TAILIEUCHUNG - Field and Service Robotics - Corke P. and Sukkarieh S.(Eds) Part 3

Tham khảo tài liệu 'field and service robotics - corke p. and sukkarieh s.(eds) part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Distinctness Analysis on Natural Landmark Descriptors 71 This involves calculating the probability of similarity between two selected landmarks from different images. Each landmark is extracted and converted into a feature descriptor . a p-dimensional vector which is subject to sources of randomness. Firstly there is random noise from the sensors. Secondly the descriptor expression is itself a simplified representation of the landmark. Lastly the two images being compared could be viewing the landmark from a different perspective which causes geometric distortion. Therefore each landmark can be considered as a single sample of the observing object. In making inferences from two landmarks in two different images it is in principle a standard significance test. However comparison is only made between two single samples. For this reason the ANOVA test The Analysis of Variance cannot be used because the sample size required should be large. For multidimensional vector comparison the X2 Chi-Squared distribution test is appropriate. Chi-Squared distribution is a combined distribution of all dimensions which are assumed to be normally distributed. It includes an additional variable v describing the degrees of freedom. Details can be found in 13 . In multidimensional space the Xv variable is defined by x2 N x - y ir-1 x - y 7 where x and y are the mean of the measurements of X and Y respectively s is the covariance matrix of noise N is a function related to the sample size of the two measurements. Since our sample size is one then N 1 x x and y y. Equation 7 simplifies to X x - y iX-1 x - y 8 If the noise of each dimension is independent of the other the inverse covariance is a diagonal matrix and hence can be further simplified to X2 Ỷ 2 9 i 1 i where p is the number of dimensions of x. Since x contains p independent dimensions then the degree of freedom v is p not p - 1 as usually defined for the categorical statistic. Also ơị ự2ơ where Ơ is the standard deviation for

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