An image processing apparatus (1-1, 1-2) comprising: means (25, 281) for recognising a three-dimensional shape of a palm from a luminance distribution of an image of the palm captured by a camera by using a Shape from Shading, SFS, technique, and fitting data of the three-dimensional shape of the palm to a quadric surface to approximate the shape of the three-dimensional shape of the palm by the quadric surface; means (28-1, 28-2, 282) for computing an expansion plane and computing coordinates of an expansion centre (Pc) of the expansion plane; means (28-1, 28-2, 283) for computing a plurality of pairs of corresponding points, each comprising a first point (X2') being on the quadric surface and a second point being on a straight line of the expansion plane, the straight line passing through the coordinates of the expansion centre (Pc) and contacting a point on the quadric surface at the coordinates of the expansion centre (Pc); and means for generating an image from information of the plurality of pairs of corresponding points that are computed, wherein computing each pair of the plurality of pairs of corresponding points comprises: selecting the second point on the straight line; determining an imaginary straight line passing through the second point and extending in a direction of a first vector that is normal to the expansion plane; determining an intersection point of the imaginary straight line with the quadric surface; determining a second vector that is normal to the quadric surface at the intersection point of the imaginary straight line with the quadric surface; obtaining an average normal vector of the first vector, and the second vector; determining a second imaginary straight line passing through the second point and extending in a direction of the average normal vector; determining, as the first point, an intersection point (X2') of the second imaginary straight line with the quadric surface, wherein the first point (X2') on the quadric surface, and the second point on the straight line of the expansion plane, of each of the plurality of pairs of corresponding points, are located at corresponding distances from the expansion centre (Pc). means (25, 281) for recognising a three-dimensional shape of a palm from a luminance distribution of an image of the palm captured by a camera by using a Shape from Shading, SFS, technique, and fitting data of the three-dimensional shape of the palm to a quadric surface to approximate the shape of the three-dimensional shape of the palm by the quadric surface; means (28-1, 28-2, 282) for computing an expansion plane and computing coordinates of an expansion centre (Pc) of the expansion plane; means (28-1, 28-2, 283) for computing a plurality of pairs of corresponding points, each comprising a first point (X2') being on the quadric surface and a second point being on a straight line of the expansion plane, the straight line passing through the coordinates of the expansion centre (Pc) and contacting a point on the quadric surface at the coordinates of the expansion centre (Pc); and means for generating an image from information of the plurality of pairs of corresponding points that are computed, wherein computing each pair of the plurality of pairs of corresponding points comprises: selecting the second point on the straight line; determining an imaginary straight line passing through the second point and extending in a direction of a first vector that is normal to the expansion plane; determining an intersection point of the imaginary straight line with the quadric surface; determining a second vector that is normal to the quadric surface at the intersection point of the imaginary straight line with the quadric surface; obtaining an average normal vector of the first vector, and the second vector; determining a second imaginary straight line passing through the second point and extending in a direction of the average normal vector; determining, as the first point, an intersection point (X2') of the second imaginary straight line with the quadric surface, wherein the first point (X2') on the quadric surface, and the second point on the straight line of the expansion plane, of each of the plurality of pairs of corresponding points, are located at corresponding distances from the expansion centre (Pc). selecting the second point on the straight line; determining an imaginary straight line passing through the second point and extending in a direction of a first vector that is normal to the expansion plane; determining an intersection point of the imaginary straight line with the quadric surface; determining a second vector that is normal to the quadric surface at the intersection point of the imaginary straight line with the quadric surface; obtaining an average normal vector of the first vector, and the second vector; determining a second imaginary straight line passing through the second point and extending in a direction of the average normal vector; determining, as the first point, an intersection point (X2') of the second imaginary straight line with the quadric surface, wherein the first point (X2') on the quadric surface, and the second point on the straight line of the expansion plane, of each of the plurality of pairs of corresponding points, are located at corresponding distances from the expansion centre (Pc).