| Summary: | The precision of target-based registration is related to the geometry distribution of targets, while the current method of setting the targets mainly depends on experience, and the impact is only evaluated qualitatively by the findings from empirical experiments and through simulations. In this paper, we propose a new quantitative evaluation model, which is comprised of the rotation dilution of precision (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>r</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>, assessing the impact of targets’ geometry distribution on the rotation parameters) and the translation dilution of precision (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>t</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>, assessing the impact of targets’ geometry distribution on the translation parameters). Here, the definitions and derivation of relevant formulas of the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>r</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>t</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> are given, the experience conclusions are theoretically proven by the model of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>r</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>t</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>, and an accurate method for determining the optimal placement location of targets and the scanner is proposed by calculating the minimum value of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>r</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>t</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>. Furthermore, we can refer to the model (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>r</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>t</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>) as a unified model of the geometric distribution evaluation model, which includes the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> model in GPS.
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