立体足迹压痕特征定量化检验的统计方法

STATISTICAL METHOD ON QUANTITATIVE TESTING THE CHARACTERISTICS OF THE HUMAN SOLID FOOTMARKS

  • 摘要: 足迹是犯罪现场最常见的痕迹之一,尤其是单个足迹和残缺足迹。以往公安系统对其提供的罪犯信息利用率很低,还停留在凭经验进行目估尺测的阶段。本文是在1、2、3对成趟步幅特征定量化统计检验方法的基础上,对单个足迹或残缺足迹,找到了主要特征指标;对这些特征指标研制成功了定量化测试的仪器;提供了检验的统计方法。经三年多来的反复试验,已取得成功,并用于实际破案,为刑事技术增添了新的破案工具,已于一九八七年四月通过了部级鉴定。

     

    Abstract: It is very probably for criminals to have their characteristics of footmarks left in the crime scene. But the investigators make little use of it. They simply analysed and compared the features of footmarks by experience. In the references (1), (2), and (3), we had presented successfully four statistical methods for testing characteristics of step magnitude. On the basis of above methods, this paper presented a new statistical method for testing characteristics of solid footmarks, it had gained success in many occasions. At first, in the plaster models of the solid footmark Descartes coordinate system was established. In coordinates, point (0, 12) (length in unit of CM) at the fore sole of the foot (not thumb) was chosen as the centre. Height of the point in the plaster model was measured, and recorded as h0 (height in unit of MM). A special instrument was used to measure the height. Then we chose points (0, 13), (0, 11), (-1, 12), (1, 12), (1, 13), (-1, 13), (-1, 11), (1, 11), and called them as middle points. Their heights were noted as h1,h2, h3, h4, h5, h6, h7, h8 respectively. Similarly (0, 15), (0, 9), (-3, 12), (3, 12), (3, 15), (-3, 15), (-3, 9) and (3, 9) were called as marginal points, their heights were noted as h1, h2, h3, h4, h5, h6, h7, h8. By testing, it was indicated that hO, hj and h’jj=1, 2, …, 8) all had normal distribution. Let gj=hO-hj, Then gj obviously had normal distribution. The values of this variable of the criminal and the suspect were noted as gOj, giji=1, 2,., n, n is number of suspects) respectively. Suppose gOjN (μOj, σOj2), gij~N (μij, σij2). The results obtained by testing 2000 footmarks of 20 persons (100 footmarks per person) indicated \sigma_0 f^2=\sigma_i j^2 \triangleq \sigma_1^2, \quad i=1,2, \cdots, n ; j=1,2, \cdots, 8. σ12= 1. 12 was obtained from 2000 data. Hence gOj-gijN (μOj-μij, 2σ12, Under hypothesis H_0: \mu_0 j-\mu_8 y=0, \fracg_o j-g_i j\sqrt2 \sigma_1 \sim N(0,1) Therefore \boldsymbolC_16 \triangleq \sum_j=1^8 \frac\left(g_0 j-g_i j\right)^22 \sigma_1^2 \sim \chi^2(8) For \alpha given, there is P\left(C_15>\chi_\alpha^2(8)\right)=\alpha, That is, statistio C_1 s can be used to test hypothesis H_0. Similarly, the statisties C_\text sr and O_3 of characteristios at the fore sole and thumb of the foot are constructed respectively, O_2, O_\mathbf3 i bave Ohi-square distributions with 8 and 5 degrees of freedom respeotively. If C_14 \leqslant \chi_\alpha^2(8), O_24 \leqslant \chi_\alpha^2(8), C_31 \leqslant \chi_\alpha^2(5) happen at the same time, then the suspect and the oriminal have same charaoteristios of the footmark, otherwise, the suspect can be eliminated. At last, this paper gives a practical example.

     

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