Fit image inside the canvas

To prevent the image from being inside the canvas it is necessary to limit the positioning of the obj object that contains the image. The top and left position can not be greater than 0.

var canvas = window._canvas = new fabric.Canvas('canvas', {
    preserveObjectStacking: true
});

var imageObj = new Image(), path = 'http://i.imgur.com/tEeSJcr.jpg';

imageObj.src = path;

imageObj.onload = function () {
    var image = new fabric.Image(imageObj);

    canvas.setHeight(250);
    canvas.setWidth(250);
    image.set({
        id: 'img',
        left: 0,
        top: 0,
        selectable: true,
        hasBorders: false,
        hasControls: false,
        hasRotatingPoint: false
    });
    canvas.add(image);
};


canvas.on('object:moving', function (e) {
    var obj;
    obj = e.target;
    obj.setCoords();

    var boundingRect = obj.getBoundingRect();
    var zoom = canvas.getZoom();
    var viewportMatrix = canvas.viewportTransform;

    //there is a bug in fabric that causes bounding rects to not be transformed by viewport matrix
    //this code should compensate for the bug for now
    boundingRect.top = (boundingRect.top - viewportMatrix[5]) / zoom;
    boundingRect.left = (boundingRect.left - viewportMatrix[4]) / zoom;
    boundingRect.width /= zoom;
    boundingRect.height /= zoom;

    var canvasHeight = obj.canvas.height / zoom,
        canvasWidth = obj.canvas.width / zoom;

    if(boundingRect.top > 0){
        obj.top = 0;
    }

    if(boundingRect.left > 0){
        obj.left = 0;
    }

    if (boundingRect.top < canvasHeight - boundingRect.height){
        obj.top = canvasHeight - boundingRect.height;
    }

    if (boundingRect.left < canvasWidth - boundingRect.width){
        obj.left = canvasWidth - boundingRect.width;
    }

});

Avoid raising the resolution of the image so the image must be larger than the canvas. Then you need to check if the height is larger than the width to work with various image sizes.

<canvas id="c" height="600" width="600" style="border:1px solid #000"></canvas>

var c = new fabric.Canvas('c');

var imageSrc = "http://marketingdeconteudo.com/wp-content/uploads/2017/01/formatos-de-imagem-2.jpg";

var w = 600;
var h = 600;


fabric.Image.fromURL(imageSrc, function(img) {
  if (img.width > img.height) {
    img.scaleToWidth(w);
  }
  else if (img.height > img.width) {
    img.scaleToWidth(h);
  }
  else {
    img.scaleToWidth(w);
  }

  img.set('selectable', true);
  img.set('hasControls', false);
  c.add(img);
});