1. An article pickup device, comprising: a robot including a hand capable of holding an article; a three-dimensional measurement instrument measuring surface positions of a plurality of articles disposed in a three-dimensional space to acquire a position information of a plurality of three-dimensional points; a camera imaging an area including the plurality of articles to acquire image data; a connected set calculation part determining a connected set made by connecting three-dimensional points present in the vicinity of each other among the plurality of three-dimensional points, based on the position information of the plurality of three-dimensional points acquired by the three-dimensional measurement instrument and the image data acquired by the camera; an article identification part identifying a position and posture of the article, based on the position information of the three-dimensional points belonging to the connected set; a hand position posture calculation part determining a hand position posture as a position and posture of the hand capable of picking up the article identified by the article identification part; and a robot control part controlling the robot so as to move the hand to the hand position posture determined by the hand position posture calculation part to pick up the article, wherein the connected set calculation part comprises: a three-dimensional point selection part selecting a first three-dimensional point and a second three-dimensional point present in the vicinity of each other among the plurality of three-dimensional points acquired by the three-dimensional measurement instrument; a gradient information acquisition part acquiring an image gradient information indicating a gradient state of a surface of the article in a partial image region including points on an image corresponding to respective the first three-dimensional point and the second three-dimensional point, based on the image data acquired by the camera; and a judgment part judging whether the first three-dimensional point and the second three-dimensional point are present on the same article, based on a position information of the first three-dimensional point, a position information of the second three-dimensional point, and the image gradient information acquired by the gradient information acquisition part, and wherein the connected set calculation part prepares a list including one three-dimensional point, sets the one three-dimensional point as a reference three-dimensional point, selects one or more three-dimensional points in the vicinity of the reference three-dimensional point by the three-dimensional point selection part, judges whether selected three-dimensional points and the reference three-dimensional point are present on the same article by the judgment part, and performs a control in which the three-dimensional point which is present on the same article is included in the list, the connected set calculation part sets a three-dimensional point, which is not selected as the reference three-dimensional point among the three-dimensional points included in the list, as the reference three-dimensional point, selects one or more three-dimensional points in the vicinity of the reference three-dimensional point by the three-dimensional point selection part, judges whether selected three-dimensional points and the reference three-dimensional point are present on the same article by the judgment part, and performs a control in which the three-dimensional point which is present on the same article is added in the list, and the connected set calculation part repeats the control in which the three-dimensional point is added until all three-dimensional points included in the list are set as the reference three-dimensional point, determines all three-dimensional points included in the final list as the connected set.