title: A simple algorithm for medial axis transform computation

authors: Au, Chi Kit

subjects: medial axis

abstract: Although medial axis transform is introduced as a shape description for many engineering applications, the computational algorithm is still challenging. This is especially true for the shape with free form boundary. This paper presents an algorithm for medial axis transform computation from a perspective of minimum distance between the points in a two-dimensional shape and its boundary. The minimum distance is given by a resultant distance function which is a superposition of the individual distance function between a point within a shape and each boundary point. By elaborating the resultant distance function, the medial axis transform will be obtained naturally. The distance function is modeled as a solid cone and the superposition is equivalent to the union Boolean set operation. The implementation of the approach is simplified using a solid modeling kernel. Several examples of two-dimensional shapes with free form boundaries are raised to illustrate the concept and algorithm.

text: A simple algorithm for medial axis transform computation Although medial axis transform is introduced as a shape description for many engineering applications, the computational algorithm is still challenging. This is especially true for the shape with free form boundary. This paper presents an algorithm for medial axis transform computation from a perspective of minimum distance between the points in a two-dimensional shape and its boundary. The minimum distance is given by a resultant distance function which is a superposition of the individual distance function between a point within a shape and each boundary point. By elaborating the resultant distance function, the medial axis transform will be obtained naturally. The distance function is modeled as a solid cone and the superposition is equivalent to the union Boolean set operation. The implementation of the approach is simplified using a solid modeling kernel. Several examples of two-dimensional shapes with free form boundaries are raised to illustrate the concept and algorithm.

year: 2013

title: Supplemental Material for Enhancing Precision of the Telephone Interview for Cognitive Status–Modified (TICS-M) Using the Rasch Model

authors: Truong, Quoc Cuong

abstract: Rasch analysis begins with examining the overall data fit to the Rasch model as well as individual item fit. It also includes the evaluation of residual correlations across items because it possibly influences fit to the Rasch model. Firstly, the overall model fit requires the estimate of item-trait interaction to be not significant, which is reflected by chi square index (p > .05). Secondly, the fit residuals for individual items should be in the range between −2.50 and +2.50. Thirdly, the residual correlations between individual items should be examined because values above 0.20  indicate local dependency that can affect both individual items and the overall model fit (1). Finally, there should be no DIF due to relevant individual characteristics (i.e. personal factors) meaning that all items should be invariant across different groups (e.g. age, sex). In addition, PSI is used to evaluate reliability in Rasch analysis, which is not the Rasch model fit criteria but reflects how well the scale discriminates between individuals with different levels of the latent trait (e.g. SCC). PSI is interpreted somewhat similar to Cronbach's alpha with values above 0.70 indicating acceptable reliability for group assessments and 0.80 and higher for individual assessments (2).

text: Supplemental Material for Enhancing Precision of the Telephone Interview for Cognitive Status–Modified (TICS-M) Using the Rasch Model Rasch analysis begins with examining the overall data fit to the Rasch model as well as individual item fit. It also includes the evaluation of residual correlations across items because it possibly influences fit to the Rasch model. Firstly, the overall model fit requires the estimate of item-trait interaction to be not significant, which is reflected by chi square index (p > .05). Secondly, the fit residuals for individual items should be in the range between −2.50 and +2.50. Thirdly, the residual correlations between individual items should be examined because values above 0.20  indicate local dependency that can affect both individual items and the overall model fit (1). Finally, there should be no DIF due to relevant individual characteristics (i.e. personal factors) meaning that all items should be invariant across different groups (e.g. age, sex). In addition, PSI is used to evaluate reliability in Rasch analysis, which is not the Rasch model fit criteria but reflects how well the scale discriminates between individuals with different levels of the latent trait (e.g. SCC). PSI is interpreted somewhat similar to Cronbach's alpha with values above 0.70 indicating acceptable reliability for group assessments and 0.80 and higher for individual assessments (2).

year: 2023-05-25

title: Hoera Te Mimiha

authors: Hart, Philip

abstract: Hoera Te Mimiha was a rangatira of Ngati Koi, an inferior hapu to Ngati Tamatera, and had affiliations to other hapu. Although to Pakeha he was a mere labourer, in Maori society in Ohinemuri in the 1870s and 1880s he was a leading figure. Details have been traced of his whakapapa, his wider family, and especially his children, one of whom married Hone Werahiko. 
Mimiha spent much time in the Maori Land Court trying to prove his entitlement to be included as an owner of several blocks of land, not always successfully, for he could not prove some of his cases either through ancestry or occupation. Other rangatira with superior whakapapa were able to show the weaknesses of some of his claims, forcing him into giving evasive answers to cross-examination. His evidence did reveal what land he had occupied and farmed.
Mimiha willingly sold land, including his interest in the Ohinemuri goldfield (the boundaries of which he had pointed out to surveyors), and obtained a good income, for a time. Being interested in mining from the early 1870s onwards, he was one of the few Maori willing to descend a shaft at Thames, an experience that encouraged him to push for opening Ohinemuri to mining, even, it seemed, if that endangered Maori control of their land. Having prospected at Karangahake before it was opened to mining in 1875, he participated in this rush and subsequently in the Te Aroha one of 1880, having interests in claims at all three portions of the latter field. When his daughter’s partner was murdered at Te Aroha, he calmed Maori anger, once again winning the gratitude of Pakeha.
Because of selling much of his land, he struggled financially, although unlike some Maori he did not drink his money away. Cutting off part of the ear of a Pakeha accused of raping his wife resulted in several court cases marked by dubious evidence presented by both sides. After being imprisoned for perjury, efforts by Pakeha to have his conviction reviewed resulted in his being judged to have been the only witness not to have lied to the court, but this sordid affair blackened his character.

text: Hoera Te Mimiha Hoera Te Mimiha was a rangatira of Ngati Koi, an inferior hapu to Ngati Tamatera, and had affiliations to other hapu. Although to Pakeha he was a mere labourer, in Maori society in Ohinemuri in the 1870s and 1880s he was a leading figure. Details have been traced of his whakapapa, his wider family, and especially his children, one of whom married Hone Werahiko. 
Mimiha spent much time in the Maori Land Court trying to prove his entitlement to be included as an owner of several blocks of land, not always successfully, for he could not prove some of his cases either through ancestry or occupation. Other rangatira with superior whakapapa were able to show the weaknesses of some of his claims, forcing him into giving evasive answers to cross-examination. His evidence did reveal what land he had occupied and farmed.
Mimiha willingly sold land, including his interest in the Ohinemuri goldfield (the boundaries of which he had pointed out to surveyors), and obtained a good income, for a time. Being interested in mining from the early 1870s onwards, he was one of the few Maori willing to descend a shaft at Thames, an experience that encouraged him to push for opening Ohinemuri to mining, even, it seemed, if that endangered Maori control of their land. Having prospected at Karangahake before it was opened to mining in 1875, he participated in this rush and subsequently in the Te Aroha one of 1880, having interests in claims at all three portions of the latter field. When his daughter’s partner was murdered at Te Aroha, he calmed Maori anger, once again winning the gratitude of Pakeha.
Because of selling much of his land, he struggled financially, although unlike some Maori he did not drink his money away. Cutting off part of the ear of a Pakeha accused of raping his wife resulted in several court cases marked by dubious evidence presented by both sides. After being imprisoned for perjury, efforts by Pakeha to have his conviction reviewed resulted in his being judged to have been the only witness not to have lied to the court, but this sordid affair blackened his character.

year: 2016