An authentication method performed by an authentication apparatus, the method comprising: (a) obtaining an image signal, obtained as a result of imaging a biometric subject with near infra-red rays, wherein the image signal is an image signal of the imaged biometric subject (SP 1); (b) performing a binarization on the image signal (S 2, S 20), thereby arriving at a binary image (SP 1); (c) performing a Hough transform on the binary image (SP 2); (d) extracting those parameter points from a Hough parameter space obtained as a result of the Hough transform at which a number of overlapping points between curved lines is at least an extraction threshold value set in default, and setting a number of those parameter points as a number of extracted parameter points (SP 3); (e) comparing said number of extracted parameters points with a specified number (SP 4); (f) if the number of extracted parameter points is less than the specified number, performing method step (g), otherwise, if the number of said extracted parameters is equal to or exceeds the specified number, increasing the extraction threshold value (SP 5) by a predetermined value and performing steps (d) - (f) until the number of extracted parameter points is less than the specified number; (g) determining whether the extraction threshold value falls within a range between an upper limit set value and a lower limit set value within an allowable extracting threshold value range (SP 6); the method characterized by the steps: (h) if no in step (g), ending the method; (i) if yes in step (g), selecting one of multiple group ranges by determining in which one of the multiple group ranges the extraction threshold value falls in, wherein the allowable extracting threshold value range is divided into the multiple group ranges; (j) selecting registrant identification data registered in advance in the group range selected in step (i); and (k) collating the parameter points extracted in step (d) with the parameter points extracted for the registrant identification data selected in step (j) and determining as the collating result if the biometric subject belongs to the registrant or not. (a) obtaining an image signal, obtained as a result of imaging a biometric subject with near infra-red rays, wherein the image signal is an image signal of the imaged biometric subject (SP 1); (b) performing a binarization on the image signal (S 2, S 20), thereby arriving at a binary image (SP 1); (c) performing a Hough transform on the binary image (SP 2); (d) extracting those parameter points from a Hough parameter space obtained as a result of the Hough transform at which a number of overlapping points between curved lines is at least an extraction threshold value set in default, and setting a number of those parameter points as a number of extracted parameter points (SP 3); (e) comparing said number of extracted parameters points with a specified number (SP 4); (f) if the number of extracted parameter points is less than the specified number, performing method step (g), otherwise, if the number of said extracted parameters is equal to or exceeds the specified number, increasing the extraction threshold value (SP 5) by a predetermined value and performing steps (d) - (f) until the number of extracted parameter points is less than the specified number; (g) determining whether the extraction threshold value falls within a range between an upper limit set value and a lower limit set value within an allowable extracting threshold value range (SP 6); the method characterized by the steps: (h) if no in step (g), ending the method; (i) if yes in step (g), selecting one of multiple group ranges by determining in which one of the multiple group ranges the extraction threshold value falls in, wherein the allowable extracting threshold value range is divided into the multiple group ranges; (j) selecting registrant identification data registered in advance in the group range selected in step (i); and (k) collating the parameter points extracted in step (d) with the parameter points extracted for the registrant identification data selected in step (j) and determining as the collating result if the biometric subject belongs to the registrant or not. (h) if no in step (g), ending the method; (i) if yes in step (g), selecting one of multiple group ranges by determining in which one of the multiple group ranges the extraction threshold value falls in, wherein the allowable extracting threshold value range is divided into the multiple group ranges; (j) selecting registrant identification data registered in advance in the group range selected in step (i); and (k) collating the parameter points extracted in step (d) with the parameter points extracted for the registrant identification data selected in step (j) and determining as the collating result if the biometric subject belongs to the registrant or not.