Setting the image using picture.ImageLocation() works fine, but you are using a relative path. Check your path against the location of the .exe after it is built.
For example, if your .exe is located at:
<project folder>/bin/Debug/app.exe
The image would have to be at:
<project folder>/bin/Image/1.jpg
Of course, you could just set the image at design-time (the Image property on the PictureBox property sheet).
If you must set it at run-time, one way to make sure you know the location of the image is to add the image file to your project. For example, add a new folder to your project, name it Image. Right-click the folder, choose "Add existing item" and browse to your image (be sure the file filter is set to show image files). After adding the image, in the property sheet set the Copy to Output Directory to Copy if newer.
At this point the image file will be copied when you build the application and you can use
picture.ImageLocation = @"Image\1.jpg";