Read e-book online A Probabilistic Framework for Point-Based Shape Modeling in PDF

By Heike Hufnagel

ISBN-10: 3834817228

ISBN-13: 9783834817228

Heike Hufnagel develops a mathematically sound statistical form version. as a result specific attributes of the version, the demanding integration of particular and implicit representations should be played in a sublime mathematical formula, hence combining the benefits of either specific version and implicit segmentation process.

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Extra resources for A Probabilistic Framework for Point-Based Shape Modeling in Medical Image Analysis (Medizintechnik)

Example text

25 ? 20 mj ? 35 mj ?

Mij = CP (si , M ) Û Ö mij × Ø ÐÓ× ×Ø ÔÓ ÒØ Ò M ØÓ × ÓÐÐÓÛ× Ì Á È Ð ÓÖ Ø Ñ ÓÑÔÙØ Ò T × ÑÔÐ Ñ ÒØ ½º T (0) = T k × Ó× Ò × Ò Ø Ð ×Ø Ñ Ø Ó Ø Ú Ò × Ò ÔÓ ÒØ si º ØÖ Ò× ÓÖÑ Ø ÓÒ T º ¾º Ê Ô Ø ÓÖ k Ø Ö Ø ÓÒ× ÓÖ ÙÒØ Ð ÓÒÚ Ö Ò • ÐÓ× ×Ø ÔÓ ÒØ mij ∈ M Ò Ø ÑÓ Ð ÓÖ Ó × ÖÚ Ø ÓÒ ÔÓ ÒØ ÓÐÐ Ø ÓÒ Ó Ö ×ÙÐØ Ò ÔÓ ÒØ Ô Ö× (si , mij ) × ÐÐ × Ø Ó ÓÖÖ ¹ ×ÔÓÒ Ò × C Û Ø ÓÑÔÙØ Ø si ∈ S º Ì k−1 s Ck−1 = ∪N si , M )}. i=1 {si , CP (T • ÓÖ Ö ÓÑÔÙØ T k Ø Ò Cº Ö ×ØÖ Ø ÓÒ¸ Ø Ø ÑÒÑÞ × Ø ÖÖÓÖ Ø ÓÒ Ó T ØÓ S ÐÓÓ × Ð ÔÔÐ T Ñ Ò ×ÕÙ Ö si = Rsi + t ØÛ Ò ÐÐ ÔÓ ÒØ Ô Ö× Ø × ∀i Û Ø Ø ÖÓØ Ø ÓÒ Ñ ØÖ Ü R ∈ R3x3 Ò Ø ØÖ Ò×Ð Ø ÓÒ Ú ØÓÖ t ∈ R3 º Ì Ñ Ò Ñ Þ Ø ÓÒ Ó Ø ÖÖÓÖ ØÛ Ò ÐÐ ÔÓ ÒØ Ô Ö× Ò C × ÓÑÔÙØ Ù× Ò Ø Ä ×Ø ËÕÙ Ö × Ö Ø Ö ÓÒ T = argmin T = argmin R,t 1 Ns 1 Ns Ns mij − T i=1 Ns si 2 mij − Rsi − t 2 .

Mij = CP (si , M ) Û Ö mij × Ø ÐÓ× ×Ø ÔÓ ÒØ Ò M ØÓ × ÓÐÐÓÛ× Ì Á È Ð ÓÖ Ø Ñ ÓÑÔÙØ Ò T × ÑÔÐ Ñ ÒØ ½º T (0) = T k × Ó× Ò × Ò Ø Ð ×Ø Ñ Ø Ó Ø Ú Ò × Ò ÔÓ ÒØ si º ØÖ Ò× ÓÖÑ Ø ÓÒ T º ¾º Ê Ô Ø ÓÖ k Ø Ö Ø ÓÒ× ÓÖ ÙÒØ Ð ÓÒÚ Ö Ò • ÐÓ× ×Ø ÔÓ ÒØ mij ∈ M Ò Ø ÑÓ Ð ÓÖ Ó × ÖÚ Ø ÓÒ ÔÓ ÒØ ÓÐÐ Ø ÓÒ Ó Ö ×ÙÐØ Ò ÔÓ ÒØ Ô Ö× (si , mij ) × ÐÐ × Ø Ó ÓÖÖ ¹ ×ÔÓÒ Ò × C Û Ø ÓÑÔÙØ Ø si ∈ S º Ì k−1 s Ck−1 = ∪N si , M )}. i=1 {si , CP (T • ÓÖ Ö ÓÑÔÙØ T k Ø Ò Cº Ö ×ØÖ Ø ÓÒ¸ Ø Ø ÑÒÑÞ × Ø ÖÖÓÖ Ø ÓÒ Ó T ØÓ S ÐÓÓ × Ð ÔÔÐ T Ñ Ò ×ÕÙ Ö si = Rsi + t ØÛ Ò ÐÐ ÔÓ ÒØ Ô Ö× Ø × ∀i Û Ø Ø ÖÓØ Ø ÓÒ Ñ ØÖ Ü R ∈ R3x3 Ò Ø ØÖ Ò×Ð Ø ÓÒ Ú ØÓÖ t ∈ R3 º Ì Ñ Ò Ñ Þ Ø ÓÒ Ó Ø ÖÖÓÖ ØÛ Ò ÐÐ ÔÓ ÒØ Ô Ö× Ò C × ÓÑÔÙØ Ù× Ò Ø Ä ×Ø ËÕÙ Ö × Ö Ø Ö ÓÒ T = argmin T = argmin R,t 1 Ns 1 Ns Ns mij − T i=1 Ns si 2 mij − Rsi − t 2 .

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A Probabilistic Framework for Point-Based Shape Modeling in Medical Image Analysis (Medizintechnik) by Heike Hufnagel


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