or image processing point of view. Can measures of statistical variability be used in distinguishing between dogs and cats?
LPC Surfaces One canonically constructs a surface (LPC surface) from the analysis of local correlations of an image.
LPC Surfaces (cont.)
LPC Surfaces (cont.)
LPC Surfaces (cont.) LPC surfaces are highly non-differentiable. Discrete geometry of LPC surfaces. Curvature of a triangulated surface.
Triangulation of a Surface
Curvature of a triangulation Curvature at a vertex v is 6 – number of edges incident on v General Conclusion: Count the number of triangles to obtain measure of statistical variability of the surface.
Counting triangles
Counting Triangles Statistical Variability of textures of cats and dogs reflected in discrete curvature LPC surfaces. It can be achieved more simply by a judicious method for counting triangles per unit area. Can tell the difference between a REAL dog and a REAL cat!
Singular Value Decomposition SVD decomposition of sliding windows S=UDV Diagonal entries positive and in decreasing order. Do the diagonal matrices D contain significant information about structural content of an image?
SVD (continued)
SVD (continued)
SVD (continued)
SVD (continued)
SVD Transforms From Diagonal entries of SVD decomposition of sliding windows on an image we construct the SVD transform or SVD surface.
SVD Transform (cont.)
SVD Transform
Application of SVD Transforms 1. Detection of objects in a texture background. 2. Detection of fractures or defects. 3. Segmentation of Images. 4. Determination of location of eyes.
Detection
Detection (continued)
Detection (continued)
Detection of Fractures
Segmentation
Segmentation (continued)
Effect of change in lighting and blurring on segmentation
Segmentation (continued)
Segmentation (continued)
Segmentation (continued) Conclusion: Segmentation via SVD transforms isolates objects on the basis of their local texture structures. Is not sensitive to changes in lighting, orientation, or similar distortions.
Locating the Eyes = - SVD Transform Edge detection with noise removal
Robust
Analysis of SVD Understanding the meaning and implications of the SVD decomposition Substituting the diagonal part D from one image into another.
Analysis of SVD (cont.) ws=4 D woman in U,V Lena
Analysis of SVD (cont.) ws=4 D Lena in U,V woman
Analysis of SVD (cont.) ws=32 D Lena in U,V woman
Analysis of SVD ws=4 D Lena in U,V random
Analysis of SVD (cont.) ws=32 D random in U,V Lena
Conclusion Diagonal SVD contains significant information. Relative importance of D relative to U,V decreases as window size increases. U, V contain information about correlational structure of image. For small window sizes U and V behave like high frequencies.
Other Research 1. Eye/Iris Printing 2. Shape Matching 3. Robotic Motion