Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Projective shape consists of the information in a configura- tion of points invariant under projective transformations. It is usually studied through projective invariants, the most familiar example being the cross ratio for four collinear points.  a standardized rep- resentation of the configuration is investigated which is better suited for quantitative comparisons beten different projective shapes. Kent and Mardia (1) gave a new approach to the study of projective shape through the use of "Tyler standardized" configurations.   shall give some further details about the implications of this standardization.  start with a review of the projective shape of k landmarks in R m ,m ≥ 1, and describe the relevance to machine vision. The classical approach to projective shape is through the use of projective invariants. Hover, the use of Tyler standardiza- tion is better suited for the construction of metrics to compare quantitatively different projective shapes. A detailed examination is given for the 1-dimensional case, m = 1, especially for k = 4 landmarks. Sections 1-3 are largely review; Section 4 is mainly new material. Start with a configuration X0(k × m )o fk points or landmarks in m dimen- sional space. The projective shape of X0 consists of the information in X0 that is invariant under projective transformations. The easiest way to deal with projec- tive transformations is to introduce homogeneous coordinates. Thus introduce an augmented matrix X = � X0 1 � , where 1 is a k-vector of ones. Then X is a k × p matrix, where throughout the paper  set p = m + 1.  can write X in terms of its rows and columns as
['John T. Kent']
I am writing a research paper on a idea Visualizing projective shape space
[{"from": "human", "value": "I am writing a research paper on a idea Visualizing projective shape space"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Projective shape consists of the information in a configura- tion of points invariant under projective transformations. It is usually studied through projective invariants, the most familiar example being the cross ratio for four collinear points.  a standardized rep- resentation of the configuration is investigated which is better suited for quantitative comparisons beten different projective shapes. Kent and Mardia (1) gave a new approach to the study of projective shape through the use of \"Tyler standardized\" configurations.   shall give some further details about the implications of this standardization.  start with a review of the projective shape of k landmarks in R m ,m \u2265 1, and describe the relevance to machine vision. The classical approach to projective shape is through the use of projective invariants. Hover, the use of Tyler standardiza- tion is better suited for the construction of metrics to compare quantitatively different projective shapes. A detailed examination is given for the 1-dimensional case, m = 1, especially for k = 4 landmarks. Sections 1-3 are largely review; Section 4 is mainly new material. Start with a configuration X0(k \u00d7 m )o fk points or landmarks in m dimen- sional space. The projective shape of X0 consists of the information in X0 that is invariant under projective transformations. The easiest way to deal with projec- tive transformations is to introduce homogeneous coordinates. Thus introduce an augmented matrix X = \ufffd X0 1 \ufffd , where 1 is a k-vector of ones. Then X is a k \u00d7 p matrix, where throughout the paper  set p = m + 1.  can write X in terms of its rows and columns as"}]