Computer-implemented method for determining an explanation map s x * of an image x, in which map all those pixels of the image x which are crucial for a classification of the image x determined by means of a deep neural network f are highlighted, wherein the explanation map s x * is selected in such a way as to optimize an optimization problem with a constraint for a loss function L: s x * = argmin L s x; s x 0 = x; where: h l s x ≤ h l x ∀ l wherein the optimization problem is solved by means of a mask b, which is either multiplicative, i.e. s x = x. b, where b ∈ [0,1] is optimized, or additive, i.e. s x = x + b, where b is optimized, with the start condition b = 0; wherein the loss function L has a first component (L h), wherein the first component (L h) is given by an L1-norm: l h ( s x) = ∥ s x ∥ 1, wherein the loss function L has a second component (L w), wherein the second component (L w) is selected such that the explanation map s x *, when it is supplied to the deep neural network ( f) for classification, leads to the same classification result f s x * | θ as the image x, wherein the constraint h l ( s x) ≤ h l ( x)∀ l that, for all activation function layers, an activation h l ( s x) of the l-th activation function layer in the deep neural network f by the explanation map s x does not exceed an activation h l ( x) of the l-th activation function layer of the deep neural network f by the image x is achieved by virtue of the fact that the activation h l ( s x) of the respective l-th activation function layer, when determining the explanation map s x, is set to a predefinable value, in particular the maximum permissible activation h l ( x) in accordance with the constraint, or is achieved by virtue of the fact that a gradient-based optimization method is used and a gradient ( δ l) of a backpropagation of the activation h l ( s x) of a layer l of the deep neural network is set to be equal to a predefinable gradient, in particular equal to zero, if the activation by the explanation map s x exceeds the activation h l ( x) by the image x in the layer, or is achieved by virtue of the fact that the loss function L has a third component ( L c), wherein the third component ( L c) of the loss function L penalizes an exceedance of the activation h l ( x) by the explanation map s x beyond the activation h l ( x) by the image x. wherein the explanation map s x * is selected in such a way as to optimize an optimization problem with a constraint for a loss function L: s x * = argmin L s x; s x 0 = x; where: h l s x ≤ h l x ∀ l wherein the optimization problem is solved by means of a mask b, which is either multiplicative, i.e. s x = x. b, where b ∈ [0,1] is optimized, or additive, i.e. s x = x + b, where b is optimized, with the start condition b = 0; wherein the loss function L has a first component (L h), wherein the first component (L h) is given by an L1-norm: l h ( s x) = ∥ s x ∥ 1, wherein the loss function L has a second component (L w), wherein the second component (L w) is selected such that the explanation map s x *, when it is supplied to the deep neural network ( f) for classification, leads to the same classification result f s x * | θ as the image x, wherein the constraint h l ( s x) ≤ h l ( x)∀ l that, for all activation function layers, an activation h l ( s x) of the l-th activation function layer in the deep neural network f by the explanation map s x does not exceed an activation h l ( x) of the l-th activation function layer of the deep neural network f by the image x is achieved by virtue of the fact that the activation h l ( s x) of the respective l-th activation function layer, when determining the explanation map s x, is set to a predefinable value, in particular the maximum permissible activation h l ( x) in accordance with the constraint, or is achieved by virtue of the fact that a gradient-based optimization method is used and a gradient ( δ l) of a backpropagation of the activation h l ( s x) of a layer l of the deep neural network is set to be equal to a predefinable gradient, in particular equal to zero, if the activation by the explanation map s x exceeds the activation h l ( x) by the image x in the layer, or is achieved by virtue of the fact that the loss function L has a third component ( L c), wherein the third component ( L c) of the loss function L penalizes an exceedance of the activation h l ( x) by the explanation map s x beyond the activation h l ( x) by the image x. that the activation h l ( s x) of the respective l-th activation function layer, when determining the explanation map s x, is set to a predefinable value, in particular the maximum permissible activation h l ( x) in accordance with the constraint, or is achieved by virtue of the fact that a gradient-based optimization method is used and a gradient ( δ l) of a backpropagation of the activation h l ( s x) of a layer l of the deep neural network is set to be equal to a predefinable gradient, in particular equal to zero, if the activation by the explanation map s x exceeds the activation h l ( x) by the image x in the layer, or is achieved by virtue of the fact that the loss function L has a third component ( L c), wherein the third component ( L c) of the loss function L penalizes an exceedance of the activation h l ( x) by the explanation map s x beyond the activation h l ( x) by the image x.